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-{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-10T11:47:28","documenter_version":"1.7.0"}}
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+ K = allocate_matrix(dh, ch)</code></pre></li></ul><h3 id="Added"><a class="docs-heading-anchor" href="#Added">Added</a><a id="Added-1"></a><a class="docs-heading-anchor-permalink" href="#Added" title="Permalink"></a></h3><ul><li><p><code>InterfaceValues</code> for computing jumps and averages over interfaces. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/743">#743</a>)</p></li><li><p><code>InterfaceIterator</code> and <code>InterfaceCache</code> for iterating over interfaces. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/747">#747</a>)</p></li><li><p><code>FacetQuadratureRule</code> implementation for <code>RefPrism</code> and <code>RefPyramid</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/779">#779</a>)</p></li><li><p>The <code>DofHandler</code> now support selectively adding fields on sub-domains (rather than the full domain). This new functionality is included with the new <code>SubDofHandler</code> struct, which, as the name suggest, is a <code>DofHandler</code> for a subdomain. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/624">#624</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/667">#667</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/735">#735</a>)</p></li><li><p>New reference shape structs <code>RefLine</code>, <code>RefTriangle</code>, <code>RefQuadrilateral</code>, <code>RefTetrahedron</code>, <code>RefHexahedron</code>, and <code>RefPrism</code> have been added. These encode the reference dimension, and will thus replace the old reference shapes for which it was necessary to always pair with an explicit dimension (i.e. <code>RefLine</code> replaces <code>(RefCube, 1)</code>, <code>RefTriangle</code> replaces <code>(RefTetrahedron, 2)</code>, etc.). For writing "dimension independent code" it is possible to use <code>Ferrite.RefHypercube{dim}</code> and <code>Ferrite.RefSimplex{dim}</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/679">#679</a>)</p></li><li><p>New methods for adding entitysets that are located on the boundary of the grid: <code>addboundaryfacetset!</code> and <code>addboundaryvertexset!</code>. These work similar to <code>addfacetset!</code> and <code>addvertexset!</code>, but filters out all instances not on the boundary (this can be used to avoid accidental inclusion of internal entities in sets used for boundary conditions, for example). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/606">#606</a>)</p></li><li><p>New interpolation <code>VectorizedInterpolation</code> which vectorizes scalar interpolations for vector-valued problems. A <code>VectorizedInterpolation</code> is created from a (scalar) interpolation <code>ip</code> using either <code>ip ^ dim</code> or <code>VectorizedInterpolation{dim}(ip)</code>. For convenience, the method <code>VectorizedInterpolation(ip)</code> vectorizes the interpolation to the reference dimension of the interpolation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/694">#694</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/736">#736</a>)</p></li><li><p>New (scalar) interpolation <code>Lagrange{RefQuadrilateral, 3}()</code>, i.e. third order Lagrange interpolation for 2D quadrilaterals. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/701">#701</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/731">#731</a>)</p></li><li><p><code>CellValues</code> now support embedded elements. Specifically you can now embed elements with reference dimension 1 into spatial dimension 2 or 3, and elements with reference dimension 2 in to spatial dimension 3. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/651">#651</a>)</p></li><li><p><code>CellValues</code> now support (vector) interpolations with dimension different from the spatial dimension. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/651">#651</a>)</p></li><li><p><code>FacetQuadratureRule</code> have been added and should be used for <code>FacetValues</code>. A <code>FacetQuadratureRule</code> for integration of the facets of e.g. a triangle can be constructed by <code>FacetQuadratureRule{RefTriangle}(order)</code> (similar to how <code>QuadratureRule</code> is constructed). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/716">#716</a>)</p></li><li><p>New functions <code>Ferrite.reference_shape_value(::Interpolation, ξ::Vec, i::Int)</code> and <code>Ferrite.reference_shape_gradient(::Interpolation, ξ::Vec, i::Int)</code> for evaluating the value/gradient of the <code>i</code>th shape function of an interpolation in local reference coordinate <code>ξ</code>. These methods are public but not exported. (Note that these methods return the value/gradient wrt. the reference coordinate <code>ξ</code>, whereas the corresponding methods for <code>CellValues</code> etc return the value/gradient wrt the spatial coordinate <code>x</code>.) (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/721">#721</a>)</p></li><li><p><code>FacetIterator</code> and <code>FacetCache</code> have been added. These work similarly to <code>CellIterator</code> and <code>CellCache</code> but are used to iterate over (boundary) face sets instead. These simplify boundary integrals in general, and in particular Neumann boundary conditions are more convenient to implement now that you can loop directly over the face set instead of checking all faces of a cell inside the element routine. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/495">#495</a>)</p></li><li><p>The <code>ConstraintHandler</code> now support adding Dirichlet boundary conditions on discontinuous interpolations. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/729">#729</a>)</p></li><li><p><code>collect_periodic_faces</code> now have a keyword argument <code>tol</code> that can be used to relax the default tolerance when necessary. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/749">#749</a>)</p></li><li><p>VTK export now work with <code>QuadraticHexahedron</code> elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/714">#714</a>)</p></li><li><p>The function <code>bounding_box(::AbstractGrid)</code> has been added. It computes the bounding box for a given grid (based on its node coordinates), and returns the minimum and maximum vertices of the bounding box. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/880">#880</a>)</p></li><li><p>Support for working with sparsity patterns has been added. This means that Ferrite exposes the intermediate "state" between the DofHandler and the instantiated matrix as the new struct <code>SparsityPattern</code>. This make it possible to insert custom equations or couplings in the pattern before instantiating the matrix. The function <code>create_sparsity_pattern</code> have been removed. The new function <code>allocate_matrix</code> is instead used to instantiate the matrix. Refer to the documentation for more details. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/888">#888</a>)</p><p><strong>To upgrade</strong>: if you want to recover the old functionality and don't need to work with the pattern, replace any usage of <code>create_sparsity_pattern</code> with <code>allocate_matrix</code>.</p></li><li><p>A new function, <code>geometric_interpolation</code>, is exported, which gives the geometric interpolation for each cell type. This is equivalent to the deprecated <code>Ferrite.default_interpolation</code> function. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/953">#953</a>)</p></li><li><p>CellValues and FacetValues can now store and map second order gradients (Hessians). The number of gradients computed in CellValues/FacetValues is specified using the keyword arguments <code>update_gradients::Bool</code> (default true) and <code>update_hessians::Bool</code> (default false) in the constructors, i.e. <code>CellValues(...; update_hessians=true)</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/953">#953</a>)</p></li><li><p><code>L2Projector</code> supports projecting on grids with mixed celltypes. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/949">#949</a>)</p></li></ul><h3 id="Changed"><a class="docs-heading-anchor" href="#Changed">Changed</a><a id="Changed-1"></a><a class="docs-heading-anchor-permalink" href="#Changed" title="Permalink"></a></h3><ul><li><p>It is now possible to create sparsity patterns with interface couplings, see the new function <code>add_interface_entries!</code> and the rework of sparsity pattern construction. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/710">#710</a>)</p></li><li><p>The <code>AbstractCell</code> interface has been reworked. This change should not affect user code, but may in some cases be relevant for code parsing external mesh files. In particular, the generic <code>Cell</code> struct have been removed in favor of concrete cell implementations (<code>Line</code>, <code>Triangle</code>, ...). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/679">#679</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/712">#712</a>)</p><p><strong>To upgrade</strong> replace any usage of <code>Cell{...}(...)</code> with calls to the concrete implementations.</p></li><li><p>The default geometric mapping in <code>CellValues</code> and <code>FacetValues</code> have changed. The new default is to always use <code>Lagrange{refshape, 1}()</code>, i.e. linear Lagrange polynomials, for the geometric interpolation. Previously, the function interpolation was (re) used also for the geometry interpolation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/695">#695</a>)</p><p><strong>To upgrade</strong>, if you relied on the previous default, simply pass the function interpolation also as the third argument (the geometric interpolation).</p></li><li><p>All interpolations are now categorized as either scalar or vector interpolations. All (previously) existing interpolations are scalar. (Scalar) interpolations must now be explicitly vectorized, using the new <code>VectorizedInterpolation</code>, when used for vector problems. (Previously implicit vectorization happened in the <code>CellValues</code> constructor, and when adding fields to the <code>DofHandler</code>). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/694">#694</a>)</p></li><li><p>It is now required to explicitly pass the interpolation to the <code>DofHandler</code> when adding a new field using <code>add!</code>. For vector fields the interpolation should be vectorized, instead of passing number of components as an integer. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/694">#694</a>)</p><p><strong>To upgrade</strong> don't pass the dimension as an integer, and pass the interpolation explicitly. See more details in <a href="#upgrading-code-from-ferrite-03-to-10">Upgrading code from Ferrite 0.3 to 1.0</a>.</p></li><li><p><code>Interpolation</code>s should now be constructed using the new reference shapes. Since the new reference shapes encode the reference dimension the first type parameter of interpolations have been removed. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/711">#711</a>) <strong>To upgrade</strong> replace e.g. <code>Lagrange{1, RefCube, 1}()</code> with <code>Lagrange{RefLine, 1}()</code>, and <code>Lagrange{2, RefTetrahedron, 1}()</code> with <code>Lagrange{RefTriangle, 1}()</code>, etc.</p></li><li><p><code>QuadratureRule</code>s should now be constructed using the new reference shapes. Since the new reference shapes encode the reference dimension the first type parameter of <code>QuadratureRule</code> have been removed. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/711">#711</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/716">#716</a>) <strong>To upgrade</strong> replace e.g. <code>QuadratureRule{1, RefCube}(order)</code> with <code>QuadratureRule{RefLine}(order)</code>, and <code>QuadratureRule{2, RefTetrahedron}(1)</code> with <code>Lagrange{RefTriangle}(order)</code>, etc.</p></li><li><p><code>CellScalarValues</code> and <code>CellVectorValues</code> have been merged into <code>CellValues</code>, <code>FaceScalarValues</code> and <code>FaceVectorValues</code> have been merged into <code>FacetValues</code>, and <code>PointScalarValues</code> and <code>PointVectorValues</code> have been merged into <code>PointValues</code>. The differentiation between scalar and vector have thus been moved to the interpolation (see above). Note that previously <code>CellValues</code>, <code>FaceValues</code>, and <code>PointValues</code> where abstract types, but they are now concrete implementations with <em>different type parameters</em>, except <code>FaceValues</code> which is now <code>FacetValues</code> (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/708">#708</a>) <strong>To upgrade</strong>, for scalar problems, it is enough to replace <code>CellScalarValues</code> with <code>CellValues</code>, <code>FaceScalarValues</code> with <code>FacetValues</code> and <code>PointScalarValues</code> with <code>PointValues</code>, respectively. For vector problems, make sure to vectorize the interpolation (see above) and then replace <code>CellVectorValues</code> with <code>CellValues</code>, <code>FaceVectorValues</code> with <code>FacetValues</code>, and <code>PointVectorValues</code> with <code>PointValues</code>.</p></li><li><p>The quadrature rule passed to <code>FacetValues</code> should now be of type <code>FacetQuadratureRule</code> rather than of type <code>QuadratureRule</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/716">#716</a>) <strong>To upgrade</strong> replace the quadrature rule passed to <code>FacetValues</code> with a <code>FacetQuadratureRule</code>.</p></li><li><p>Checking if a face <code>(ele_id, local_face_id) ∈ faceset</code> has been previously implemented by type piracy. In order to be invariant to the underlying <code>Set</code> datatype as well as omitting type piracy, (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/835">#835</a>) implemented <code>isequal</code> and <code>hash</code> for <code>BoundaryIndex</code> datatypes.</p></li><li><p><strong>VTK export</strong>: Ferrite no longer extends <code>WriteVTK.vtk_grid</code> and associated functions, instead the new type <code>VTKGridFile</code> should be used instead. New methods exists for writing to a <code>VTKGridFile</code>, e.g. <code>write_solution</code>, <code>write_cell_data</code>, <code>write_node_data</code>, and <code>write_projection</code>. See <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/692">#692</a>.</p></li><li><p><strong>Definitions</strong>: Previously, <code>face</code> and <code>edge</code> referred to codimension 1 relative reference shape. In Ferrite v1, <code>volume</code>, <code>face</code>, <code>edge</code>, and <code>vertex</code> refer to 3, 2, 1, and 0 dimensional entities, and <code>facet</code> replaces the old definition of <code>face</code>. No direct replacement for <code>edges</code> exits. See <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/914">#914</a> and <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/914">#914</a>. The main implications of this change are</p><ul><li><code>FaceIndex</code> -> <code>FacetIndex</code> (<code>FaceIndex</code> still exists, but has a different meaning)</li><li><code>FaceValues</code> -> <code>FacetValues</code></li><li><code>nfaces</code> -> <code>nfacets</code> (<code>nfaces</code> is now an internal method with different meaning)</li><li><code>addfaceset!</code> -> <code>addfacetset</code></li><li><code>getfaceset</code> -> <code>getfacetset</code></li></ul><p>Furthermore, subtypes of <code>Interpolation</code> should now define <code>vertexdof_indices</code>, <code>edgedof_indices</code>, <code>facedof_indices</code>, <code>volumedof_indices</code> (and similar) according to these definitions.</p></li><li><p><code>Ferrite.getdim</code> has been changed into <code>Ferrite.getrefdim</code> for getting the dimension of the reference shape and <code>Ferrite.getspatialdim</code> to get the spatial dimension (of the grid). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/943">#943</a>)</p></li><li><p><code>Ferrite.getfielddim(::AbstractDofHandler, args...)</code> has been renamed to <code>Ferrite.n_components</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/943">#943</a>)</p></li><li><p>The constructor for <code>ExclusiveTopology</code> only accept an <code>AbstractGrid</code> as input, removing the alternative of providing a <code>Vector{<:AbstractCell}</code>, as knowing the spatial dimension is required for correct code paths. Furthermore, it uses a new internal data structure, <code>ArrayOfVectorViews</code>, to store the neighborhood information more efficiently The datatype for the neighborhood has thus changed to a view of a vector, instead of the now removed <code>EntityNeighborhood</code> container. This also applies to <code>vertex_star_stencils</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/974">#974</a>).</p></li><li><p><code>project(::L2Projector, data, qr_rhs)</code> now expects data to be indexed by the cellid, as opposed to the index in the vector of cellids passed to the <code>L2Projector</code>. The data may be passed as an <code>AbstractDict{Int, <:AbstractVector}</code>, as an alternative to <code>AbstractArray{<:AbstractVector}</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/949">#949</a>)</p></li></ul><h3 id="Deprecated"><a class="docs-heading-anchor" href="#Deprecated">Deprecated</a><a id="Deprecated-1"></a><a class="docs-heading-anchor-permalink" href="#Deprecated" title="Permalink"></a></h3><ul><li><p>The rarely (if ever) used methods of <code>function_value</code>, <code>function_gradient</code>, <code>function_divergence</code>, and <code>function_curl</code> taking <em>vectorized dof values</em> as in put have been deprecated. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/698">#698</a>)</p></li><li><p>The function <code>reshape_to_nodes</code> have been deprecated in favor of <code>evaluate_at_grid_nodes</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/703">#703</a>)</p></li><li><p><code>start_assemble([n::Int])</code> has been deprecated in favor of calling <code>Ferrite.COOAssembler()</code> directly (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/916">#916</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/1058">#1058</a>).</p></li><li><p><code>start_assemble(f, K)</code> have been deprecated in favor of the "canonical" <code>start_assemble(K, f)</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/707">#707</a>)</p></li><li><p><code>assemble!(assembler, dofs, fe, Ke)</code> have been deprecated in favor of the "canonical" <code>assemble!(assembler, dofs, Ke, fe)</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/1059">#1059</a>)</p></li><li><p><code>end_assemble</code> have been deprecated in favor of <code>finish_assemble</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/754">#754</a>)</p></li><li><p><code>get_point_values</code> have been deprecated in favor of <code>evaluate_at_points</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/754">#754</a>)</p></li><li><p><code>transform!</code> have been deprecated in favor of <code>transform_coordinates!</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/754">#754</a>)</p></li><li><p><code>Ferrite.default_interpolation</code> has been deprecated in favor of <code>geometric_interpolation</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/953">#953</a>)</p></li></ul><h3 id="Removed-2"><a class="docs-heading-anchor" href="#Removed-2">Removed</a><a class="docs-heading-anchor-permalink" href="#Removed-2" title="Permalink"></a></h3><ul><li><p><code>MixedDofHandler</code> + <code>FieldHandler</code> have been removed in favor of <code>DofHandler</code> + <code>SubDofHandler</code>. Note that the syntax has changed, and note that <code>SubDofHandler</code> is much more capable compared to <code>FieldHandler</code>. Previously it was often required to pass both the <code>MixedDofHandler</code> and the <code>FieldHandler</code> to e.g. the assembly routine, but now it is enough to pass the <code>SubDofHandler</code> since it can be used for e.g. DoF queries etc. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/624">#624</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/667">#667</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/735">#735</a>)</p></li><li><p>Some old methods to construct the <code>L2Projector</code> have been removed after being deprecated for several releases. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/697">#697</a>)</p></li><li><p>The option <code>project_to_nodes</code> have been removed from <code>project(::L2Projector, ...)</code>. The returned values are now always ordered according to the projectors internal <code>DofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/699">#699</a>)</p></li><li><p>The function <code>compute_vertex_values</code> have been removed. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/700">#700</a>)</p></li><li><p>The names <code>getweights</code>, <code>getpoints</code>, <code>getcellsets</code>, <code>getnodesets</code>, <code>getfacesets</code>, <code>getedgesets</code>, and <code>getvertexsets</code> have been removed from the list of exported names. (For now you can still use them by prefixing <code>Ferrite.</code>, e.g. <code>Ferrite.getweights</code>.) (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/754">#754</a>)</p></li><li><p>The <code>onboundary</code> function (and the associated <code>boundary_matrix</code> property of the <code>Grid</code> datastructure) have been removed (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/924">#924</a>). Instead of first checking <code>onboundary</code> and then check whether a facet belong to a specific facetset, check the facetset directly. For example:</p><pre><code class="language-diff hljs">- if onboundary(cell, local_face_id) && (cell_id, local_face_id) in getfacesets(grid, "traction_boundary")
+ if (cell_id, local_face_id) in getfacesets(grid, "traction_boundary")
# integrate the "traction_boundary" boundary
- end</code></pre></li></ul><h3 id="Fixed"><a class="docs-heading-anchor" href="#Fixed">Fixed</a><a id="Fixed-1"></a><a class="docs-heading-anchor-permalink" href="#Fixed" title="Permalink"></a></h3><ul><li><p>Benchmarks now work with master branch. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/751">#751</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/855">#855</a>)</p></li><li><p>Topology construction have been generalized to, in particular, fix construction for 1D and for wedge elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/641">#641</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/670">#670</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/684">#684</a>)</p></li></ul><h3 id="Other-improvements"><a class="docs-heading-anchor" href="#Other-improvements">Other improvements</a><a id="Other-improvements-1"></a><a class="docs-heading-anchor-permalink" href="#Other-improvements" title="Permalink"></a></h3><ul><li><p>Documentation:</p><ul><li>The documentation is now structured according to the Diataxis framework. There is now also clear separation between tutorials (for teaching) and code gallery (for showing off). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/737">#737</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/756">#756</a>)</li><li>New section in the developer documentation that describes the (new) reference shapes and their numbering scheme. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/688">#688</a>)</li></ul></li><li><p>Performance:</p><ul><li><code>Ferrite.transform!(grid, f)</code> (for transforming the node coordinates in the <code>grid</code> according to a function <code>f</code>) is now faster and allocates less. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/675">#675</a>)</li><li>Slight performance improvement in construction of <code>PointEvalHandler</code> (faster reverse coordinate lookup). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/719">#719</a>)</li><li>Various performance improvements to topology construction. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/753">#753</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/759">#759</a>)</li></ul></li><li><p>Internal improvements:</p><ul><li>The dof distribution interface have been updated to support higher order elements (future work). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/627">#627</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/732">#732</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/733">#733</a>)</li><li>The <code>AbstractGrid</code> and <code>AbstractDofHandler</code> interfaces are now used more consistently internally. This will help with the implementation of distributed grids and DofHandlers. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/655">#655</a>)</li><li>VTK export now uses the (geometric) interpolation directly when evaluating the finite element field instead of trying to work backwards how DoFs map to nodes. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/703">#703</a>)</li><li>Improved bounds checking in <code>assemble!</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/706">#706</a>)</li><li>Internal methods <code>Ferrite.value</code> and <code>Ferrite.derivative</code> for computing the value/gradient of <em>all</em> shape functions have been removed. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/720">#720</a>)</li><li><code>Ferrite.create_incidence_matrix</code> now work with any <code>AbstractGrid</code> (not just <code>Grid</code>). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/726">#726</a>)</li></ul></li></ul><h2 id="[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03"><a class="docs-heading-anchor" href="#[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14">v0.3.14</a> - 2023-04-03</a><a id="[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03" title="Permalink"></a></h2><h3 id="Added-2"><a class="docs-heading-anchor" href="#Added-2">Added</a><a class="docs-heading-anchor-permalink" href="#Added-2" title="Permalink"></a></h3><ul><li>Support reordering dofs of a <code>MixedDofHandler</code> by the built-in orderings <code>FieldWise</code> and <code>ComponentWise</code>. This includes support for reordering dofs of fields on subdomains. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/645">#645</a>)</li><li>Support specifying the coupling between fields in a <code>MixedDofHandler</code> when creating the sparsity pattern. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/650">#650</a>)</li><li>Support Metis dof reordering with coupling information for <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/650">#650</a>)</li><li>Pretty printing for <code>MixedDofHandler</code> and <code>L2Projector</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/465">#465</a>)</li></ul><h3 id="Other-improvements-2"><a class="docs-heading-anchor" href="#Other-improvements-2">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-2" title="Permalink"></a></h3><ul><li>The <code>MixedDofHandler</code> have gone through a performance review (see <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/629">#629</a>) and now performs the same as <code>DofHandler</code>. This was part of the push to merge the two DoF handlers. Since <code>MixedDofHandler</code> is strictly more flexible, and now equally performant, it will replace <code>DofHandler</code> in the next breaking release. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/637">#637</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/639">#639</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/642">#642</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/643">#643</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/656">#656</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/660">#660</a>)</li></ul><h3 id="Internal-changes"><a class="docs-heading-anchor" href="#Internal-changes">Internal changes</a><a id="Internal-changes-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-changes" title="Permalink"></a></h3><p>Changes listed here should not affect regular usage, but listed here in case you have been poking into Ferrite internals:</p><ul><li><code>Ferrite.ndim(dh, fieldname)</code> has been removed, use <code>Ferrite.getfielddim(dh, fieldname)</code> instead. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/658">#658</a>)</li><li><code>Ferrite.nfields(dh)</code> has been removed, use <code>length(Ferrite.getfieldnames(dh))</code> instead. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/444">#444</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/653">#653</a>)</li><li><code>getfielddims(::FieldHandler)</code> and <code>getfieldinterpolations(::FieldHandler)</code> have been removed (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/647">#647</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/659">#659</a>)</li></ul><h2 id="[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23"><a class="docs-heading-anchor" href="#[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13">v0.3.13</a> - 2023-03-23</a><a id="[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23" title="Permalink"></a></h2><h3 id="Added-3"><a class="docs-heading-anchor" href="#Added-3">Added</a><a class="docs-heading-anchor-permalink" href="#Added-3" title="Permalink"></a></h3><ul><li>Support for classical trilinear and triquadratic wedge elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Symmetric quadrature rules up to order 10 for prismatic elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Finer granulation of dof distribution, allowing to distribute different amounts of dofs per entity. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li></ul><h3 id="Fixed-2"><a class="docs-heading-anchor" href="#Fixed-2">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-2" title="Permalink"></a></h3><ul><li>Dof distribution for embedded elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Improve numerical accuracy in shape function evaluation for the <code>Lagrange{2,Tetrahedron,(3|4|5)}</code> interpolations. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/582">#582</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/633">#633</a>)</li></ul><h3 id="Other-improvements-3"><a class="docs-heading-anchor" href="#Other-improvements-3">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-3" title="Permalink"></a></h3><ul><li>Documentation:<ul><li>New "Developer documentation" section in the manual for documenting Ferrite.jl internals and developer tools. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/611">#611</a>)</li><li>Fix a bug in constraint computation in Stoke's flow example. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/614">#614</a>)</li></ul></li><li>Performance:<ul><li>Benchmarking infrastructure to help tracking performance changes. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/388">#388</a>)</li><li>Performance improvements for various accessor functions for <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/621">#621</a>)</li></ul></li></ul><h3 id="Internal-changes-2"><a class="docs-heading-anchor" href="#Internal-changes-2">Internal changes</a><a class="docs-heading-anchor-permalink" href="#Internal-changes-2" title="Permalink"></a></h3><ul><li>To clarify the dof management <code>vertices(ip)</code>, <code>edges(ip)</code> and <code>faces(ip)</code> has been deprecated in favor of <code>vertexdof_indices(ip)</code>, <code>edgedof_indices(ip)</code> and <code>facedof_indices(ip)</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Duplicate grid representation has been removed from the <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/577">#577</a>)</li></ul><h2 id="[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28"><a class="docs-heading-anchor" href="#[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12">v0.3.12</a> - 2023-02-28</a><a id="[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28" title="Permalink"></a></h2><h3 id="Added-4"><a class="docs-heading-anchor" href="#Added-4">Added</a><a class="docs-heading-anchor-permalink" href="#Added-4" title="Permalink"></a></h3><ul><li>Added a basic <code>show</code> method for assemblers. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/598">#598</a>)</li></ul><h3 id="Fixed-3"><a class="docs-heading-anchor" href="#Fixed-3">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-3" title="Permalink"></a></h3><ul><li>Fix an issue in constraint application of <code>Symmetric</code>-wrapped sparse matrices (i.e. obtained from <code>create_symmatric_sparsity_pattern</code>). In particular, <code>apply!(K::Symmetric, f, ch)</code> would incorrectly modify <code>f</code> if any of the constraints were inhomogeneous. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/592">#592</a>)</li><li>Properly disable the Metis extension on Julia 1.9 instead of causing precompilation errors. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/588">#588</a>)</li><li>Fix adding Dirichlet boundary conditions on nodes when using MixedDofHandler. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/593">#593</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/594">#594</a>)</li><li>Fix accidentally slow implementation of <code>show</code> for <code>Grid</code>s. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/599">#599</a>)</li><li>Fixes to topology functionality. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/453">#453</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/518">#518</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/455">#455</a>)</li><li>Fix grid coloring for cell sets with 0 or 1 cells. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/600">#600</a>)</li></ul><h3 id="Other-improvements-4"><a class="docs-heading-anchor" href="#Other-improvements-4">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-4" title="Permalink"></a></h3><ul><li>Documentation improvements:<ul><li>Simplications and clarifications to hyperelasticity example. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/591">#591</a>)</li><li>Remove duplicate docstring entry for <code>vtk_point_data</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/602">#602</a>)</li><li>Update documentation about initial conditions. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/601">#601</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/604">#604</a>)</li></ul></li></ul><h2 id="[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17"><a class="docs-heading-anchor" href="#[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11">v0.3.11</a> - 2023-01-17</a><a id="[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17" title="Permalink"></a></h2><h3 id="Added-5"><a class="docs-heading-anchor" href="#Added-5">Added</a><a class="docs-heading-anchor-permalink" href="#Added-5" title="Permalink"></a></h3><ul><li><a href="https://github.com/JuliaSparse/Metis.jl">Metis.jl</a> extension for fill-reducing DoF permutation. This uses Julias new package extension mechanism (requires Julia 1.10) to support a new DoF renumbering order <code>DofOrder.Ext{Metis}()</code> that can be passed to <code>renumber!</code> to renumber DoFs using the Metis.jl library. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/393">#393</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/549">#549</a>)</li><li><a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> extension for creating a globally blocked system matrix. <code>create_sparsity_pattern(BlockMatrix, dh, ch; kwargs...)</code> return a matrix that is blocked by field (requires DoFs to be (re)numbered by field, i.e. <code>renumber!(dh, DofOrder.FieldWise())</code>). For custom blocking it is possible to pass an uninitialized <code>BlockMatrix</code> with the correct block sizes (see <code>BlockArrays.jl</code> docs). This functionality is useful for e.g. special solvers where individual blocks need to be extracted. Requires Julia version 1.9 or above. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/567">#567</a>)</li><li>New function <code>apply_analytical!</code> for setting the values of the degrees of freedom for a specific field according to a spatial function <code>f(x)</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/532">#532</a>)</li><li>New cache struct <code>CellCache</code> to be used when iterating over the cells in a grid or DoF handler. <code>CellCache</code> caches nodes, coordinates, and DoFs, for the cell. The cache <code>cc</code> can be re-initialized for a new cell index <code>ci</code> by calling <code>reinit!(cc, ci)</code>. This can be used as an alternative to <code>CellIterator</code> when more control over which element to loop over is needed. See documentation for <code>CellCache</code> for more information. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/546">#546</a>)</li><li>It is now possible to create the sparsity pattern without constrained entries (they will be zeroed out later anyway) by passing <code>keep_constrained=false</code> to <code>create_sparsity_pattern</code>. This naturally only works together with local condensation of constraints since there won't be space allocated in the global matrix for the full (i.e. "non-condensed") element matrix. Creating the matrix without constrained entries reduces the memory footprint, but unless a significant amount of DoFs are constrained (e.g. high mesh resolution at a boundary) the savings are negligible. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/539">#539</a>)</li></ul><h3 id="Changed-2"><a class="docs-heading-anchor" href="#Changed-2">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-2" title="Permalink"></a></h3><ul><li><code>ConstraintHandler</code>: <code>update!</code> is now called implicitly in <code>close!</code>. This was easy to miss, and somewhat of a strange requirement when solving problems without time stepping. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/459">#459</a>)</li><li>The function for computing the inhomogeneity in a <code>Dirichlet</code> constraint can now be specified as either <code>f(x)</code> or <code>f(x, t)</code>, where <code>x</code> is the spatial coordinate and <code>t</code> the time. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/459">#459</a>)</li><li>The elements of a <code>CellIterator</code> are now <code>CellCache</code> instead of the iterator itself, which was confusing in some cases. This change does not affect typical user code. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/546">#546</a>)</li></ul><h3 id="Deprecated-2"><a class="docs-heading-anchor" href="#Deprecated-2">Deprecated</a><a class="docs-heading-anchor-permalink" href="#Deprecated-2" title="Permalink"></a></h3><ul><li>Adding fields to a DoF handler with <code>push!(dh, ...)</code> has been deprecated in favor of <code>add!(dh, ...)</code>. This is to make it consistent with how constraints are added to a constraint handler. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/578">#578</a>)</li></ul><h3 id="Fixed-4"><a class="docs-heading-anchor" href="#Fixed-4">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-4" title="Permalink"></a></h3><ul><li>Fix <code>shape_value</code> for the linear, discontinuous Lagrange interpolation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/553">#553</a>)</li><li>Fix <code>reference_coordinate</code> dispatch for discontinuous Lagrange interpolations. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/559">#559</a>)</li><li>Fix <code>show(::Grid)</code> for custom cell types. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/570">#570</a>)</li><li>Fix <code>apply_zero!(Δa, ch)</code> when using inhomogeneous affine constraints (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/575">#575</a>)</li></ul><h3 id="Other-improvements-5"><a class="docs-heading-anchor" href="#Other-improvements-5">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-5" title="Permalink"></a></h3><ul><li>Internal changes defining a new global matrix/vector "interface". These changes make it easy to enable more array types (e.g. <code>BlockMatrix</code> support added in this release) and solvers in the future. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/562">#562</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/571">#571</a>)</li><li>Performance improvements:<ul><li>Reduced time and memory allocations for global sparse matrix creation (Julia >= 1.10). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/563">#563</a>)</li></ul></li><li>Documentation improvements:<ul><li>Added an overview of the Examples section. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/531">#531</a>)</li><li>Added an example showing topology optimization. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/531">#531</a>)</li><li>Various typo fixes. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/574">#574</a>)</li><li>Fix broken links. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/583">#583</a>)</li></ul></li></ul><h2 id="[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11"><a class="docs-heading-anchor" href="#[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10">v0.3.10</a> - 2022-12-11</a><a id="[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11" title="Permalink"></a></h2><h3 id="Added-6"><a class="docs-heading-anchor" href="#Added-6">Added</a><a class="docs-heading-anchor-permalink" href="#Added-6" title="Permalink"></a></h3><ul><li>New functions <code>apply_local!</code> and <code>apply_assemble!</code> for applying constraints locally on the element level before assembling to the global system. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/528">#528</a>)</li><li>New functionality to renumber DoFs by fields or by components. This is useful when you need the global matrix to be blocked. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/378">#378</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/545">#545</a>)</li><li>Functionality to renumber DoFs in DofHandler and ConstraintHandler simultaneously: <code>renumber!(dh::DofHandler, ch::ConstraintHandler, order)</code>. Previously renumbering had to be done <em>before</em> creating the ConstraintHandler since otherwise DoF numbers would be inconsistent. However, this was inconvenient in cases where the constraints impact the new DoF order permutation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/542">#542</a>)</li><li>The coupling between fields can now be specified when creating the global matrix with <code>create_sparsity_pattern</code> by passing a <code>Matrix{Bool}</code>. For example, in a problem with unknowns <code>(u, p)</code> and corresponding test functions <code>(v, q)</code>, if there is no coupling between <code>p</code> and <code>q</code> it is unnecessary to allocate entries in the global matrix corresponding to these DoFs. This can now be communicated to <code>create_sparsity_pattern</code> by passing the coupling matrix <code>[true true; true false]</code> in the keyword argument <code>coupling</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/544">#544</a>)</li></ul><h3 id="Changed-3"><a class="docs-heading-anchor" href="#Changed-3">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-3" title="Permalink"></a></h3><ul><li>Runtime and allocations for application of boundary conditions in <code>apply!</code> and <code>apply_zero!</code> have been improved. As a result, the <code>strategy</code> keyword argument is obsolete and thus ignored. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/489">#489</a>)</li><li>The internal representation of <code>Dirichlet</code> boundary conditions and <code>AffineConstraint</code>s in the <code>ConstraintHandler</code> have been unified. As a result, conflicting constraints on DoFs are handled more consistently: the constraint added last to the <code>ConstraintHandler</code> now always override any previous constraints. Conflicting constraints could previously cause problems when a DoF where prescribed by both <code>Dirichlet</code> and <code>AffineConstraint</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/529">#529</a>)</li><li>Entries in local matrix/vector are now ignored in the assembly procedure. This allows, for example, using a dense local matrix <code>[a b; c d]</code> even if no entries exist in the global matrix for the <code>d</code> block, i.e. in <code>[A B; C D]</code> the <code>D</code> block is zero, and these global entries might not exist in the sparse matrix. (Such sparsity patterns can now be created by <code>create_sparsity_pattern</code>, see <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/544">#544</a>.) (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/543">#543</a>)</li></ul><h3 id="Fixed-5"><a class="docs-heading-anchor" href="#Fixed-5">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-5" title="Permalink"></a></h3><ul><li>Fix affine constraints with prescribed DoFs in the right-hand-side. In particular, DoFs that are prescribed by just an inhomogeneity are now handled correctly, and nested affine constraints now give an error instead of silently giving the wrong result. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/530">#530</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/535">#535</a>)</li><li>Fixed internal inconsistency in edge ordering for 2nd order RefTetrahedron and RefCube. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/520">#520</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/523">#523</a>)</li></ul><h3 id="Other-improvements-6"><a class="docs-heading-anchor" href="#Other-improvements-6">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-6" title="Permalink"></a></h3><ul><li>Performance improvements:<ul><li>Reduced time and memory allocations in DoF distribution for <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/533">#533</a>)</li><li>Reduced time and memory allocations reductions in <code>getcoordinates!</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/536">#536</a>)</li><li>Reduced time and memory allocations in affine constraint condensation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/537">#537</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/541">#541</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/550">#550</a>)</li></ul></li><li>Documentation improvements:<ul><li>Use <code>:static</code> scheduling for threaded <code>for</code>-loop (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/534">#534</a>)</li><li>Remove use of <code>@inbounds</code> (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/547">#547</a>)</li></ul></li><li>Unification of <code>create_sparsity_pattern</code> methods to remove code duplication between <code>DofHandler</code> and <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/538">#538</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/540">#540</a>)</li></ul><h2 id="[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19"><a class="docs-heading-anchor" href="#[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9">v0.3.9</a> - 2022-10-19</a><a id="[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19" title="Permalink"></a></h2><h3 id="Added-7"><a class="docs-heading-anchor" href="#Added-7">Added</a><a class="docs-heading-anchor-permalink" href="#Added-7" title="Permalink"></a></h3><ul><li>New higher order function interpolations for triangles (<code>Lagrange{2,RefTetrahedron,3}</code>, <code>Lagrange{2,RefTetrahedron,4}</code>, and <code>Lagrange{2,RefTetrahedron,5}</code>). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/482">#482</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/512">#512</a>)</li><li>New Gaussian quadrature formula for triangles up to order 15. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/514">#514</a>)</li><li>Add debug mode for working with Ferrite internals. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/524">#524</a>)</li></ul><h3 id="Changed-4"><a class="docs-heading-anchor" href="#Changed-4">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-4" title="Permalink"></a></h3><ul><li>The default components to constrain in <code>Dirichlet</code> and <code>PeriodicDirichlet</code> have changed from component 1 to all components of the field. For scalar problems this has no effect. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/506">#506</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/509">#509</a>)</li></ul><h2 id="[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05"><a class="docs-heading-anchor" href="#[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8">v0.3.8</a> - 2022-10-05</a><a id="[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05" title="Permalink"></a></h2><h3 id="Added-8"><a class="docs-heading-anchor" href="#Added-8">Added</a><a class="docs-heading-anchor-permalink" href="#Added-8" title="Permalink"></a></h3><ul><li>Ferrite.jl now has a logo! (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/464">#464</a>)</li><li>New keyword argument <code>search_nneighbors::Int</code> in <code>PointEvalHandler</code> for specifying how many neighboring elements to consider in the kNN search. The default is still 3 (usually sufficient). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/466">#466</a>)</li><li>The IJV-assembler now support assembling non-square matrices. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/471">#471</a>)</li><li>Periodic boundary conditions have been reworked and generalized. It now supports arbitrary relations between the mirror and image boundaries (e.g. not only translations in x/y/z direction). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/478">#478</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/481">#481</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/496">#496</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/501">#501</a>)</li></ul><h3 id="Fixed-6"><a class="docs-heading-anchor" href="#Fixed-6">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-6" title="Permalink"></a></h3><ul><li>Fix <code>PointEvalHandler</code> when the first point is missing. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/466">#466</a>)</li><li>Fix the ordering of nodes on the face for <code>(Quadratic)Tetrahedron</code> cells. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/475">#475</a>)</li></ul><h3 id="Other-improvements-7"><a class="docs-heading-anchor" href="#Other-improvements-7">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-7" title="Permalink"></a></h3><ul><li>Many improvements to the documentation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/467">#467</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/473">#473</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/487">#487</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/494">#494</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/500">#500</a>)</li><li>Improved error messages in <code>reinit!</code> when number of geometric base functions and number of element coordinates mismatch. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/469">#469</a>)</li><li>Remove some unnecessary function parametrizations. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/503">#503</a>)</li><li>Remove some unnecessary allocations in grid coloring. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/505">#505</a>)</li><li>More efficient way of creating the sparsity pattern when using <code>AffineConstraints</code> and/or <code>PeriodicDirichlet</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/436">#436</a>)</li></ul><h2 id="[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05"><a class="docs-heading-anchor" href="#[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7">v0.3.7</a> - 2022-07-05</a><a id="[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05" title="Permalink"></a></h2><h3 id="Fixed-7"><a class="docs-heading-anchor" href="#Fixed-7">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-7" title="Permalink"></a></h3><ul><li>Fix tests for newer version of WriteVTK (no functional change). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/462">#462</a>)</li></ul><h3 id="Other-improvements-8"><a class="docs-heading-anchor" href="#Other-improvements-8">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-8" title="Permalink"></a></h3><ul><li>Various improvements to the heat equation example and the hyperelasticity example in the documentation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/460">#460</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/461">#461</a>)</li></ul><h2 id="[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30"><a class="docs-heading-anchor" href="#[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6">v0.3.6</a> - 2022-06-30</a><a id="[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30" title="Permalink"></a></h2><h3 id="Fixed-8"><a class="docs-heading-anchor" href="#Fixed-8">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-8" title="Permalink"></a></h3><ul><li>Fix a bug with <code>L2Projection</code> of mixed grid. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/456">#456</a>)</li></ul><h3 id="Other-improvements-9"><a class="docs-heading-anchor" href="#Other-improvements-9">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-9" title="Permalink"></a></h3><ul><li>Expanded manual section of Dirichlet BCs. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/458">#458</a>)</li></ul><h2 id="[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30"><a class="docs-heading-anchor" href="#[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5">v0.3.5</a> - 2022-05-30</a><a id="[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30" title="Permalink"></a></h2><h3 id="Added-9"><a class="docs-heading-anchor" href="#Added-9">Added</a><a class="docs-heading-anchor-permalink" href="#Added-9" title="Permalink"></a></h3><ul><li>Functionality for querying information about the grid topology (e.g. neighboring cells, boundaries, ...). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/363">#363</a>)</li></ul><h3 id="Fixed-9"><a class="docs-heading-anchor" href="#Fixed-9">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-9" title="Permalink"></a></h3><ul><li>Fix application of boundary conditions when combining RHSData and affine constraints. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/431">#431</a>)</li></ul><h2 id="[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25"><a class="docs-heading-anchor" href="#[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4">v0.3.4</a> - 2022-02-25</a><a id="[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25" title="Permalink"></a></h2><h3 id="Added-10"><a class="docs-heading-anchor" href="#Added-10">Added</a><a class="docs-heading-anchor-permalink" href="#Added-10" title="Permalink"></a></h3><ul><li>Affine (linear) constraints between degrees-of-freedom. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/401">#401</a>)</li><li>Periodic Dirichlet boundary conditions. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/418">#418</a>)</li><li>Evaluation of arbitrary quantities in FE space. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/425">#425</a>)</li></ul><h3 id="Changed-5"><a class="docs-heading-anchor" href="#Changed-5">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-5" title="Permalink"></a></h3><ul><li>Interpolation(s) and the quadrature rule are now stored as part of the <code>CellValues</code> structs (<code>cv.func_interp</code>, <code>cv.geo_interp</code>, and <code>cv.qr</code>). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/428">#428</a>)</li></ul><h2 id="[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04"><a class="docs-heading-anchor" href="#[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3">v0.3.3</a> - 2022-02-04</a><a id="[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04" title="Permalink"></a></h2><h3 id="Changed-6"><a class="docs-heading-anchor" href="#Changed-6">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-6" title="Permalink"></a></h3><ul><li>Verify user input in various functions to eliminate possible out-of-bounds accesses. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/407">#407</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/411">#411</a>)</li></ul><h2 id="[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18"><a class="docs-heading-anchor" href="#[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2">v0.3.2</a> - 2022-01-18</a><a id="[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18" title="Permalink"></a></h2><h3 id="Added-11"><a class="docs-heading-anchor" href="#Added-11">Added</a><a class="docs-heading-anchor-permalink" href="#Added-11" title="Permalink"></a></h3><ul><li>Support for new interpolation types: <code>DiscontinuousLagrange</code>, <code>BubbleEnrichedLagrange</code>, and <code>CrouzeixRaviart</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/352">#352</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/392">#392</a>)</li></ul><h3 id="Changed-7"><a class="docs-heading-anchor" href="#Changed-7">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-7" title="Permalink"></a></h3><ul><li>Julia version 1.0 is no longer supported for Ferrite versions >= 0.3.2. Use Julia version >= 1.6. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/385">#385</a>)</li><li>Quadrature data for L2 projection can now be given as a matrix of size "number of elements" x "number of quadrature points per element". (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/386">#386</a>)</li><li>Projected values from L2 projection can now be exported directly to VTK. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/390">#390</a>)</li><li>Grid coloring can now act on a subset of cells. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/402">#402</a>)</li><li>Various functions related to cell values now use traits to make it easier to extend and reuse functionality in external code. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/404">#404</a>)</li></ul><h3 id="Fixed-10"><a class="docs-heading-anchor" href="#Fixed-10">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-10" title="Permalink"></a></h3><ul><li>Exporting tensors to VTK now use correct names for the components. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/406">#406</a>)</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorials/">Tutorials overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ end</code></pre></li></ul><h3 id="Fixed"><a class="docs-heading-anchor" href="#Fixed">Fixed</a><a id="Fixed-1"></a><a class="docs-heading-anchor-permalink" href="#Fixed" title="Permalink"></a></h3><ul><li><p>Benchmarks now work with master branch. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/751">#751</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/855">#855</a>)</p></li><li><p>Topology construction have been generalized to, in particular, fix construction for 1D and for wedge elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/641">#641</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/670">#670</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/684">#684</a>)</p></li></ul><h3 id="Other-improvements"><a class="docs-heading-anchor" href="#Other-improvements">Other improvements</a><a id="Other-improvements-1"></a><a class="docs-heading-anchor-permalink" href="#Other-improvements" title="Permalink"></a></h3><ul><li><p>Documentation:</p><ul><li>The documentation is now structured according to the Diataxis framework. There is now also clear separation between tutorials (for teaching) and code gallery (for showing off). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/737">#737</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/756">#756</a>)</li><li>New section in the developer documentation that describes the (new) reference shapes and their numbering scheme. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/688">#688</a>)</li></ul></li><li><p>Performance:</p><ul><li><code>Ferrite.transform!(grid, f)</code> (for transforming the node coordinates in the <code>grid</code> according to a function <code>f</code>) is now faster and allocates less. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/675">#675</a>)</li><li>Slight performance improvement in construction of <code>PointEvalHandler</code> (faster reverse coordinate lookup). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/719">#719</a>)</li><li>Various performance improvements to topology construction. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/753">#753</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/759">#759</a>)</li></ul></li><li><p>Internal improvements:</p><ul><li>The dof distribution interface have been updated to support higher order elements (future work). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/627">#627</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/732">#732</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/733">#733</a>)</li><li>The <code>AbstractGrid</code> and <code>AbstractDofHandler</code> interfaces are now used more consistently internally. This will help with the implementation of distributed grids and DofHandlers. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/655">#655</a>)</li><li>VTK export now uses the (geometric) interpolation directly when evaluating the finite element field instead of trying to work backwards how DoFs map to nodes. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/703">#703</a>)</li><li>Improved bounds checking in <code>assemble!</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/706">#706</a>)</li><li>Internal methods <code>Ferrite.value</code> and <code>Ferrite.derivative</code> for computing the value/gradient of <em>all</em> shape functions have been removed. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/720">#720</a>)</li><li><code>Ferrite.create_incidence_matrix</code> now work with any <code>AbstractGrid</code> (not just <code>Grid</code>). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/726">#726</a>)</li></ul></li></ul><h2 id="[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03"><a class="docs-heading-anchor" href="#[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14">v0.3.14</a> - 2023-04-03</a><a id="[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.14](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.14)-2023-04-03" title="Permalink"></a></h2><h3 id="Added-2"><a class="docs-heading-anchor" href="#Added-2">Added</a><a class="docs-heading-anchor-permalink" href="#Added-2" title="Permalink"></a></h3><ul><li>Support reordering dofs of a <code>MixedDofHandler</code> by the built-in orderings <code>FieldWise</code> and <code>ComponentWise</code>. This includes support for reordering dofs of fields on subdomains. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/645">#645</a>)</li><li>Support specifying the coupling between fields in a <code>MixedDofHandler</code> when creating the sparsity pattern. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/650">#650</a>)</li><li>Support Metis dof reordering with coupling information for <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/650">#650</a>)</li><li>Pretty printing for <code>MixedDofHandler</code> and <code>L2Projector</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/465">#465</a>)</li></ul><h3 id="Other-improvements-2"><a class="docs-heading-anchor" href="#Other-improvements-2">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-2" title="Permalink"></a></h3><ul><li>The <code>MixedDofHandler</code> have gone through a performance review (see <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/629">#629</a>) and now performs the same as <code>DofHandler</code>. This was part of the push to merge the two DoF handlers. Since <code>MixedDofHandler</code> is strictly more flexible, and now equally performant, it will replace <code>DofHandler</code> in the next breaking release. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/637">#637</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/639">#639</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/642">#642</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/643">#643</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/656">#656</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/660">#660</a>)</li></ul><h3 id="Internal-changes"><a class="docs-heading-anchor" href="#Internal-changes">Internal changes</a><a id="Internal-changes-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-changes" title="Permalink"></a></h3><p>Changes listed here should not affect regular usage, but listed here in case you have been poking into Ferrite internals:</p><ul><li><code>Ferrite.ndim(dh, fieldname)</code> has been removed, use <code>Ferrite.getfielddim(dh, fieldname)</code> instead. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/658">#658</a>)</li><li><code>Ferrite.nfields(dh)</code> has been removed, use <code>length(Ferrite.getfieldnames(dh))</code> instead. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/444">#444</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/653">#653</a>)</li><li><code>getfielddims(::FieldHandler)</code> and <code>getfieldinterpolations(::FieldHandler)</code> have been removed (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/647">#647</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/659">#659</a>)</li></ul><h2 id="[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23"><a class="docs-heading-anchor" href="#[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13">v0.3.13</a> - 2023-03-23</a><a id="[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.13](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.13)-2023-03-23" title="Permalink"></a></h2><h3 id="Added-3"><a class="docs-heading-anchor" href="#Added-3">Added</a><a class="docs-heading-anchor-permalink" href="#Added-3" title="Permalink"></a></h3><ul><li>Support for classical trilinear and triquadratic wedge elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Symmetric quadrature rules up to order 10 for prismatic elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Finer granulation of dof distribution, allowing to distribute different amounts of dofs per entity. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li></ul><h3 id="Fixed-2"><a class="docs-heading-anchor" href="#Fixed-2">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-2" title="Permalink"></a></h3><ul><li>Dof distribution for embedded elements. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Improve numerical accuracy in shape function evaluation for the <code>Lagrange{2,Tetrahedron,(3|4|5)}</code> interpolations. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/582">#582</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/633">#633</a>)</li></ul><h3 id="Other-improvements-3"><a class="docs-heading-anchor" href="#Other-improvements-3">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-3" title="Permalink"></a></h3><ul><li>Documentation:<ul><li>New "Developer documentation" section in the manual for documenting Ferrite.jl internals and developer tools. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/611">#611</a>)</li><li>Fix a bug in constraint computation in Stoke's flow example. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/614">#614</a>)</li></ul></li><li>Performance:<ul><li>Benchmarking infrastructure to help tracking performance changes. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/388">#388</a>)</li><li>Performance improvements for various accessor functions for <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/621">#621</a>)</li></ul></li></ul><h3 id="Internal-changes-2"><a class="docs-heading-anchor" href="#Internal-changes-2">Internal changes</a><a class="docs-heading-anchor-permalink" href="#Internal-changes-2" title="Permalink"></a></h3><ul><li>To clarify the dof management <code>vertices(ip)</code>, <code>edges(ip)</code> and <code>faces(ip)</code> has been deprecated in favor of <code>vertexdof_indices(ip)</code>, <code>edgedof_indices(ip)</code> and <code>facedof_indices(ip)</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/581">#581</a>)</li><li>Duplicate grid representation has been removed from the <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/577">#577</a>)</li></ul><h2 id="[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28"><a class="docs-heading-anchor" href="#[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12">v0.3.12</a> - 2023-02-28</a><a id="[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.12](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.12)-2023-02-28" title="Permalink"></a></h2><h3 id="Added-4"><a class="docs-heading-anchor" href="#Added-4">Added</a><a class="docs-heading-anchor-permalink" href="#Added-4" title="Permalink"></a></h3><ul><li>Added a basic <code>show</code> method for assemblers. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/598">#598</a>)</li></ul><h3 id="Fixed-3"><a class="docs-heading-anchor" href="#Fixed-3">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-3" title="Permalink"></a></h3><ul><li>Fix an issue in constraint application of <code>Symmetric</code>-wrapped sparse matrices (i.e. obtained from <code>create_symmatric_sparsity_pattern</code>). In particular, <code>apply!(K::Symmetric, f, ch)</code> would incorrectly modify <code>f</code> if any of the constraints were inhomogeneous. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/592">#592</a>)</li><li>Properly disable the Metis extension on Julia 1.9 instead of causing precompilation errors. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/588">#588</a>)</li><li>Fix adding Dirichlet boundary conditions on nodes when using MixedDofHandler. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/593">#593</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/594">#594</a>)</li><li>Fix accidentally slow implementation of <code>show</code> for <code>Grid</code>s. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/599">#599</a>)</li><li>Fixes to topology functionality. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/453">#453</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/518">#518</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/455">#455</a>)</li><li>Fix grid coloring for cell sets with 0 or 1 cells. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/600">#600</a>)</li></ul><h3 id="Other-improvements-4"><a class="docs-heading-anchor" href="#Other-improvements-4">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-4" title="Permalink"></a></h3><ul><li>Documentation improvements:<ul><li>Simplications and clarifications to hyperelasticity example. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/591">#591</a>)</li><li>Remove duplicate docstring entry for <code>vtk_point_data</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/602">#602</a>)</li><li>Update documentation about initial conditions. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/601">#601</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/604">#604</a>)</li></ul></li></ul><h2 id="[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17"><a class="docs-heading-anchor" href="#[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11">v0.3.11</a> - 2023-01-17</a><a id="[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.11](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.11)-2023-01-17" title="Permalink"></a></h2><h3 id="Added-5"><a class="docs-heading-anchor" href="#Added-5">Added</a><a class="docs-heading-anchor-permalink" href="#Added-5" title="Permalink"></a></h3><ul><li><a href="https://github.com/JuliaSparse/Metis.jl">Metis.jl</a> extension for fill-reducing DoF permutation. This uses Julias new package extension mechanism (requires Julia 1.10) to support a new DoF renumbering order <code>DofOrder.Ext{Metis}()</code> that can be passed to <code>renumber!</code> to renumber DoFs using the Metis.jl library. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/393">#393</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/549">#549</a>)</li><li><a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> extension for creating a globally blocked system matrix. <code>create_sparsity_pattern(BlockMatrix, dh, ch; kwargs...)</code> return a matrix that is blocked by field (requires DoFs to be (re)numbered by field, i.e. <code>renumber!(dh, DofOrder.FieldWise())</code>). For custom blocking it is possible to pass an uninitialized <code>BlockMatrix</code> with the correct block sizes (see <code>BlockArrays.jl</code> docs). This functionality is useful for e.g. special solvers where individual blocks need to be extracted. Requires Julia version 1.9 or above. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/567">#567</a>)</li><li>New function <code>apply_analytical!</code> for setting the values of the degrees of freedom for a specific field according to a spatial function <code>f(x)</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/532">#532</a>)</li><li>New cache struct <code>CellCache</code> to be used when iterating over the cells in a grid or DoF handler. <code>CellCache</code> caches nodes, coordinates, and DoFs, for the cell. The cache <code>cc</code> can be re-initialized for a new cell index <code>ci</code> by calling <code>reinit!(cc, ci)</code>. This can be used as an alternative to <code>CellIterator</code> when more control over which element to loop over is needed. See documentation for <code>CellCache</code> for more information. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/546">#546</a>)</li><li>It is now possible to create the sparsity pattern without constrained entries (they will be zeroed out later anyway) by passing <code>keep_constrained=false</code> to <code>create_sparsity_pattern</code>. This naturally only works together with local condensation of constraints since there won't be space allocated in the global matrix for the full (i.e. "non-condensed") element matrix. Creating the matrix without constrained entries reduces the memory footprint, but unless a significant amount of DoFs are constrained (e.g. high mesh resolution at a boundary) the savings are negligible. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/539">#539</a>)</li></ul><h3 id="Changed-2"><a class="docs-heading-anchor" href="#Changed-2">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-2" title="Permalink"></a></h3><ul><li><code>ConstraintHandler</code>: <code>update!</code> is now called implicitly in <code>close!</code>. This was easy to miss, and somewhat of a strange requirement when solving problems without time stepping. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/459">#459</a>)</li><li>The function for computing the inhomogeneity in a <code>Dirichlet</code> constraint can now be specified as either <code>f(x)</code> or <code>f(x, t)</code>, where <code>x</code> is the spatial coordinate and <code>t</code> the time. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/459">#459</a>)</li><li>The elements of a <code>CellIterator</code> are now <code>CellCache</code> instead of the iterator itself, which was confusing in some cases. This change does not affect typical user code. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/546">#546</a>)</li></ul><h3 id="Deprecated-2"><a class="docs-heading-anchor" href="#Deprecated-2">Deprecated</a><a class="docs-heading-anchor-permalink" href="#Deprecated-2" title="Permalink"></a></h3><ul><li>Adding fields to a DoF handler with <code>push!(dh, ...)</code> has been deprecated in favor of <code>add!(dh, ...)</code>. This is to make it consistent with how constraints are added to a constraint handler. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/578">#578</a>)</li></ul><h3 id="Fixed-4"><a class="docs-heading-anchor" href="#Fixed-4">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-4" title="Permalink"></a></h3><ul><li>Fix <code>shape_value</code> for the linear, discontinuous Lagrange interpolation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/553">#553</a>)</li><li>Fix <code>reference_coordinate</code> dispatch for discontinuous Lagrange interpolations. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/559">#559</a>)</li><li>Fix <code>show(::Grid)</code> for custom cell types. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/570">#570</a>)</li><li>Fix <code>apply_zero!(Δa, ch)</code> when using inhomogeneous affine constraints (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/575">#575</a>)</li></ul><h3 id="Other-improvements-5"><a class="docs-heading-anchor" href="#Other-improvements-5">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-5" title="Permalink"></a></h3><ul><li>Internal changes defining a new global matrix/vector "interface". These changes make it easy to enable more array types (e.g. <code>BlockMatrix</code> support added in this release) and solvers in the future. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/562">#562</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/571">#571</a>)</li><li>Performance improvements:<ul><li>Reduced time and memory allocations for global sparse matrix creation (Julia >= 1.10). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/563">#563</a>)</li></ul></li><li>Documentation improvements:<ul><li>Added an overview of the Examples section. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/531">#531</a>)</li><li>Added an example showing topology optimization. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/531">#531</a>)</li><li>Various typo fixes. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/574">#574</a>)</li><li>Fix broken links. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/583">#583</a>)</li></ul></li></ul><h2 id="[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11"><a class="docs-heading-anchor" href="#[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10">v0.3.10</a> - 2022-12-11</a><a id="[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.10](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.10)-2022-12-11" title="Permalink"></a></h2><h3 id="Added-6"><a class="docs-heading-anchor" href="#Added-6">Added</a><a class="docs-heading-anchor-permalink" href="#Added-6" title="Permalink"></a></h3><ul><li>New functions <code>apply_local!</code> and <code>apply_assemble!</code> for applying constraints locally on the element level before assembling to the global system. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/528">#528</a>)</li><li>New functionality to renumber DoFs by fields or by components. This is useful when you need the global matrix to be blocked. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/378">#378</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/545">#545</a>)</li><li>Functionality to renumber DoFs in DofHandler and ConstraintHandler simultaneously: <code>renumber!(dh::DofHandler, ch::ConstraintHandler, order)</code>. Previously renumbering had to be done <em>before</em> creating the ConstraintHandler since otherwise DoF numbers would be inconsistent. However, this was inconvenient in cases where the constraints impact the new DoF order permutation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/542">#542</a>)</li><li>The coupling between fields can now be specified when creating the global matrix with <code>create_sparsity_pattern</code> by passing a <code>Matrix{Bool}</code>. For example, in a problem with unknowns <code>(u, p)</code> and corresponding test functions <code>(v, q)</code>, if there is no coupling between <code>p</code> and <code>q</code> it is unnecessary to allocate entries in the global matrix corresponding to these DoFs. This can now be communicated to <code>create_sparsity_pattern</code> by passing the coupling matrix <code>[true true; true false]</code> in the keyword argument <code>coupling</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/544">#544</a>)</li></ul><h3 id="Changed-3"><a class="docs-heading-anchor" href="#Changed-3">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-3" title="Permalink"></a></h3><ul><li>Runtime and allocations for application of boundary conditions in <code>apply!</code> and <code>apply_zero!</code> have been improved. As a result, the <code>strategy</code> keyword argument is obsolete and thus ignored. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/489">#489</a>)</li><li>The internal representation of <code>Dirichlet</code> boundary conditions and <code>AffineConstraint</code>s in the <code>ConstraintHandler</code> have been unified. As a result, conflicting constraints on DoFs are handled more consistently: the constraint added last to the <code>ConstraintHandler</code> now always override any previous constraints. Conflicting constraints could previously cause problems when a DoF where prescribed by both <code>Dirichlet</code> and <code>AffineConstraint</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/529">#529</a>)</li><li>Entries in local matrix/vector are now ignored in the assembly procedure. This allows, for example, using a dense local matrix <code>[a b; c d]</code> even if no entries exist in the global matrix for the <code>d</code> block, i.e. in <code>[A B; C D]</code> the <code>D</code> block is zero, and these global entries might not exist in the sparse matrix. (Such sparsity patterns can now be created by <code>create_sparsity_pattern</code>, see <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/544">#544</a>.) (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/543">#543</a>)</li></ul><h3 id="Fixed-5"><a class="docs-heading-anchor" href="#Fixed-5">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-5" title="Permalink"></a></h3><ul><li>Fix affine constraints with prescribed DoFs in the right-hand-side. In particular, DoFs that are prescribed by just an inhomogeneity are now handled correctly, and nested affine constraints now give an error instead of silently giving the wrong result. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/530">#530</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/535">#535</a>)</li><li>Fixed internal inconsistency in edge ordering for 2nd order RefTetrahedron and RefCube. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/520">#520</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/523">#523</a>)</li></ul><h3 id="Other-improvements-6"><a class="docs-heading-anchor" href="#Other-improvements-6">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-6" title="Permalink"></a></h3><ul><li>Performance improvements:<ul><li>Reduced time and memory allocations in DoF distribution for <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/533">#533</a>)</li><li>Reduced time and memory allocations reductions in <code>getcoordinates!</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/536">#536</a>)</li><li>Reduced time and memory allocations in affine constraint condensation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/537">#537</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/541">#541</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/550">#550</a>)</li></ul></li><li>Documentation improvements:<ul><li>Use <code>:static</code> scheduling for threaded <code>for</code>-loop (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/534">#534</a>)</li><li>Remove use of <code>@inbounds</code> (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/547">#547</a>)</li></ul></li><li>Unification of <code>create_sparsity_pattern</code> methods to remove code duplication between <code>DofHandler</code> and <code>MixedDofHandler</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/538">#538</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/540">#540</a>)</li></ul><h2 id="[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19"><a class="docs-heading-anchor" href="#[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9">v0.3.9</a> - 2022-10-19</a><a id="[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.9](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.9)-2022-10-19" title="Permalink"></a></h2><h3 id="Added-7"><a class="docs-heading-anchor" href="#Added-7">Added</a><a class="docs-heading-anchor-permalink" href="#Added-7" title="Permalink"></a></h3><ul><li>New higher order function interpolations for triangles (<code>Lagrange{2,RefTetrahedron,3}</code>, <code>Lagrange{2,RefTetrahedron,4}</code>, and <code>Lagrange{2,RefTetrahedron,5}</code>). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/482">#482</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/512">#512</a>)</li><li>New Gaussian quadrature formula for triangles up to order 15. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/514">#514</a>)</li><li>Add debug mode for working with Ferrite internals. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/524">#524</a>)</li></ul><h3 id="Changed-4"><a class="docs-heading-anchor" href="#Changed-4">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-4" title="Permalink"></a></h3><ul><li>The default components to constrain in <code>Dirichlet</code> and <code>PeriodicDirichlet</code> have changed from component 1 to all components of the field. For scalar problems this has no effect. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/506">#506</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/509">#509</a>)</li></ul><h2 id="[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05"><a class="docs-heading-anchor" href="#[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8">v0.3.8</a> - 2022-10-05</a><a id="[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.8](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.8)-2022-10-05" title="Permalink"></a></h2><h3 id="Added-8"><a class="docs-heading-anchor" href="#Added-8">Added</a><a class="docs-heading-anchor-permalink" href="#Added-8" title="Permalink"></a></h3><ul><li>Ferrite.jl now has a logo! (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/464">#464</a>)</li><li>New keyword argument <code>search_nneighbors::Int</code> in <code>PointEvalHandler</code> for specifying how many neighboring elements to consider in the kNN search. The default is still 3 (usually sufficient). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/466">#466</a>)</li><li>The IJV-assembler now support assembling non-square matrices. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/471">#471</a>)</li><li>Periodic boundary conditions have been reworked and generalized. It now supports arbitrary relations between the mirror and image boundaries (e.g. not only translations in x/y/z direction). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/478">#478</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/481">#481</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/496">#496</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/501">#501</a>)</li></ul><h3 id="Fixed-6"><a class="docs-heading-anchor" href="#Fixed-6">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-6" title="Permalink"></a></h3><ul><li>Fix <code>PointEvalHandler</code> when the first point is missing. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/466">#466</a>)</li><li>Fix the ordering of nodes on the face for <code>(Quadratic)Tetrahedron</code> cells. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/475">#475</a>)</li></ul><h3 id="Other-improvements-7"><a class="docs-heading-anchor" href="#Other-improvements-7">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-7" title="Permalink"></a></h3><ul><li>Many improvements to the documentation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/467">#467</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/473">#473</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/487">#487</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/494">#494</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/500">#500</a>)</li><li>Improved error messages in <code>reinit!</code> when number of geometric base functions and number of element coordinates mismatch. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/469">#469</a>)</li><li>Remove some unnecessary function parametrizations. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/503">#503</a>)</li><li>Remove some unnecessary allocations in grid coloring. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/505">#505</a>)</li><li>More efficient way of creating the sparsity pattern when using <code>AffineConstraints</code> and/or <code>PeriodicDirichlet</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/436">#436</a>)</li></ul><h2 id="[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05"><a class="docs-heading-anchor" href="#[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7">v0.3.7</a> - 2022-07-05</a><a id="[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.7](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.7)-2022-07-05" title="Permalink"></a></h2><h3 id="Fixed-7"><a class="docs-heading-anchor" href="#Fixed-7">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-7" title="Permalink"></a></h3><ul><li>Fix tests for newer version of WriteVTK (no functional change). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/462">#462</a>)</li></ul><h3 id="Other-improvements-8"><a class="docs-heading-anchor" href="#Other-improvements-8">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-8" title="Permalink"></a></h3><ul><li>Various improvements to the heat equation example and the hyperelasticity example in the documentation. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/460">#460</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/461">#461</a>)</li></ul><h2 id="[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30"><a class="docs-heading-anchor" href="#[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6">v0.3.6</a> - 2022-06-30</a><a id="[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.6](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.6)-2022-06-30" title="Permalink"></a></h2><h3 id="Fixed-8"><a class="docs-heading-anchor" href="#Fixed-8">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-8" title="Permalink"></a></h3><ul><li>Fix a bug with <code>L2Projection</code> of mixed grid. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/456">#456</a>)</li></ul><h3 id="Other-improvements-9"><a class="docs-heading-anchor" href="#Other-improvements-9">Other improvements</a><a class="docs-heading-anchor-permalink" href="#Other-improvements-9" title="Permalink"></a></h3><ul><li>Expanded manual section of Dirichlet BCs. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/458">#458</a>)</li></ul><h2 id="[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30"><a class="docs-heading-anchor" href="#[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5">v0.3.5</a> - 2022-05-30</a><a id="[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.5](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.5)-2022-05-30" title="Permalink"></a></h2><h3 id="Added-9"><a class="docs-heading-anchor" href="#Added-9">Added</a><a class="docs-heading-anchor-permalink" href="#Added-9" title="Permalink"></a></h3><ul><li>Functionality for querying information about the grid topology (e.g. neighboring cells, boundaries, ...). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/363">#363</a>)</li></ul><h3 id="Fixed-9"><a class="docs-heading-anchor" href="#Fixed-9">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-9" title="Permalink"></a></h3><ul><li>Fix application of boundary conditions when combining RHSData and affine constraints. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/431">#431</a>)</li></ul><h2 id="[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25"><a class="docs-heading-anchor" href="#[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4">v0.3.4</a> - 2022-02-25</a><a id="[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.4](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.4)-2022-02-25" title="Permalink"></a></h2><h3 id="Added-10"><a class="docs-heading-anchor" href="#Added-10">Added</a><a class="docs-heading-anchor-permalink" href="#Added-10" title="Permalink"></a></h3><ul><li>Affine (linear) constraints between degrees-of-freedom. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/401">#401</a>)</li><li>Periodic Dirichlet boundary conditions. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/418">#418</a>)</li><li>Evaluation of arbitrary quantities in FE space. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/425">#425</a>)</li></ul><h3 id="Changed-5"><a class="docs-heading-anchor" href="#Changed-5">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-5" title="Permalink"></a></h3><ul><li>Interpolation(s) and the quadrature rule are now stored as part of the <code>CellValues</code> structs (<code>cv.func_interp</code>, <code>cv.geo_interp</code>, and <code>cv.qr</code>). (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/428">#428</a>)</li></ul><h2 id="[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04"><a class="docs-heading-anchor" href="#[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3">v0.3.3</a> - 2022-02-04</a><a id="[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.3](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.3)-2022-02-04" title="Permalink"></a></h2><h3 id="Changed-6"><a class="docs-heading-anchor" href="#Changed-6">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-6" title="Permalink"></a></h3><ul><li>Verify user input in various functions to eliminate possible out-of-bounds accesses. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/407">#407</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/411">#411</a>)</li></ul><h2 id="[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18"><a class="docs-heading-anchor" href="#[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18"><a href="https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2">v0.3.2</a> - 2022-01-18</a><a id="[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18-1"></a><a class="docs-heading-anchor-permalink" href="#[v0.3.2](https://github.com/Ferrite-FEM/Ferrite.jl/releases/tag/v0.3.2)-2022-01-18" title="Permalink"></a></h2><h3 id="Added-11"><a class="docs-heading-anchor" href="#Added-11">Added</a><a class="docs-heading-anchor-permalink" href="#Added-11" title="Permalink"></a></h3><ul><li>Support for new interpolation types: <code>DiscontinuousLagrange</code>, <code>BubbleEnrichedLagrange</code>, and <code>CrouzeixRaviart</code>. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/352">#352</a>, <a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/392">#392</a>)</li></ul><h3 id="Changed-7"><a class="docs-heading-anchor" href="#Changed-7">Changed</a><a class="docs-heading-anchor-permalink" href="#Changed-7" title="Permalink"></a></h3><ul><li>Julia version 1.0 is no longer supported for Ferrite versions >= 0.3.2. Use Julia version >= 1.6. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/385">#385</a>)</li><li>Quadrature data for L2 projection can now be given as a matrix of size "number of elements" x "number of quadrature points per element". (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/386">#386</a>)</li><li>Projected values from L2 projection can now be exported directly to VTK. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/390">#390</a>)</li><li>Grid coloring can now act on a subset of cells. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/402">#402</a>)</li><li>Various functions related to cell values now use traits to make it easier to extend and reuse functionality in external code. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/404">#404</a>)</li></ul><h3 id="Fixed-10"><a class="docs-heading-anchor" href="#Fixed-10">Fixed</a><a class="docs-heading-anchor-permalink" href="#Fixed-10" title="Permalink"></a></h3><ul><li>Exporting tensors to VTK now use correct names for the components. (<a href="https://github.com/Ferrite-FEM/Ferrite.jl/issues/406">#406</a>)</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorials/">Tutorials overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. 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documentation</a></li><li class="is-active"><a class="tocitem" href>Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Cited literature</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Cited literature</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/cited-literature.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Cited-literature"><a class="docs-heading-anchor" href="#Cited-literature">Cited literature</a><a id="Cited-literature-1"></a><a class="docs-heading-anchor-permalink" href="#Cited-literature" title="Permalink"></a></h1><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="Hol">G. A. Holzapfel. <em>Nonlinear Solid Mechanics: A Continuum Approach for Engineering</em> (Wiley, Chichester ; New York, 2000).</div></dd><dt>[2]</dt><dd><div id="SimMie">J. Simo and C. Miehe. <a href="https://www.sciencedirect.com/science/article/pii/004578259290170O"><em>Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation</em></a>. <a href="https://doi.org/10.1016/0045-7825(92)90170-O">Computer Methods in Applied Mechanics and Engineering <strong>98</strong>, 41–104</a> (1992).</div></dd><dt>[3]</dt><dd><div id="Mu">L. Mu, J. Wang, Y. Wang and X. Ye. <a href="https://www.sciencedirect.com/science/article/pii/S0377042713002999"><em>Interior penalty discontinuous Galerkin method on very general polygonal and polyhedral meshes</em></a>. <a href="https://doi.org/10.1016/j.cam.2013.06.003">Journal of Computational and Applied Mathematics <strong>255</strong>, 432–440</a> (2014).</div></dd><dt>[4]</dt><dd><div id="Cockburn">D. N. Arnold, F. Brezzi, B. Cockburn and L. D. Marini. <a href="http://www.jstor.org/stable/4101034"><em>Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems</em></a>. SIAM Journal on Numerical Analysis <strong>39</strong>, 1749–1779 (2002). Accessed on Dec 20, 2023.</div></dd><dt>[5]</dt><dd><div id="Kirby2017">R. C. Kirby. <a href="https://doi.org/10.48550/arXiv.1706.09017"><em>A general approach to transforming finite elements</em></a> (2017), <a href="https://arxiv.org/abs/1706.09017">arXiv:1706.09017 [math.NA]</a>.</div></dd><dt>[6]</dt><dd><div id="Dun">D. Dunavant. <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1620210612"><em>High degree efficient symmetrical Gaussian quadrature rules for the triangle</em></a>. <a href="https://doi.org/10.1002/nme.1620210612">International journal for numerical methods in engineering <strong>21</strong>, 1129–1148</a> (1985).</div></dd><dt>[7]</dt><dd><div id="Keast">P. Keast. <a href="https://www.sciencedirect.com/science/article/pii/0045782586900599"><em>Moderate-degree tetrahedral quadrature formulas</em></a>. <a href="https://doi.org/10.1016/0045-7825(86)90059-9">Computer methods in applied mechanics and engineering <strong>55</strong>, 339–348</a> (1986).</div></dd><dt>[8]</dt><dd><div id="WitVin">F. D. Witherden and P. E. Vincent. <em>On the identification of symmetric quadrature rules for finite element methods</em>. Computers & Mathematics with Applications <strong>69</strong>, 1232–1241 (2015).</div></dd><dt>[9]</dt><dd><div id="CroRav">M. Crouzeix and P.-A. Raviart. <em>Conforming and nonconforming finite element methods for solving the stationary Stokes equations I</em>. Revue française d'automatique informatique recherche opérationnelle. Mathématique <strong>7</strong>, 33–75 (1973).</div></dd><dt>[10]</dt><dd><div id="RanTur">R. Rannacher and S. Turek. <em>Simple nonconforming quadrilateral Stokes element</em>. Numerical Methods for Partial Differential Equations <strong>8</strong>, 97–111 (1992).</div></dd><dt>[11]</dt><dd><div id="Turcksin2016">B. Turcksin, M. Kronbichler and W. Bangerth. <a href="https://doi.org/10.1145/2851488"><em>WorkStream – A Design Pattern for Multicore-Enabled Finite Element Computations</em></a>. <a href="https://doi.org/10.1145/2851488">ACM Trans. Math. Softw. <strong>43</strong></a> (2016).</div></dd><dt>[12]</dt><dd><div id="Cenanovic2017">M. Cenanovic. <em>Finite element methods for surface problems</em>. Ph.D. Thesis, Jönköping University, School of Engineering (2017).</div></dd><dt>[13]</dt><dd><div id="Scroggs2022">M. W. Scroggs, J. S. Dokken, C. N. Richardson and G. N. Wells. <a href="https://doi.org/10.1145/3524456"><em>Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes</em></a>. <a href="https://doi.org/10.1145/3524456">ACM Trans. Math. Softw. <strong>48</strong></a> (2022).</div></dd><dt>[14]</dt><dd><div id="JanHacJun2019regularizedthermotopopt">D. R. Jantos, K. Hackl and P. Junker. <a href="https://doi.org/10.1002/nme.5988"><em>An accurate and fast regularization approach to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1002/nme.5988">International Journal for Numerical Methods in Engineering <strong>117</strong>, 991–1017</a> (2019).</div></dd><dt>[15]</dt><dd><div id="BlaJanJun2022taylorwlsthermotopopt">M. Blaszczyk, D. R. Jantos and P. Junker. <a href="https://doi.org/10.1016/j.cma.2022.114698"><em>Application of Taylor series combined with the weighted least square method to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1016/j.cma.2022.114698">Computer Methods in Applied Mechanics and Engineering <strong>393</strong>, 114698</a> (2022).</div></dd></dl></div><!--<p>Workaround for https://github.com/JuliaDocs/DocumenterCitations.jl/issues/39</p><ul><li>[<a href="#Turcksin2016">11</a>]</li><li>[<a href="#Cenanovic2017">12</a>]</li><li>[<a href="#Scroggs2022">13</a>]</li></ul>--></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../devdocs/">« Developer documentation</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. 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documentation</a></li><li class="is-active"><a class="tocitem" href>Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Cited literature</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Cited literature</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/cited-literature.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Cited-literature"><a class="docs-heading-anchor" href="#Cited-literature">Cited literature</a><a id="Cited-literature-1"></a><a class="docs-heading-anchor-permalink" href="#Cited-literature" title="Permalink"></a></h1><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="Hol">G. A. Holzapfel. <em>Nonlinear Solid Mechanics: A Continuum Approach for Engineering</em> (Wiley, Chichester ; New York, 2000).</div></dd><dt>[2]</dt><dd><div id="SimMie">J. Simo and C. Miehe. <a href="https://www.sciencedirect.com/science/article/pii/004578259290170O"><em>Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation</em></a>. <a href="https://doi.org/10.1016/0045-7825(92)90170-O">Computer Methods in Applied Mechanics and Engineering <strong>98</strong>, 41–104</a> (1992).</div></dd><dt>[3]</dt><dd><div id="Mu">L. Mu, J. Wang, Y. Wang and X. Ye. <a href="https://www.sciencedirect.com/science/article/pii/S0377042713002999"><em>Interior penalty discontinuous Galerkin method on very general polygonal and polyhedral meshes</em></a>. <a href="https://doi.org/10.1016/j.cam.2013.06.003">Journal of Computational and Applied Mathematics <strong>255</strong>, 432–440</a> (2014).</div></dd><dt>[4]</dt><dd><div id="Cockburn">D. N. Arnold, F. Brezzi, B. Cockburn and L. D. Marini. <a href="http://www.jstor.org/stable/4101034"><em>Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems</em></a>. SIAM Journal on Numerical Analysis <strong>39</strong>, 1749–1779 (2002). Accessed on Dec 20, 2023.</div></dd><dt>[5]</dt><dd><div id="Kirby2017">R. C. Kirby. <a href="https://doi.org/10.48550/arXiv.1706.09017"><em>A general approach to transforming finite elements</em></a> (2017), <a href="https://arxiv.org/abs/1706.09017">arXiv:1706.09017 [math.NA]</a>.</div></dd><dt>[6]</dt><dd><div id="Dun">D. Dunavant. <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1620210612"><em>High degree efficient symmetrical Gaussian quadrature rules for the triangle</em></a>. <a href="https://doi.org/10.1002/nme.1620210612">International journal for numerical methods in engineering <strong>21</strong>, 1129–1148</a> (1985).</div></dd><dt>[7]</dt><dd><div id="Keast">P. Keast. <a href="https://www.sciencedirect.com/science/article/pii/0045782586900599"><em>Moderate-degree tetrahedral quadrature formulas</em></a>. <a href="https://doi.org/10.1016/0045-7825(86)90059-9">Computer methods in applied mechanics and engineering <strong>55</strong>, 339–348</a> (1986).</div></dd><dt>[8]</dt><dd><div id="WitVin">F. D. Witherden and P. E. Vincent. <em>On the identification of symmetric quadrature rules for finite element methods</em>. Computers & Mathematics with Applications <strong>69</strong>, 1232–1241 (2015).</div></dd><dt>[9]</dt><dd><div id="CroRav">M. Crouzeix and P.-A. Raviart. <em>Conforming and nonconforming finite element methods for solving the stationary Stokes equations I</em>. Revue française d'automatique informatique recherche opérationnelle. Mathématique <strong>7</strong>, 33–75 (1973).</div></dd><dt>[10]</dt><dd><div id="RanTur">R. Rannacher and S. Turek. <em>Simple nonconforming quadrilateral Stokes element</em>. Numerical Methods for Partial Differential Equations <strong>8</strong>, 97–111 (1992).</div></dd><dt>[11]</dt><dd><div id="Turcksin2016">B. Turcksin, M. Kronbichler and W. Bangerth. <a href="https://doi.org/10.1145/2851488"><em>WorkStream – A Design Pattern for Multicore-Enabled Finite Element Computations</em></a>. <a href="https://doi.org/10.1145/2851488">ACM Trans. Math. Softw. <strong>43</strong></a> (2016).</div></dd><dt>[12]</dt><dd><div id="Cenanovic2017">M. Cenanovic. <em>Finite element methods for surface problems</em>. Ph.D. Thesis, Jönköping University, School of Engineering (2017).</div></dd><dt>[13]</dt><dd><div id="Scroggs2022">M. W. Scroggs, J. S. Dokken, C. N. Richardson and G. N. Wells. <a href="https://doi.org/10.1145/3524456"><em>Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes</em></a>. <a href="https://doi.org/10.1145/3524456">ACM Trans. Math. Softw. <strong>48</strong></a> (2022).</div></dd><dt>[14]</dt><dd><div id="JanHacJun2019regularizedthermotopopt">D. R. Jantos, K. Hackl and P. Junker. <a href="https://doi.org/10.1002/nme.5988"><em>An accurate and fast regularization approach to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1002/nme.5988">International Journal for Numerical Methods in Engineering <strong>117</strong>, 991–1017</a> (2019).</div></dd><dt>[15]</dt><dd><div id="BlaJanJun2022taylorwlsthermotopopt">M. Blaszczyk, D. R. Jantos and P. Junker. <a href="https://doi.org/10.1016/j.cma.2022.114698"><em>Application of Taylor series combined with the weighted least square method to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1016/j.cma.2022.114698">Computer Methods in Applied Mechanics and Engineering <strong>393</strong>, 114698</a> (2022).</div></dd></dl></div><!--<p>Workaround for https://github.com/JuliaDocs/DocumenterCitations.jl/issues/39</p><ul><li>[<a href="#Turcksin2016">11</a>]</li><li>[<a href="#Cenanovic2017">12</a>]</li><li>[<a href="#Scroggs2022">13</a>]</li></ul>--></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../devdocs/">« Developer documentation</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. 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class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/FEValues.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-fevalues"><a class="docs-heading-anchor" href="#devdocs-fevalues">FEValues</a><a id="devdocs-fevalues-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-fevalues" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><ul><li><code>AbstractValues</code><ul><li><code>AbstractCellValues</code><ul><li><a href="../../reference/fevalues/#Ferrite.CellValues"><code>CellValues</code></a></li></ul></li><li><code>AbstractFacetValues</code><ul><li><a href="../../reference/fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a></li><li><a href="#Ferrite.BCValues"><code>BCValues</code></a></li></ul></li><li><a href="../../reference/export/#Ferrite.PointValues"><code>PointValues</code></a></li><li><a href="../../reference/fevalues/#Ferrite.InterfaceValues"><code>InterfaceValues</code></a></li></ul></li></ul><h2 id="Internal-types"><a class="docs-heading-anchor" href="#Internal-types">Internal types</a><a id="Internal-types-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-types" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.GeometryMapping" href="#Ferrite.GeometryMapping"><code>Ferrite.GeometryMapping</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">GeometryMapping{DiffOrder}(::Type{T}, ip_geo, qr::QuadratureRule)</code></pre><p>Create a <code>GeometryMapping</code> object which contains the geometric</p><ul><li>shape values</li><li>gradient values (if DiffOrder ≥ 1)</li><li>hessians values (if DiffOrder ≥ 2)</li></ul><p><code>T<:AbstractFloat</code> gives the numeric type of the values.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/GeometryMapping.jl#L20-L30">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.MappingValues" href="#Ferrite.MappingValues"><code>Ferrite.MappingValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">MappingValues(J, H)</code></pre><p>The mapping values are calculated based on a <code>geometric_mapping::GeometryMapping</code> along with the cell coordinates, and the stored jacobian, <code>J</code>, and potentially hessian, <code>H</code>, are used when mapping the <code>FunctionValues</code> to the current cell during <code>reinit!</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/GeometryMapping.jl#L1-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FunctionValues" href="#Ferrite.FunctionValues"><code>Ferrite.FunctionValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FunctionValues{DiffOrder}(::Type{T}, ip_fun, qr::QuadratureRule, ip_geo::VectorizedInterpolation)</code></pre><p>Create a <code>FunctionValues</code> object containing the shape values and gradients (up to order <code>DiffOrder</code>) for both the reference cell (precalculated) and the real cell (updated in <code>reinit!</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/FunctionValues.jl#L38-L43">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BCValues" href="#Ferrite.BCValues"><code>Ferrite.BCValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">BCValues(func_interpol::Interpolation, geom_interpol::Interpolation, boundary_type::Union{Type{<:BoundaryIndex}})</code></pre><p><code>BCValues</code> stores the shape values at all facet/faces/edges/vertices (depending on <code>boundary_type</code>) for the geometric interpolation (<code>geom_interpol</code>), for each dof-position determined by the <code>func_interpol</code>. Used mainly by the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/FacetValues.jl#L177-L182">source</a></section></article><h2 id="Internal-utilities"><a class="docs-heading-anchor" href="#Internal-utilities">Internal utilities</a><a id="Internal-utilities-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-utilities" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.embedding_det" href="#Ferrite.embedding_det"><code>Ferrite.embedding_det</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">embedding_det(J::SMatrix{3, 2})</code></pre><p>Embedding determinant for surfaces in 3D.</p><p>TLDR: "det(J) =" ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂</p><p>The transformation theorem for some function f on a 2D surface in 3D space leads to ∫ f ⋅ dS = ∫ f ⋅ (∂x/∂ξ₁ × ∂x/∂ξ₂) dξ₁dξ₂ = ∫ f ⋅ n ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂ dξ₁dξ₂ where ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂ is "detJ" and n is the unit normal. See e.g. https://scicomp.stackexchange.com/questions/41741/integration-of-d-1-dimensional-functions-on-finite-element-surfaces for simple explanation. For more details see e.g. the doctoral thesis by Mirza Cenanovic <strong>Tangential Calculus</strong> [<a href="../../cited-literature/#Cenanovic2017">12</a>].</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/GeometryMapping.jl#L201-L213">source</a></section><section><div><pre><code class="language-julia hljs">embedding_det(J::Union{SMatrix{2, 1}, SMatrix{3, 1}})</code></pre><p>Embedding determinant for curves in 2D and 3D.</p><p>TLDR: "det(J) =" ||∂x/∂ξ||₂</p><p>The transformation theorem for some function f on a 1D curve in 2D and 3D space leads to ∫ f ⋅ dE = ∫ f ⋅ ∂x/∂ξ dξ = ∫ f ⋅ t ||∂x/∂ξ||₂ dξ where ||∂x/∂ξ||₂ is "detJ" and t is "the unit tangent". See e.g. https://scicomp.stackexchange.com/questions/41741/integration-of-d-1-dimensional-functions-on-finite-element-surfaces for simple explanation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/GeometryMapping.jl#L216-L227">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_type-Tuple{Ferrite.AbstractValues}" href="#Ferrite.shape_value_type-Tuple{Ferrite.AbstractValues}"><code>Ferrite.shape_value_type</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_type(fe_v::AbstractValues)</code></pre><p>Return the type of <code>shape_value(fe_v, q_point, base_function)</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L163-L167">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient_type" href="#Ferrite.shape_gradient_type"><code>Ferrite.shape_gradient_type</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient_type(fe_v::AbstractValues)</code></pre><p>Return the type of <code>shape_gradient(fe_v, q_point, base_function)</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L215-L219">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ValuesUpdateFlags" href="#Ferrite.ValuesUpdateFlags"><code>Ferrite.ValuesUpdateFlags</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ValuesUpdateFlags(ip_fun::Interpolation; update_gradients = Val(true), update_hessians = Val(false), update_detJdV = Val(true))</code></pre><p>Creates a singleton type for specifying what parts of the AbstractValues should be updated. Note that this is internal API used to get type-stable construction. Keyword arguments in <code>AbstractValues</code> constructors are forwarded, and the public API is passing these as <code>Bool</code>, while the <code>ValuesUpdateFlags</code> method supports both boolean and <code>Val(::Bool)</code> keyword args.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L26-L32">source</a></section></article><h2 id="Custom-FEValues"><a class="docs-heading-anchor" href="#Custom-FEValues">Custom FEValues</a><a id="Custom-FEValues-1"></a><a class="docs-heading-anchor-permalink" href="#Custom-FEValues" title="Permalink"></a></h2><p>Custom FEValues, <code>fe_v::AbstractValues</code>, should normally implement the <a href="../../reference/fevalues/#Ferrite.reinit!"><code>reinit!</code></a> method. Subtypes of <code>AbstractValues</code> have default implementations for some functions, but require some lower-level access functions, specifically</p><ul><li><a href="../../reference/fevalues/#Ferrite.function_value"><code>function_value</code></a>, requires<ul><li><a href="../../reference/fevalues/#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></li><li><a href="../../reference/fevalues/#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></li><li><a href="../../reference/interpolations/#Ferrite.getnbasefunctions"><code>getnbasefunctions</code></a></li></ul></li><li><a href="../../reference/fevalues/#Ferrite.function_gradient"><code>function_gradient</code></a>, <a href="../../reference/fevalues/#Ferrite.function_divergence"><code>function_divergence</code></a>, <a href="../../reference/fevalues/#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a>, and <a href="../../reference/fevalues/#Ferrite.function_curl"><code>function_curl</code></a> requires<ul><li><a href="../../reference/fevalues/#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></li><li><a href="../../reference/fevalues/#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></li><li><a href="../../reference/interpolations/#Ferrite.getnbasefunctions"><code>getnbasefunctions</code></a></li></ul></li><li><a href="../../reference/fevalues/#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a>, requires<ul><li><a href="../../reference/fevalues/#Ferrite.geometric_value"><code>geometric_value</code></a></li><li><code>getngeobasefunctions</code></li><li><a href="../../reference/fevalues/#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></li></ul></li></ul><h3 id="Array-bounds"><a class="docs-heading-anchor" href="#Array-bounds">Array bounds</a><a id="Array-bounds-1"></a><a class="docs-heading-anchor-permalink" href="#Array-bounds" title="Permalink"></a></h3><ul><li>Asking for the <code>n</code>th quadrature point must be inside array bounds if <code>1 <= n <= getnquadpoints(fe_v)</code>. (<code>checkquadpoint</code> can, alternatively, be dispatched to check that <code>n</code> is inbounds.)</li><li>Asking for the <code>i</code>th shape value or gradient must be inside array bounds if <code>1 <= i <= getnbasefunctions(fe_v)</code></li><li>Asking for the <code>i</code>th geometric value must be inside array bounds if <code>1 <= i <= getngeobasefunctions(fe_v)</code></li></ul></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. 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class="tocitem" href="../../howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../../gallery/">Code gallery</a></li><li><a class="tocitem" href="../">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>FEValues</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>FEValues</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/FEValues.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-fevalues"><a class="docs-heading-anchor" href="#devdocs-fevalues">FEValues</a><a id="devdocs-fevalues-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-fevalues" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><ul><li><code>AbstractValues</code><ul><li><code>AbstractCellValues</code><ul><li><a href="../../reference/fevalues/#Ferrite.CellValues"><code>CellValues</code></a></li></ul></li><li><code>AbstractFacetValues</code><ul><li><a href="../../reference/fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a></li><li><a href="#Ferrite.BCValues"><code>BCValues</code></a></li></ul></li><li><a href="../../reference/export/#Ferrite.PointValues"><code>PointValues</code></a></li><li><a href="../../reference/fevalues/#Ferrite.InterfaceValues"><code>InterfaceValues</code></a></li></ul></li></ul><h2 id="Internal-types"><a class="docs-heading-anchor" href="#Internal-types">Internal types</a><a id="Internal-types-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-types" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.GeometryMapping" href="#Ferrite.GeometryMapping"><code>Ferrite.GeometryMapping</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">GeometryMapping{DiffOrder}(::Type{T}, ip_geo, qr::QuadratureRule)</code></pre><p>Create a <code>GeometryMapping</code> object which contains the geometric</p><ul><li>shape values</li><li>gradient values (if DiffOrder ≥ 1)</li><li>hessians values (if DiffOrder ≥ 2)</li></ul><p><code>T<:AbstractFloat</code> gives the numeric type of the values.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/GeometryMapping.jl#L20-L30">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.MappingValues" href="#Ferrite.MappingValues"><code>Ferrite.MappingValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">MappingValues(J, H)</code></pre><p>The mapping values are calculated based on a <code>geometric_mapping::GeometryMapping</code> along with the cell coordinates, and the stored jacobian, <code>J</code>, and potentially hessian, <code>H</code>, are used when mapping the <code>FunctionValues</code> to the current cell during <code>reinit!</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/GeometryMapping.jl#L1-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FunctionValues" href="#Ferrite.FunctionValues"><code>Ferrite.FunctionValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FunctionValues{DiffOrder}(::Type{T}, ip_fun, qr::QuadratureRule, ip_geo::VectorizedInterpolation)</code></pre><p>Create a <code>FunctionValues</code> object containing the shape values and gradients (up to order <code>DiffOrder</code>) for both the reference cell (precalculated) and the real cell (updated in <code>reinit!</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/FunctionValues.jl#L38-L43">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BCValues" href="#Ferrite.BCValues"><code>Ferrite.BCValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">BCValues(func_interpol::Interpolation, geom_interpol::Interpolation, boundary_type::Union{Type{<:BoundaryIndex}})</code></pre><p><code>BCValues</code> stores the shape values at all facet/faces/edges/vertices (depending on <code>boundary_type</code>) for the geometric interpolation (<code>geom_interpol</code>), for each dof-position determined by the <code>func_interpol</code>. Used mainly by the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/FacetValues.jl#L177-L182">source</a></section></article><h2 id="Internal-utilities"><a class="docs-heading-anchor" href="#Internal-utilities">Internal utilities</a><a id="Internal-utilities-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-utilities" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.embedding_det" href="#Ferrite.embedding_det"><code>Ferrite.embedding_det</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">embedding_det(J::SMatrix{3, 2})</code></pre><p>Embedding determinant for surfaces in 3D.</p><p>TLDR: "det(J) =" ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂</p><p>The transformation theorem for some function f on a 2D surface in 3D space leads to ∫ f ⋅ dS = ∫ f ⋅ (∂x/∂ξ₁ × ∂x/∂ξ₂) dξ₁dξ₂ = ∫ f ⋅ n ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂ dξ₁dξ₂ where ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂ is "detJ" and n is the unit normal. See e.g. https://scicomp.stackexchange.com/questions/41741/integration-of-d-1-dimensional-functions-on-finite-element-surfaces for simple explanation. For more details see e.g. the doctoral thesis by Mirza Cenanovic <strong>Tangential Calculus</strong> [<a href="../../cited-literature/#Cenanovic2017">12</a>].</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/GeometryMapping.jl#L201-L213">source</a></section><section><div><pre><code class="language-julia hljs">embedding_det(J::Union{SMatrix{2, 1}, SMatrix{3, 1}})</code></pre><p>Embedding determinant for curves in 2D and 3D.</p><p>TLDR: "det(J) =" ||∂x/∂ξ||₂</p><p>The transformation theorem for some function f on a 1D curve in 2D and 3D space leads to ∫ f ⋅ dE = ∫ f ⋅ ∂x/∂ξ dξ = ∫ f ⋅ t ||∂x/∂ξ||₂ dξ where ||∂x/∂ξ||₂ is "detJ" and t is "the unit tangent". See e.g. https://scicomp.stackexchange.com/questions/41741/integration-of-d-1-dimensional-functions-on-finite-element-surfaces for simple explanation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/GeometryMapping.jl#L216-L227">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_type-Tuple{Ferrite.AbstractValues}" href="#Ferrite.shape_value_type-Tuple{Ferrite.AbstractValues}"><code>Ferrite.shape_value_type</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_type(fe_v::AbstractValues)</code></pre><p>Return the type of <code>shape_value(fe_v, q_point, base_function)</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L163-L167">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient_type" href="#Ferrite.shape_gradient_type"><code>Ferrite.shape_gradient_type</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient_type(fe_v::AbstractValues)</code></pre><p>Return the type of <code>shape_gradient(fe_v, q_point, base_function)</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L215-L219">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ValuesUpdateFlags" href="#Ferrite.ValuesUpdateFlags"><code>Ferrite.ValuesUpdateFlags</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ValuesUpdateFlags(ip_fun::Interpolation; update_gradients = Val(true), update_hessians = Val(false), update_detJdV = Val(true))</code></pre><p>Creates a singleton type for specifying what parts of the AbstractValues should be updated. Note that this is internal API used to get type-stable construction. Keyword arguments in <code>AbstractValues</code> constructors are forwarded, and the public API is passing these as <code>Bool</code>, while the <code>ValuesUpdateFlags</code> method supports both boolean and <code>Val(::Bool)</code> keyword args.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L26-L32">source</a></section></article><h2 id="Custom-FEValues"><a class="docs-heading-anchor" href="#Custom-FEValues">Custom FEValues</a><a id="Custom-FEValues-1"></a><a class="docs-heading-anchor-permalink" href="#Custom-FEValues" title="Permalink"></a></h2><p>Custom FEValues, <code>fe_v::AbstractValues</code>, should normally implement the <a href="../../reference/fevalues/#Ferrite.reinit!"><code>reinit!</code></a> method. Subtypes of <code>AbstractValues</code> have default implementations for some functions, but require some lower-level access functions, specifically</p><ul><li><a href="../../reference/fevalues/#Ferrite.function_value"><code>function_value</code></a>, requires<ul><li><a href="../../reference/fevalues/#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></li><li><a href="../../reference/fevalues/#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></li><li><a href="../../reference/interpolations/#Ferrite.getnbasefunctions"><code>getnbasefunctions</code></a></li></ul></li><li><a href="../../reference/fevalues/#Ferrite.function_gradient"><code>function_gradient</code></a>, <a href="../../reference/fevalues/#Ferrite.function_divergence"><code>function_divergence</code></a>, <a href="../../reference/fevalues/#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a>, and <a href="../../reference/fevalues/#Ferrite.function_curl"><code>function_curl</code></a> requires<ul><li><a href="../../reference/fevalues/#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></li><li><a href="../../reference/fevalues/#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></li><li><a href="../../reference/interpolations/#Ferrite.getnbasefunctions"><code>getnbasefunctions</code></a></li></ul></li><li><a href="../../reference/fevalues/#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a>, requires<ul><li><a href="../../reference/fevalues/#Ferrite.geometric_value"><code>geometric_value</code></a></li><li><code>getngeobasefunctions</code></li><li><a href="../../reference/fevalues/#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></li></ul></li></ul><h3 id="Array-bounds"><a class="docs-heading-anchor" href="#Array-bounds">Array bounds</a><a id="Array-bounds-1"></a><a class="docs-heading-anchor-permalink" href="#Array-bounds" title="Permalink"></a></h3><ul><li>Asking for the <code>n</code>th quadrature point must be inside array bounds if <code>1 <= n <= getnquadpoints(fe_v)</code>. (<code>checkquadpoint</code> can, alternatively, be dispatched to check that <code>n</code> is inbounds.)</li><li>Asking for the <code>i</code>th shape value or gradient must be inside array bounds if <code>1 <= i <= getnbasefunctions(fe_v)</code></li><li>Asking for the <code>i</code>th geometric value must be inside array bounds if <code>1 <= i <= getngeobasefunctions(fe_v)</code></li></ul></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. 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class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/assembly.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-assembly"><a class="docs-heading-anchor" href="#devdocs-assembly">Assembly</a><a id="devdocs-assembly-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-assembly" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.COOAssembler" href="#Ferrite.COOAssembler"><code>Ferrite.COOAssembler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">struct COOAssembler{Tv, Ti}</code></pre><p>This assembler creates a COO (<strong>coo</strong>rdinate format) representation of a sparse matrix during assembly and converts it into a <code>SparseMatrixCSC{Tv, Ti}</code> on finalization.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L4-L9">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CSCAssembler" href="#Ferrite.CSCAssembler"><code>Ferrite.CSCAssembler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assembler for sparse matrix with CSC storage type.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L172-L174">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SymmetricCSCAssembler" href="#Ferrite.SymmetricCSCAssembler"><code>Ferrite.SymmetricCSCAssembler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assembler for symmetric sparse matrix with CSC storage type.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L182-L184">source</a></section></article><h2 id="Utility-functions"><a class="docs-heading-anchor" href="#Utility-functions">Utility functions</a><a id="Utility-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Utility-functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.matrix_handle" href="#Ferrite.matrix_handle"><code>Ferrite.matrix_handle</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">matrix_handle(a::AbstractAssembler)
-vector_handle(a::AbstractAssembler)</code></pre><p>Return a reference to the underlying matrix/vector of the assembler used during assembly operations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L163-L169">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vector_handle" href="#Ferrite.vector_handle"><code>Ferrite.vector_handle</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">matrix_handle(a::AbstractAssembler)
-vector_handle(a::AbstractAssembler)</code></pre><p>Return a reference to the underlying matrix/vector of the assembler used during assembly operations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L163-L169">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._sortdofs_for_assembly!" href="#Ferrite._sortdofs_for_assembly!"><code>Ferrite._sortdofs_for_assembly!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_sortdofs_for_assembly!(permutation::Vector{Int}, sorteddofs::Vector{Int}, dofs::AbstractVector)</code></pre><p>Sorts the dofs into a separate buffer and returns it together with a permutation vector.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L259-L263">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortperm2!" href="#Ferrite.sortperm2!"><code>Ferrite.sortperm2!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortperm2!(data::AbstractVector, permutation::AbstractVector)</code></pre><p>Sort the input vector inplace and compute the corresponding permutation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L382-L386">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/assembly.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-assembly"><a class="docs-heading-anchor" href="#devdocs-assembly">Assembly</a><a id="devdocs-assembly-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-assembly" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.COOAssembler" href="#Ferrite.COOAssembler"><code>Ferrite.COOAssembler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">struct COOAssembler{Tv, Ti}</code></pre><p>This assembler creates a COO (<strong>coo</strong>rdinate format) representation of a sparse matrix during assembly and converts it into a <code>SparseMatrixCSC{Tv, Ti}</code> on finalization.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L4-L9">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CSCAssembler" href="#Ferrite.CSCAssembler"><code>Ferrite.CSCAssembler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assembler for sparse matrix with CSC storage type.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L172-L174">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SymmetricCSCAssembler" href="#Ferrite.SymmetricCSCAssembler"><code>Ferrite.SymmetricCSCAssembler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assembler for symmetric sparse matrix with CSC storage type.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L182-L184">source</a></section></article><h2 id="Utility-functions"><a class="docs-heading-anchor" href="#Utility-functions">Utility functions</a><a id="Utility-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Utility-functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.matrix_handle" href="#Ferrite.matrix_handle"><code>Ferrite.matrix_handle</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">matrix_handle(a::AbstractAssembler)
+vector_handle(a::AbstractAssembler)</code></pre><p>Return a reference to the underlying matrix/vector of the assembler used during assembly operations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L163-L169">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vector_handle" href="#Ferrite.vector_handle"><code>Ferrite.vector_handle</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">matrix_handle(a::AbstractAssembler)
+vector_handle(a::AbstractAssembler)</code></pre><p>Return a reference to the underlying matrix/vector of the assembler used during assembly operations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L163-L169">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._sortdofs_for_assembly!" href="#Ferrite._sortdofs_for_assembly!"><code>Ferrite._sortdofs_for_assembly!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_sortdofs_for_assembly!(permutation::Vector{Int}, sorteddofs::Vector{Int}, dofs::AbstractVector)</code></pre><p>Sorts the dofs into a separate buffer and returns it together with a permutation vector.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L259-L263">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortperm2!" href="#Ferrite.sortperm2!"><code>Ferrite.sortperm2!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortperm2!(data::AbstractVector, permutation::AbstractVector)</code></pre><p>Sort the input vector inplace and compute the corresponding permutation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L382-L386">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="tocitem" href="../../howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../../gallery/">Code gallery</a></li><li><a class="tocitem" href="../">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Dof Handler</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Dof Handler</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/dofhandler.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="dofhandler-interpolations"><a class="docs-heading-anchor" href="#dofhandler-interpolations">Dof Handler</a><a id="dofhandler-interpolations-1"></a><a class="docs-heading-anchor-permalink" href="#dofhandler-interpolations" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><p>Dof handlers are subtypes of <code>AbstractDofhandler{sdim}</code>, i.e. they are parametrized by the spatial dimension. Internally a helper struct <a href="#Ferrite.InterpolationInfo"><code>InterpolationInfo</code></a> is utilized to enforce type stability during dof distribution, because the interpolations are not available as concrete types.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterpolationInfo" href="#Ferrite.InterpolationInfo"><code>Ferrite.InterpolationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterpolationInfo</code></pre><p>Gathers all the information needed to distribute dofs for a given interpolation. Note that this cache is of the same type no matter the interpolation: the purpose is to make dof-distribution type-stable.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L83-L89">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PathOrientationInfo" href="#Ferrite.PathOrientationInfo"><code>Ferrite.PathOrientationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PathOrientationInfo</code></pre><p>Orientation information for 1D entities.</p><p>The orientation for 1D entities is defined by the indices of the grid nodes associated to the vertices. To give an example, the oriented path</p><pre><code class="nohighlight hljs">1 ---> 2</code></pre><p>is called <em>regular</em>, indicated by <code>regular=true</code>, while the oriented path</p><pre><code class="nohighlight hljs">2 ---> 1</code></pre><p>is called <em>inverted</em>, indicated by <code>regular=false</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L667-L682">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SurfaceOrientationInfo" href="#Ferrite.SurfaceOrientationInfo"><code>Ferrite.SurfaceOrientationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SurfaceOrientationInfo</code></pre><p>Orientation information for 2D entities. Such an entity can be possibly flipped (i.e. the defining vertex order is reverse to the spanning vertex order) and the vertices can be rotated against each other. Take for example the faces</p><pre><code class="nohighlight hljs">1---2 2---3
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class="tocitem" href="../../howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../../gallery/">Code gallery</a></li><li><a class="tocitem" href="../">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Dof Handler</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Dof Handler</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/dofhandler.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="dofhandler-interpolations"><a class="docs-heading-anchor" href="#dofhandler-interpolations">Dof Handler</a><a id="dofhandler-interpolations-1"></a><a class="docs-heading-anchor-permalink" href="#dofhandler-interpolations" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><p>Dof handlers are subtypes of <code>AbstractDofhandler{sdim}</code>, i.e. they are parametrized by the spatial dimension. Internally a helper struct <a href="#Ferrite.InterpolationInfo"><code>InterpolationInfo</code></a> is utilized to enforce type stability during dof distribution, because the interpolations are not available as concrete types.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterpolationInfo" href="#Ferrite.InterpolationInfo"><code>Ferrite.InterpolationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterpolationInfo</code></pre><p>Gathers all the information needed to distribute dofs for a given interpolation. Note that this cache is of the same type no matter the interpolation: the purpose is to make dof-distribution type-stable.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L83-L89">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PathOrientationInfo" href="#Ferrite.PathOrientationInfo"><code>Ferrite.PathOrientationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PathOrientationInfo</code></pre><p>Orientation information for 1D entities.</p><p>The orientation for 1D entities is defined by the indices of the grid nodes associated to the vertices. To give an example, the oriented path</p><pre><code class="nohighlight hljs">1 ---> 2</code></pre><p>is called <em>regular</em>, indicated by <code>regular=true</code>, while the oriented path</p><pre><code class="nohighlight hljs">2 ---> 1</code></pre><p>is called <em>inverted</em>, indicated by <code>regular=false</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L667-L682">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SurfaceOrientationInfo" href="#Ferrite.SurfaceOrientationInfo"><code>Ferrite.SurfaceOrientationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SurfaceOrientationInfo</code></pre><p>Orientation information for 2D entities. Such an entity can be possibly flipped (i.e. the defining vertex order is reverse to the spanning vertex order) and the vertices can be rotated against each other. Take for example the faces</p><pre><code class="nohighlight hljs">1---2 2---3
| A | | B |
4---3 1---4</code></pre><p>which are rotated against each other by 90° (shift index is 1) or the faces</p><pre><code class="nohighlight hljs">1---2 2---1
| A | | B |
-4---3 3---4</code></pre><p>which are flipped against each other. Any combination of these can happen. The combination to map this local face to the defining face is encoded with this data structure via <span>$rotate \circ flip$</span> where the rotation is indiced by the shift index. !!!NOTE TODO implement me.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L687-L710">source</a></section></article><h2 id="Internal-API"><a class="docs-heading-anchor" href="#Internal-API">Internal API</a><a id="Internal-API-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-API" title="Permalink"></a></h2><p>The main entry point for dof distribution is <a href="#Ferrite.__close!"><code>__close!</code></a>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.__close!" href="#Ferrite.__close!"><code>Ferrite.__close!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">__close!(dh::DofHandler)</code></pre><p>Internal entry point for dof distribution.</p><p>Dofs are distributed as follows: For the <code>DofHandler</code> each <code>SubDofHandler</code> is visited in the order they were added. For each field in the <code>SubDofHandler</code> create dofs for the cell. This means that dofs on a particular cell will be numbered in groups for each field, so first the dofs for field 1 are distributed, then field 2, etc. For each cell dofs are first distributed on its vertices, then on the interior of edges (if applicable), then on the interior of faces (if applicable), and finally on the cell interior. The entity ordering follows the geometrical ordering found in <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices</code></a>, <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces</code></a> and <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L338-L351">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_grid" href="#Ferrite.get_grid"><code>Ferrite.get_grid</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_grid(dh::AbstractDofHandler)</code></pre><p>Access some grid representation for the dof handler.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This API function is currently not well-defined. It acts as the interface between distributed assembly and assembly on a single process, because most parts of the functionality can be handled by only acting on the locally owned cell set.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L3-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.find_field" href="#Ferrite.find_field"><code>Ferrite.find_field</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">find_field(dh::DofHandler, field_name::Symbol)::NTuple{2,Int}</code></pre><p>Return the index of the field with name <code>field_name</code> in a <code>DofHandler</code>. The index is a <code>NTuple{2,Int}</code>, where the 1st entry is the index of the <code>SubDofHandler</code> within which the field was found and the 2nd entry is the index of the field within the <code>SubDofHandler</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Always finds the 1st occurrence of a field within <code>DofHandler</code>.</p></div></div><p>See also: <a href="#Ferrite.find_field"><code>find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>, <a href="#Ferrite._find_field"><code>Ferrite._find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L791-L803">source</a></section><section><div><pre><code class="language-julia hljs">find_field(sdh::SubDofHandler, field_name::Symbol)::Int</code></pre><p>Return the index of the field with name <code>field_name</code> in a <code>SubDofHandler</code>. Throw an error if the field is not found.</p><p>See also: <a href="#Ferrite.find_field"><code>find_field(dh::DofHandler, field_name::Symbol)</code></a>, <a href="#Ferrite._find_field"><code>_find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L812-L819">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._find_field" href="#Ferrite._find_field"><code>Ferrite._find_field</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_find_field(sdh::SubDofHandler, field_name::Symbol)::Int</code></pre><p>Return the index of the field with name <code>field_name</code> in the <code>SubDofHandler</code> <code>sdh</code>. Return <code>nothing</code> if the field is not found.</p><p>See also: <a href="#Ferrite.find_field"><code>find_field(dh::DofHandler, field_name::Symbol)</code></a>, <a href="#Ferrite.find_field"><code>find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L829-L836">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._close_subdofhandler!" href="#Ferrite._close_subdofhandler!"><code>Ferrite._close_subdofhandler!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_close_subdofhandler!(dh::DofHandler{sdim}, sdh::SubDofHandler, sdh_index::Int, nextdof::Int, vertexdicts, edgedicts, facedicts) where {sdim}</code></pre><p>Main entry point to distribute dofs for a single <a href="../../reference/dofhandler/#Ferrite.SubDofHandler"><code>SubDofHandler</code></a> on its subdomain.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L401-L405">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._distribute_dofs_for_cell!" href="#Ferrite._distribute_dofs_for_cell!"><code>Ferrite._distribute_dofs_for_cell!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_distribute_dofs_for_cell!(dh::DofHandler{sdim}, cell::AbstractCell, ip_info::InterpolationInfo, nextdof::Int, vertexdict, edgedict, facedict) where {sdim}</code></pre><p>Main entry point to distribute dofs for a single cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L490-L494">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.permute_and_push!" href="#Ferrite.permute_and_push!"><code>Ferrite.permute_and_push!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">permute_and_push!</code></pre><p>For interpolations with more than one interior dof per edge it may be necessary to adjust the dofs. Since dofs are (initially) enumerated according to the local edge direction there can be a direction mismatch with the neighboring element. For example, in the following nodal interpolation example, with three interior dofs on each edge, the initial pass have distributed dofs 4, 5, 6 according to the local edge directions:</p><pre><code class="nohighlight hljs">+-----------+
+4---3 3---4</code></pre><p>which are flipped against each other. Any combination of these can happen. The combination to map this local face to the defining face is encoded with this data structure via <span>$rotate \circ flip$</span> where the rotation is indiced by the shift index. !!!NOTE TODO implement me.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L687-L710">source</a></section></article><h2 id="Internal-API"><a class="docs-heading-anchor" href="#Internal-API">Internal API</a><a id="Internal-API-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-API" title="Permalink"></a></h2><p>The main entry point for dof distribution is <a href="#Ferrite.__close!"><code>__close!</code></a>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.__close!" href="#Ferrite.__close!"><code>Ferrite.__close!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">__close!(dh::DofHandler)</code></pre><p>Internal entry point for dof distribution.</p><p>Dofs are distributed as follows: For the <code>DofHandler</code> each <code>SubDofHandler</code> is visited in the order they were added. For each field in the <code>SubDofHandler</code> create dofs for the cell. This means that dofs on a particular cell will be numbered in groups for each field, so first the dofs for field 1 are distributed, then field 2, etc. For each cell dofs are first distributed on its vertices, then on the interior of edges (if applicable), then on the interior of faces (if applicable), and finally on the cell interior. The entity ordering follows the geometrical ordering found in <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices</code></a>, <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces</code></a> and <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L338-L351">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_grid" href="#Ferrite.get_grid"><code>Ferrite.get_grid</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_grid(dh::AbstractDofHandler)</code></pre><p>Access some grid representation for the dof handler.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This API function is currently not well-defined. It acts as the interface between distributed assembly and assembly on a single process, because most parts of the functionality can be handled by only acting on the locally owned cell set.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L3-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.find_field" href="#Ferrite.find_field"><code>Ferrite.find_field</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">find_field(dh::DofHandler, field_name::Symbol)::NTuple{2,Int}</code></pre><p>Return the index of the field with name <code>field_name</code> in a <code>DofHandler</code>. The index is a <code>NTuple{2,Int}</code>, where the 1st entry is the index of the <code>SubDofHandler</code> within which the field was found and the 2nd entry is the index of the field within the <code>SubDofHandler</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Always finds the 1st occurrence of a field within <code>DofHandler</code>.</p></div></div><p>See also: <a href="#Ferrite.find_field"><code>find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>, <a href="#Ferrite._find_field"><code>Ferrite._find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L791-L803">source</a></section><section><div><pre><code class="language-julia hljs">find_field(sdh::SubDofHandler, field_name::Symbol)::Int</code></pre><p>Return the index of the field with name <code>field_name</code> in a <code>SubDofHandler</code>. Throw an error if the field is not found.</p><p>See also: <a href="#Ferrite.find_field"><code>find_field(dh::DofHandler, field_name::Symbol)</code></a>, <a href="#Ferrite._find_field"><code>_find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L812-L819">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._find_field" href="#Ferrite._find_field"><code>Ferrite._find_field</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_find_field(sdh::SubDofHandler, field_name::Symbol)::Int</code></pre><p>Return the index of the field with name <code>field_name</code> in the <code>SubDofHandler</code> <code>sdh</code>. Return <code>nothing</code> if the field is not found.</p><p>See also: <a href="#Ferrite.find_field"><code>find_field(dh::DofHandler, field_name::Symbol)</code></a>, <a href="#Ferrite.find_field"><code>find_field(sdh::SubDofHandler, field_name::Symbol)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L829-L836">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._close_subdofhandler!" href="#Ferrite._close_subdofhandler!"><code>Ferrite._close_subdofhandler!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_close_subdofhandler!(dh::DofHandler{sdim}, sdh::SubDofHandler, sdh_index::Int, nextdof::Int, vertexdicts, edgedicts, facedicts) where {sdim}</code></pre><p>Main entry point to distribute dofs for a single <a href="../../reference/dofhandler/#Ferrite.SubDofHandler"><code>SubDofHandler</code></a> on its subdomain.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L401-L405">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite._distribute_dofs_for_cell!" href="#Ferrite._distribute_dofs_for_cell!"><code>Ferrite._distribute_dofs_for_cell!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">_distribute_dofs_for_cell!(dh::DofHandler{sdim}, cell::AbstractCell, ip_info::InterpolationInfo, nextdof::Int, vertexdict, edgedict, facedict) where {sdim}</code></pre><p>Main entry point to distribute dofs for a single cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L490-L494">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.permute_and_push!" href="#Ferrite.permute_and_push!"><code>Ferrite.permute_and_push!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">permute_and_push!</code></pre><p>For interpolations with more than one interior dof per edge it may be necessary to adjust the dofs. Since dofs are (initially) enumerated according to the local edge direction there can be a direction mismatch with the neighboring element. For example, in the following nodal interpolation example, with three interior dofs on each edge, the initial pass have distributed dofs 4, 5, 6 according to the local edge directions:</p><pre><code class="nohighlight hljs">+-----------+
| A |
+--4--5--6->+ local edge on element A
@@ -11,6 +11,6 @@
+<-6--5--4--+ local edge on element B
| B |
-+-----------+</code></pre><p>For most scalar-valued interpolations we can simply compensate for this by reversing the numbering on all edges that do not match the global edge direction, i.e. for the edge on element B in the example.</p><p>In addition, we also have to preserve the ordering at each dof location.</p><p>For more details we refer to Scroggs et al. [<a href="../../cited-literature/#Scroggs2022">13</a>] as we follow the methodology described therein.</p><p><strong>References</strong></p><ul><li>[<a href="../../cited-literature/#Scroggs2022">13</a>] Scroggs et al. ACM Trans. Math. Softw. 48 (2022).</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L605-L637">source</a></section><section><div><pre><code class="language-julia hljs">!!!NOTE TODO implement me.</code></pre><p>For more details we refer to [1] as we follow the methodology described therein.</p><p>[1] Scroggs, M. W., Dokken, J. S., Richardson, C. N., & Wells, G. N. (2022). Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes. ACM Transactions on Mathematical Software (TOMS), 48(2), 1-23.</p><pre><code class="nohighlight hljs">!!!TODO citation via software.
++-----------+</code></pre><p>For most scalar-valued interpolations we can simply compensate for this by reversing the numbering on all edges that do not match the global edge direction, i.e. for the edge on element B in the example.</p><p>In addition, we also have to preserve the ordering at each dof location.</p><p>For more details we refer to Scroggs et al. [<a href="../../cited-literature/#Scroggs2022">13</a>] as we follow the methodology described therein.</p><p><strong>References</strong></p><ul><li>[<a href="../../cited-literature/#Scroggs2022">13</a>] Scroggs et al. ACM Trans. Math. Softw. 48 (2022).</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L605-L637">source</a></section><section><div><pre><code class="language-julia hljs">!!!NOTE TODO implement me.</code></pre><p>For more details we refer to [1] as we follow the methodology described therein.</p><p>[1] Scroggs, M. W., Dokken, J. S., Richardson, C. N., & Wells, G. N. (2022). Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes. ACM Transactions on Mathematical Software (TOMS), 48(2), 1-23.</p><pre><code class="nohighlight hljs">!!!TODO citation via software.
-!!!TODO Investigate if we can somehow pass the interpolation into this function in a typestable way.</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L705-L718">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+!!!TODO Investigate if we can somehow pass the interpolation into this function in a typestable way.</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L705-L718">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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index d09e534040..b9ae87a7f1 100644
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@@ -1,15 +1,15 @@
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cells</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/elements.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-elements"><a class="docs-heading-anchor" href="#devdocs-elements">Elements and cells</a><a id="devdocs-elements-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-elements" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><p>Elements or cells are subtypes of <code>AbstractCell{<:AbstractRefShape}</code>. As shown, they are parametrized by the associated reference element.</p><h3 id="Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element"><a class="docs-heading-anchor" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element">Required methods to implement for all subtypes of <code>AbstractCell</code> to define a new element</a><a id="Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element-1"></a><a class="docs-heading-anchor-permalink" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_node_ids" href="#Ferrite.get_node_ids"><code>Ferrite.get_node_ids</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.get_node_ids(c::AbstractCell)</code></pre><p>Return the node id's for cell <code>c</code> in the order determined by the cell's reference cell.</p><p>Default implementation: <code>c.nodes</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L165-L171">source</a></section></article><h3 id="Common-utilities-and-definitions-when-working-with-grids-internally."><a class="docs-heading-anchor" href="#Common-utilities-and-definitions-when-working-with-grids-internally.">Common utilities and definitions when working with grids internally.</a><a id="Common-utilities-and-definitions-when-working-with-grids-internally.-1"></a><a class="docs-heading-anchor-permalink" href="#Common-utilities-and-definitions-when-working-with-grids-internally." title="Permalink"></a></h3><p>First we have some topological queries on the element</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vertices-Tuple{Ferrite.AbstractCell}" href="#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>Ferrite.vertices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.vertices(::AbstractCell)</code></pre><p>Returns a tuple with the node indices (of the nodes in a grid) for each vertex in a given cell. This function induces the <a href="../../reference/grid/#Ferrite.VertexIndex"><code>VertexIndex</code></a>, where the second index corresponds to the local index into this tuple.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L69-L75">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.edges-Tuple{Ferrite.AbstractCell}" href="#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>Ferrite.edges</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.edges(::AbstractCell)</code></pre><p>Returns a tuple of 2-tuples containing the ordered node indices (of the nodes in a grid) corresponding to the vertices that define an <em>oriented edge</em>. This function induces the <a href="../../reference/grid/#Ferrite.EdgeIndex"><code>EdgeIndex</code></a>, where the second index corresponds to the local index into this tuple.</p><p>Note that the vertices are sufficient to define an edge uniquely.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L87-L95">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.faces-Tuple{Ferrite.AbstractCell}" href="#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>Ferrite.faces</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.faces(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered node indices (of the nodes in a grid) corresponding to the vertices that define an <em>oriented face</em>. This function induces the <a href="../../reference/grid/#Ferrite.FaceIndex"><code>FaceIndex</code></a>, where the second index corresponds to the local index into this tuple.</p><p>An <em>oriented face</em> is a face with the first node having the local index and the other nodes spanning such that the normal to the face is pointing outwards.</p><p>Note that the vertices are sufficient to define a face uniquely.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L107-L118">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facets-Tuple{Ferrite.AbstractCell}" href="#Ferrite.facets-Tuple{Ferrite.AbstractCell}"><code>Ferrite.facets</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.facets(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered node indices (of the nodes in a grid) corresponding to the vertices that define an oriented facet. This function induces the <a href="../../reference/grid/#Ferrite.FacetIndex"><code>FacetIndex</code></a>, where the second index corresponds to the local index into this tuple.</p><p>See also <a href="#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices</code></a>, <a href="#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges</code></a>, and <a href="#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces</code></a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L121-L129">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.boundaryfunction-Tuple{Type{<:Ferrite.BoundaryIndex}}" href="#Ferrite.boundaryfunction-Tuple{Type{<:Ferrite.BoundaryIndex}}"><code>Ferrite.boundaryfunction</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">boundaryfunction(::Type{<:BoundaryIndex})</code></pre><p>Helper function to dispatch on the correct entity from a given boundary index.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L632-L636">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_vertices-Tuple{Ferrite.AbstractCell}" href="#Ferrite.reference_vertices-Tuple{Ferrite.AbstractCell}"><code>Ferrite.reference_vertices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_vertices(::Type{<:AbstractRefShape})
-reference_vertices(::AbstractCell)</code></pre><p>Returns a tuple of integers containing the local node indices corresponding to the vertices (i.e. corners or endpoints) of the cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L60-L66">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_edges-Tuple{Ferrite.AbstractCell}" href="#Ferrite.reference_edges-Tuple{Ferrite.AbstractCell}"><code>Ferrite.reference_edges</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_edges(::Type{<:AbstractRefShape})
-reference_edges(::AbstractCell)</code></pre><p>Returns a tuple of 2-tuples containing the ordered local node indices (corresponding to the vertices) that define an edge.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L78-L84">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_faces-Tuple{Ferrite.AbstractCell}" href="#Ferrite.reference_faces-Tuple{Ferrite.AbstractCell}"><code>Ferrite.reference_faces</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_faces(::Type{<:AbstractRefShape})
-reference_faces(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered local node indices (corresponding to the vertices) that define a face.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L98-L104">source</a></section></article><p>and some generic utils which are commonly found in finite element codes</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BoundaryIndex" href="#Ferrite.BoundaryIndex"><code>Ferrite.BoundaryIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Abstract type which is used as identifier for faces, edges and verices</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L70-L72">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_coordinate_eltype-Tuple{Ferrite.AbstractGrid}" href="#Ferrite.get_coordinate_eltype-Tuple{Ferrite.AbstractGrid}"><code>Ferrite.get_coordinate_eltype</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Return the number type of the nodal coordinates.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L499">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_coordinate_eltype-Tuple{Node}" href="#Ferrite.get_coordinate_eltype-Tuple{Node}"><code>Ferrite.get_coordinate_eltype</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_coordinate_eltype(::Node)</code></pre><p>Get the data type of the components of the nodes coordinate.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L31-L35">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.toglobal" href="#Ferrite.toglobal"><code>Ferrite.toglobal</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">toglobal(grid::AbstractGrid, vertexidx::VertexIndex) -> Int
-toglobal(grid::AbstractGrid, vertexidx::Vector{VertexIndex}) -> Vector{Int}</code></pre><p>This function takes the local vertex representation (a <code>VertexIndex</code>) and looks up the unique global id (an <code>Int</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L422-L426">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortface" href="#Ferrite.sortface"><code>Ferrite.sortface</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortface(face::Tuple{Int})
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class="tocitem" href="../../howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../../gallery/">Code gallery</a></li><li><a class="tocitem" href="../">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Elements and cells</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Elements and cells</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/elements.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-elements"><a class="docs-heading-anchor" href="#devdocs-elements">Elements and cells</a><a id="devdocs-elements-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-elements" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><p>Elements or cells are subtypes of <code>AbstractCell{<:AbstractRefShape}</code>. As shown, they are parametrized by the associated reference element.</p><h3 id="Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element"><a class="docs-heading-anchor" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element">Required methods to implement for all subtypes of <code>AbstractCell</code> to define a new element</a><a id="Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element-1"></a><a class="docs-heading-anchor-permalink" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractCell-to-define-a-new-element" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_node_ids" href="#Ferrite.get_node_ids"><code>Ferrite.get_node_ids</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.get_node_ids(c::AbstractCell)</code></pre><p>Return the node id's for cell <code>c</code> in the order determined by the cell's reference cell.</p><p>Default implementation: <code>c.nodes</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L165-L171">source</a></section></article><h3 id="Common-utilities-and-definitions-when-working-with-grids-internally."><a class="docs-heading-anchor" href="#Common-utilities-and-definitions-when-working-with-grids-internally.">Common utilities and definitions when working with grids internally.</a><a id="Common-utilities-and-definitions-when-working-with-grids-internally.-1"></a><a class="docs-heading-anchor-permalink" href="#Common-utilities-and-definitions-when-working-with-grids-internally." title="Permalink"></a></h3><p>First we have some topological queries on the element</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vertices-Tuple{Ferrite.AbstractCell}" href="#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>Ferrite.vertices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.vertices(::AbstractCell)</code></pre><p>Returns a tuple with the node indices (of the nodes in a grid) for each vertex in a given cell. This function induces the <a href="../../reference/grid/#Ferrite.VertexIndex"><code>VertexIndex</code></a>, where the second index corresponds to the local index into this tuple.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L69-L75">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.edges-Tuple{Ferrite.AbstractCell}" href="#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>Ferrite.edges</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.edges(::AbstractCell)</code></pre><p>Returns a tuple of 2-tuples containing the ordered node indices (of the nodes in a grid) corresponding to the vertices that define an <em>oriented edge</em>. This function induces the <a href="../../reference/grid/#Ferrite.EdgeIndex"><code>EdgeIndex</code></a>, where the second index corresponds to the local index into this tuple.</p><p>Note that the vertices are sufficient to define an edge uniquely.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L87-L95">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.faces-Tuple{Ferrite.AbstractCell}" href="#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>Ferrite.faces</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.faces(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered node indices (of the nodes in a grid) corresponding to the vertices that define an <em>oriented face</em>. This function induces the <a href="../../reference/grid/#Ferrite.FaceIndex"><code>FaceIndex</code></a>, where the second index corresponds to the local index into this tuple.</p><p>An <em>oriented face</em> is a face with the first node having the local index and the other nodes spanning such that the normal to the face is pointing outwards.</p><p>Note that the vertices are sufficient to define a face uniquely.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L107-L118">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facets-Tuple{Ferrite.AbstractCell}" href="#Ferrite.facets-Tuple{Ferrite.AbstractCell}"><code>Ferrite.facets</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.facets(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered node indices (of the nodes in a grid) corresponding to the vertices that define an oriented facet. This function induces the <a href="../../reference/grid/#Ferrite.FacetIndex"><code>FacetIndex</code></a>, where the second index corresponds to the local index into this tuple.</p><p>See also <a href="#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices</code></a>, <a href="#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges</code></a>, and <a href="#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces</code></a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L121-L129">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.boundaryfunction-Tuple{Type{<:Ferrite.BoundaryIndex}}" href="#Ferrite.boundaryfunction-Tuple{Type{<:Ferrite.BoundaryIndex}}"><code>Ferrite.boundaryfunction</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">boundaryfunction(::Type{<:BoundaryIndex})</code></pre><p>Helper function to dispatch on the correct entity from a given boundary index.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L632-L636">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_vertices-Tuple{Ferrite.AbstractCell}" href="#Ferrite.reference_vertices-Tuple{Ferrite.AbstractCell}"><code>Ferrite.reference_vertices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_vertices(::Type{<:AbstractRefShape})
+reference_vertices(::AbstractCell)</code></pre><p>Returns a tuple of integers containing the local node indices corresponding to the vertices (i.e. corners or endpoints) of the cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L60-L66">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_edges-Tuple{Ferrite.AbstractCell}" href="#Ferrite.reference_edges-Tuple{Ferrite.AbstractCell}"><code>Ferrite.reference_edges</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_edges(::Type{<:AbstractRefShape})
+reference_edges(::AbstractCell)</code></pre><p>Returns a tuple of 2-tuples containing the ordered local node indices (corresponding to the vertices) that define an edge.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L78-L84">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_faces-Tuple{Ferrite.AbstractCell}" href="#Ferrite.reference_faces-Tuple{Ferrite.AbstractCell}"><code>Ferrite.reference_faces</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_faces(::Type{<:AbstractRefShape})
+reference_faces(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered local node indices (corresponding to the vertices) that define a face.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L98-L104">source</a></section></article><p>and some generic utils which are commonly found in finite element codes</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BoundaryIndex" href="#Ferrite.BoundaryIndex"><code>Ferrite.BoundaryIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Abstract type which is used as identifier for faces, edges and verices</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L70-L72">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_coordinate_eltype-Tuple{Ferrite.AbstractGrid}" href="#Ferrite.get_coordinate_eltype-Tuple{Ferrite.AbstractGrid}"><code>Ferrite.get_coordinate_eltype</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Return the number type of the nodal coordinates.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L499">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_coordinate_eltype-Tuple{Node}" href="#Ferrite.get_coordinate_eltype-Tuple{Node}"><code>Ferrite.get_coordinate_eltype</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_coordinate_eltype(::Node)</code></pre><p>Get the data type of the components of the nodes coordinate.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L31-L35">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.toglobal" href="#Ferrite.toglobal"><code>Ferrite.toglobal</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">toglobal(grid::AbstractGrid, vertexidx::VertexIndex) -> Int
+toglobal(grid::AbstractGrid, vertexidx::Vector{VertexIndex}) -> Vector{Int}</code></pre><p>This function takes the local vertex representation (a <code>VertexIndex</code>) and looks up the unique global id (an <code>Int</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L422-L426">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortface" href="#Ferrite.sortface"><code>Ferrite.sortface</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortface(face::Tuple{Int})
sortface(face::Tuple{Int,Int})
sortface(face::Tuple{Int,Int,Int})
-sortface(face::Tuple{Int,Int,Int,Int})</code></pre><p>Returns the unique representation of a face. Here the unique representation is the sorted node index tuple. Note that in 3D we only need indices to uniquely identify a face, so the unique representation is always a tuple length 3.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L679-L689">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortface_fast" href="#Ferrite.sortface_fast"><code>Ferrite.sortface_fast</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortface_fast(face::Tuple{Int})
+sortface(face::Tuple{Int,Int,Int,Int})</code></pre><p>Returns the unique representation of a face. Here the unique representation is the sorted node index tuple. Note that in 3D we only need indices to uniquely identify a face, so the unique representation is always a tuple length 3.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L679-L689">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortface_fast" href="#Ferrite.sortface_fast"><code>Ferrite.sortface_fast</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortface_fast(face::Tuple{Int})
sortface_fast(face::Tuple{Int,Int})
sortface_fast(face::Tuple{Int,Int,Int})
-sortface_fast(face::Tuple{Int,Int,Int,Int})</code></pre><p>Returns the unique representation of a face. Here the unique representation is the sorted node index tuple. Note that in 3D we only need indices to uniquely identify a face, so the unique representation is always a tuple length 3.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L692-L702">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortedge" href="#Ferrite.sortedge"><code>Ferrite.sortedge</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortedge(edge::Tuple{Int,Int})</code></pre><p>Returns the unique representation of an edge and its orientation. Here the unique representation is the sorted node index tuple. The orientation is <code>true</code> if the edge is not flipped, where it is <code>false</code> if the edge is flipped.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L655-L662">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortedge_fast" href="#Ferrite.sortedge_fast"><code>Ferrite.sortedge_fast</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>sortedge_fast(edge::Tuple{Int,Int})</p><p>Returns the unique representation of an edge. Here the unique representation is the sorted node index tuple.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L668-L673">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.element_to_facet_transformation" href="#Ferrite.element_to_facet_transformation"><code>Ferrite.element_to_facet_transformation</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">element_to_facet_transformation(point::AbstractVector, ::Type{<:AbstractRefShape}, facet::Int)</code></pre><p>Transform quadrature point from the cell's coordinates to the facet's reference coordinates, decreasing the number of dimensions by one. This is the inverse of <code>facet_to_element_transformation</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/facet_integrals.jl#L9-L14">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facet_to_element_transformation" href="#Ferrite.facet_to_element_transformation"><code>Ferrite.facet_to_element_transformation</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facet_to_element_transformation(point::Vec, ::Type{<:AbstractRefShape}, facet::Int)</code></pre><p>Transform quadrature point from the facet's reference coordinates to coordinates on the cell's facet, increasing the number of dimensions by one.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/facet_integrals.jl#L1-L6">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceOrientationInfo" href="#Ferrite.InterfaceOrientationInfo"><code>Ferrite.InterfaceOrientationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceOrientationInfo</code></pre><p>Relative orientation information for 1D and 2D interfaces in 2D and 3D elements respectively. This information is used to construct the transformation matrix to transform the quadrature points from facet<em>a to facet</em>b achieving synced spatial coordinates. Facet B's orientation relative to Facet A's can possibly be flipped (i.e. the vertices indices order is reversed) and the vertices can be rotated against each other. The reference orientation of facet B is such that the first node has the lowest vertex index. Thus, this structure also stores the shift of the lowest vertex index which is used to reorient the facet in case of flipping <a href="#Ferrite.transform_interface_points!"><code>transform_interface_points!</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L393-L406">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.transform_interface_points!" href="#Ferrite.transform_interface_points!"><code>Ferrite.transform_interface_points!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">transform_interface_points!(dst::AbstractVector{Vec{3, Float64}}, points::AbstractVector{Vec{3, Float64}}, interface_transformation::InterfaceOrientationInfo)</code></pre><p>Transform the points from facet A to facet B using the orientation information of the interface and store it in the vector dst. For 3D, the facets are transformed into regular polygons such that the rotation angle is the shift in reference node index × 2π ÷ number of edges in facet. If the facet is flipped then the flipping is about the axis that preserves the position of the first node (which is the reference node after being rotated to be in the first position, it's rotated back in the opposite direction after flipping). Take for example the interface</p><pre><code class="nohighlight hljs"> 2 3
+sortface_fast(face::Tuple{Int,Int,Int,Int})</code></pre><p>Returns the unique representation of a face. Here the unique representation is the sorted node index tuple. Note that in 3D we only need indices to uniquely identify a face, so the unique representation is always a tuple length 3.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L692-L702">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortedge" href="#Ferrite.sortedge"><code>Ferrite.sortedge</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">sortedge(edge::Tuple{Int,Int})</code></pre><p>Returns the unique representation of an edge and its orientation. Here the unique representation is the sorted node index tuple. The orientation is <code>true</code> if the edge is not flipped, where it is <code>false</code> if the edge is flipped.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L655-L662">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.sortedge_fast" href="#Ferrite.sortedge_fast"><code>Ferrite.sortedge_fast</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>sortedge_fast(edge::Tuple{Int,Int})</p><p>Returns the unique representation of an edge. Here the unique representation is the sorted node index tuple.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L668-L673">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.element_to_facet_transformation" href="#Ferrite.element_to_facet_transformation"><code>Ferrite.element_to_facet_transformation</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">element_to_facet_transformation(point::AbstractVector, ::Type{<:AbstractRefShape}, facet::Int)</code></pre><p>Transform quadrature point from the cell's coordinates to the facet's reference coordinates, decreasing the number of dimensions by one. This is the inverse of <code>facet_to_element_transformation</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/facet_integrals.jl#L9-L14">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facet_to_element_transformation" href="#Ferrite.facet_to_element_transformation"><code>Ferrite.facet_to_element_transformation</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facet_to_element_transformation(point::Vec, ::Type{<:AbstractRefShape}, facet::Int)</code></pre><p>Transform quadrature point from the facet's reference coordinates to coordinates on the cell's facet, increasing the number of dimensions by one.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/facet_integrals.jl#L1-L6">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceOrientationInfo" href="#Ferrite.InterfaceOrientationInfo"><code>Ferrite.InterfaceOrientationInfo</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceOrientationInfo</code></pre><p>Relative orientation information for 1D and 2D interfaces in 2D and 3D elements respectively. This information is used to construct the transformation matrix to transform the quadrature points from facet<em>a to facet</em>b achieving synced spatial coordinates. Facet B's orientation relative to Facet A's can possibly be flipped (i.e. the vertices indices order is reversed) and the vertices can be rotated against each other. The reference orientation of facet B is such that the first node has the lowest vertex index. Thus, this structure also stores the shift of the lowest vertex index which is used to reorient the facet in case of flipping <a href="#Ferrite.transform_interface_points!"><code>transform_interface_points!</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L393-L406">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.transform_interface_points!" href="#Ferrite.transform_interface_points!"><code>Ferrite.transform_interface_points!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">transform_interface_points!(dst::AbstractVector{Vec{3, Float64}}, points::AbstractVector{Vec{3, Float64}}, interface_transformation::InterfaceOrientationInfo)</code></pre><p>Transform the points from facet A to facet B using the orientation information of the interface and store it in the vector dst. For 3D, the facets are transformed into regular polygons such that the rotation angle is the shift in reference node index × 2π ÷ number of edges in facet. If the facet is flipped then the flipping is about the axis that preserves the position of the first node (which is the reference node after being rotated to be in the first position, it's rotated back in the opposite direction after flipping). Take for example the interface</p><pre><code class="nohighlight hljs"> 2 3
| \ | \
| \ | \
y | A \ | B \
@@ -43,4 +43,4 @@
| \
y | \
↑ | \
-→ x 1-----2</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L485-L546">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_transformation_matrix" href="#Ferrite.get_transformation_matrix"><code>Ferrite.get_transformation_matrix</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_transformation_matrix(interface_transformation::InterfaceOrientationInfo)</code></pre><p>Returns the transformation matrix corresponding to the interface orientation information stored in <code>InterfaceOrientationInfo</code>. The transformation matrix is constructed using a combination of affine transformations defined for each interface reference shape. The transformation for a flipped facet is a function of both relative orientation and the orientation of the second facet. If the facet is not flipped then the transformation is a function of relative orientation only.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L433-L440">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+→ x 1-----2</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L485-L546">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_transformation_matrix" href="#Ferrite.get_transformation_matrix"><code>Ferrite.get_transformation_matrix</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_transformation_matrix(interface_transformation::InterfaceOrientationInfo)</code></pre><p>Returns the transformation matrix corresponding to the interface orientation information stored in <code>InterfaceOrientationInfo</code>. The transformation matrix is constructed using a combination of affine transformations defined for each interface reference shape. The transformation for a flipped facet is a function of both relative orientation and the orientation of the second facet. If the facet is not flipped then the transformation is a function of relative orientation only.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L433-L440">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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pattern and sparse matrices</a></li><li><a class="tocitem" href="../../topics/assembly/">Assembly</a></li><li><a class="tocitem" href="../../topics/boundary_conditions/">Boundary and initial conditions</a></li><li><a class="tocitem" href="../../topics/constraints/">Constraints</a></li><li><a class="tocitem" href="../../topics/grid/">Grid</a></li><li><a class="tocitem" href="../../topics/export/">Export</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-5" type="checkbox"/><label class="tocitem" for="menuitem-5"><span class="docs-label">API reference</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../reference/">Reference overview</a></li><li><a class="tocitem" href="../../reference/quadrature/">Quadrature</a></li><li><a class="tocitem" href="../../reference/interpolations/">Interpolation</a></li><li><a class="tocitem" href="../../reference/fevalues/">FEValues</a></li><li><a class="tocitem" 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class="tocitem" href="../../howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../../gallery/">Code gallery</a></li><li><a class="tocitem" href="../">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Interpolations</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Interpolations</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/interpolations.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-interpolations"><a class="docs-heading-anchor" href="#devdocs-interpolations">Interpolations</a><a id="devdocs-interpolations-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-interpolations" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><p>Interpolations are subtypes of <code>Interpolation{shape, order}</code>, i.e. they are parametrized by the reference element and its characteristic order.</p><h3 id="Fallback-methods-applicable-for-all-subtypes-of-Interpolation"><a class="docs-heading-anchor" href="#Fallback-methods-applicable-for-all-subtypes-of-Interpolation">Fallback methods applicable for all subtypes of <code>Interpolation</code></a><a id="Fallback-methods-applicable-for-all-subtypes-of-Interpolation-1"></a><a class="docs-heading-anchor-permalink" href="#Fallback-methods-applicable-for-all-subtypes-of-Interpolation" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefshape-Tuple{Interpolation}" href="#Ferrite.getrefshape-Tuple{Interpolation}"><code>Ferrite.getrefshape</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefshape(::Interpolation)::AbstractRefShape</code></pre><p>Return the reference element shape of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L129-L133">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getorder-Tuple{Interpolation}" href="#Ferrite.getorder-Tuple{Interpolation}"><code>Ferrite.getorder</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getorder(::Interpolation)</code></pre><p>Return order of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L136-L140">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradient(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Evaluate the gradient of the <code>i</code>th shape function of the interpolation <code>ip</code> in reference coordinate <code>ξ</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L234-L239">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradient_and_value-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_gradient_and_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient_and_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradient_and_value(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Optimized version combining the evaluation <a href="#Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_value(::Interpolation)</code></a> and <a href="#Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient(::Interpolation)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L244-L249">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_hessian_gradient_and_value-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_hessian_gradient_and_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_hessian_gradient_and_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_hessian_gradient_and_value(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Optimized version combining the evaluation <a href="#Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_value(::Interpolation)</code></a>, <a href="#Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient(::Interpolation)</code></a>, and the gradient of the latter.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L254-L259">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.boundarydof_indices" href="#Ferrite.boundarydof_indices"><code>Ferrite.boundarydof_indices</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">boundarydof_indices(::Type{<:BoundaryIndex})</code></pre><p>Helper function to generically dispatch on the correct dof sets of a boundary entity.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L394-L398">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_boundarydof_indices" href="#Ferrite.dirichlet_boundarydof_indices"><code>Ferrite.dirichlet_boundarydof_indices</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_boundarydof_indices(::Type{<:BoundaryIndex})</code></pre><p>Helper function to generically dispatch on the correct dof sets of a boundary entity. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.boundarydof_indices"><code>boundarydof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L428-L433">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_values!" href="#Ferrite.reference_shape_values!"><code>Ferrite.reference_shape_values!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_values!(values::AbstractArray{T}, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape functions of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>values</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L161-L166">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradients!" href="#Ferrite.reference_shape_gradients!"><code>Ferrite.reference_shape_gradients!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradients!(gradients::AbstractArray, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape function gradients of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>gradients</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L175-L180">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradients_and_values!" href="#Ferrite.reference_shape_gradients_and_values!"><code>Ferrite.reference_shape_gradients_and_values!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradients_and_values!(gradients::AbstractArray, values::AbstractArray, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape function gradients and values of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>values</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L189-L194">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_hessians_gradients_and_values!" href="#Ferrite.reference_shape_hessians_gradients_and_values!"><code>Ferrite.reference_shape_hessians_gradients_and_values!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_hessians_gradients_and_values!(hessians::AbstractVector, gradients::AbstractVector, values::AbstractVector, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape function hessians, gradients and values of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>hessians</code>, <code>gradients</code>, and <code>values</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L204-L209">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_type-Union{Tuple{T}, Tuple{Interpolation, Type{T}}} where T<:Number" href="#Ferrite.shape_value_type-Union{Tuple{T}, Tuple{Interpolation, Type{T}}} where T<:Number"><code>Ferrite.shape_value_type</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_type(ip::Interpolation, ::Type{T}) where T<:Number</code></pre><p>Return the type of <code>shape_value(ip::Interpolation, ξ::Vec, ib::Int)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L60-L64">source</a></section></article><h3 id="Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element"><a class="docs-heading-anchor" href="#Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element">Required methods to implement for all subtypes of <code>Interpolation</code> to define a new finite element</a><a id="Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element-1"></a><a class="docs-heading-anchor-permalink" href="#Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element" title="Permalink"></a></h3><p>Depending on the dimension of the reference element the following functions have to be implemented</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_value(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Evaluate the value of the <code>i</code>th shape function of the interpolation <code>ip</code> at a point <code>ξ</code> on the reference element. The index <code>i</code> must match the index in <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices(::Interpolation)</code></a>, <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Interpolation)</code></a> and <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Interpolation)</code></a>.</p><p>For nodal interpolations the indices also must match the indices of <a href="#Ferrite.reference_coordinates-Tuple{Interpolation}"><code>reference_coordinates(::Interpolation)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L221-L231">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vertexdof_indices-Tuple{Interpolation}" href="#Ferrite.vertexdof_indices-Tuple{Interpolation}"><code>Ferrite.vertexdof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">vertexdof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective vertex in local enumeration on a cell defined by <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices(::Cell)</code></a>. The vertex enumeration must match the vertex enumeration of the corresponding geometrical cell.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be the 1, as vertex dofs are enumerated first.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L278-L288">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_vertexdof_indices-Tuple{Interpolation}" href="#Ferrite.dirichlet_vertexdof_indices-Tuple{Interpolation}"><code>Ferrite.dirichlet_vertexdof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_vertexdof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective vertex in local enumeration on a cell defined by <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices(::Cell)</code></a>. The vertex enumeration must match the vertex enumeration of the corresponding geometrical cell. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.vertexdof_indices-Tuple{Interpolation}"><code>vertexdof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be the 1, as vertex dofs are enumerated first.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L291-L302">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facedof_indices-Tuple{Interpolation}" href="#Ferrite.facedof_indices-Tuple{Interpolation}"><code>Ferrite.facedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of all local dof indices for the respective face in local enumeration on a cell defined by <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Cell)</code></a>. The face enumeration must match the face enumeration of the corresponding geometrical cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L344-L350">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_facedof_indices-Tuple{Interpolation}" href="#Ferrite.dirichlet_facedof_indices-Tuple{Interpolation}"><code>Ferrite.dirichlet_facedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_facedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of all local dof indices for the respective face in local enumeration on a cell defined by <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Cell)</code></a>. The face enumeration must match the face enumeration of the corresponding geometrical cell. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.facedof_indices-Tuple{Interpolation}"><code>facedof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L353-L360">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facedof_interior_indices-Tuple{Interpolation}" href="#Ferrite.facedof_interior_indices-Tuple{Interpolation}"><code>Ferrite.facedof_interior_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facedof_interior_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of the local dof indices on the interior of the respective face in local enumeration on a cell defined by <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Cell)</code></a>. The face enumeration must match the face enumeration of the corresponding geometrical cell. Note that the vertex and edge dofs are included here.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be the computed via "last edge interior dof index + 1", if face dofs exist.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L363-L374">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.edgedof_indices-Tuple{Interpolation}" href="#Ferrite.edgedof_indices-Tuple{Interpolation}"><code>Ferrite.edgedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">edgedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective edge in local enumeration on a cell defined by <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Cell)</code></a>. The edge enumeration must match the edge enumeration of the corresponding geometrical cell.</p><p>The dofs are guaranteed to be aligned with the local ordering of the entities on the oriented edge. Here the first entries are the vertex dofs, followed by the edge interior dofs.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L305-L314">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_edgedof_indices-Tuple{Interpolation}" href="#Ferrite.dirichlet_edgedof_indices-Tuple{Interpolation}"><code>Ferrite.dirichlet_edgedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_edgedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective edge in local enumeration on a cell defined by <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Cell)</code></a>. The edge enumeration must match the edge enumeration of the corresponding geometrical cell. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.edgedof_indices-Tuple{Interpolation}"><code>edgedof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p><p>The dofs are guaranteed to be aligned with the local ordering of the entities on the oriented edge. Here the first entries are the vertex dofs, followed by the edge interior dofs.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L317-L327">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.edgedof_interior_indices-Tuple{Interpolation}" href="#Ferrite.edgedof_interior_indices-Tuple{Interpolation}"><code>Ferrite.edgedof_interior_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">edgedof_interior_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of the local dof indices on the interior of the respective edge in local enumeration on a cell defined by <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Cell)</code></a>. The edge enumeration must match the edge enumeration of the corresponding geometrical cell. Note that the vertex dofs are included here.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be computed via "last vertex dof index + 1", if edge dofs exist.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L330-L341">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.volumedof_interior_indices-Tuple{Interpolation}" href="#Ferrite.volumedof_interior_indices-Tuple{Interpolation}"><code>Ferrite.volumedof_interior_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">volumedof_interior_indices(ip::Interpolation)</code></pre><p>Tuple containing the dof indices associated with the interior of a volume.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing, volumedofs are enumerated last.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L377-L385">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnbasefunctions-Tuple{Interpolation}" href="#Ferrite.getnbasefunctions-Tuple{Interpolation}"><code>Ferrite.getnbasefunctions</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getnbasefunctions(ip::Interpolation)</code></pre><p>Return the number of base functions for the interpolation <code>ip</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L148-L152">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_coordinates-Tuple{Interpolation}" href="#Ferrite.reference_coordinates-Tuple{Interpolation}"><code>Ferrite.reference_coordinates</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_coordinates(ip::Interpolation)</code></pre><p>Returns a vector of coordinates with length <a href="#Ferrite.getnbasefunctions-Tuple{Interpolation}"><code>getnbasefunctions(::Interpolation)</code></a> and indices corresponding to the indices of a dof in <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices</code></a>, <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces</code></a> and <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges</code></a>.</p><pre><code class="nohighlight hljs">Only required for nodal interpolations.
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href>Interpolations</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/interpolations.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-interpolations"><a class="docs-heading-anchor" href="#devdocs-interpolations">Interpolations</a><a id="devdocs-interpolations-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-interpolations" title="Permalink"></a></h1><h2 id="Type-definitions"><a class="docs-heading-anchor" href="#Type-definitions">Type definitions</a><a id="Type-definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Type-definitions" title="Permalink"></a></h2><p>Interpolations are subtypes of <code>Interpolation{shape, order}</code>, i.e. they are parametrized by the reference element and its characteristic order.</p><h3 id="Fallback-methods-applicable-for-all-subtypes-of-Interpolation"><a class="docs-heading-anchor" href="#Fallback-methods-applicable-for-all-subtypes-of-Interpolation">Fallback methods applicable for all subtypes of <code>Interpolation</code></a><a id="Fallback-methods-applicable-for-all-subtypes-of-Interpolation-1"></a><a class="docs-heading-anchor-permalink" href="#Fallback-methods-applicable-for-all-subtypes-of-Interpolation" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefshape-Tuple{Interpolation}" href="#Ferrite.getrefshape-Tuple{Interpolation}"><code>Ferrite.getrefshape</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefshape(::Interpolation)::AbstractRefShape</code></pre><p>Return the reference element shape of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L129-L133">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getorder-Tuple{Interpolation}" href="#Ferrite.getorder-Tuple{Interpolation}"><code>Ferrite.getorder</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getorder(::Interpolation)</code></pre><p>Return order of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L136-L140">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradient(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Evaluate the gradient of the <code>i</code>th shape function of the interpolation <code>ip</code> in reference coordinate <code>ξ</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L234-L239">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradient_and_value-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_gradient_and_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient_and_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradient_and_value(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Optimized version combining the evaluation <a href="#Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_value(::Interpolation)</code></a> and <a href="#Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient(::Interpolation)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L244-L249">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_hessian_gradient_and_value-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_hessian_gradient_and_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_hessian_gradient_and_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_hessian_gradient_and_value(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Optimized version combining the evaluation <a href="#Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_value(::Interpolation)</code></a>, <a href="#Ferrite.reference_shape_gradient-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_gradient(::Interpolation)</code></a>, and the gradient of the latter.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L254-L259">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.boundarydof_indices" href="#Ferrite.boundarydof_indices"><code>Ferrite.boundarydof_indices</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">boundarydof_indices(::Type{<:BoundaryIndex})</code></pre><p>Helper function to generically dispatch on the correct dof sets of a boundary entity.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L394-L398">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_boundarydof_indices" href="#Ferrite.dirichlet_boundarydof_indices"><code>Ferrite.dirichlet_boundarydof_indices</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_boundarydof_indices(::Type{<:BoundaryIndex})</code></pre><p>Helper function to generically dispatch on the correct dof sets of a boundary entity. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.boundarydof_indices"><code>boundarydof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L428-L433">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_values!" href="#Ferrite.reference_shape_values!"><code>Ferrite.reference_shape_values!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_values!(values::AbstractArray{T}, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape functions of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>values</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L161-L166">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradients!" href="#Ferrite.reference_shape_gradients!"><code>Ferrite.reference_shape_gradients!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradients!(gradients::AbstractArray, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape function gradients of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>gradients</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L175-L180">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_gradients_and_values!" href="#Ferrite.reference_shape_gradients_and_values!"><code>Ferrite.reference_shape_gradients_and_values!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_gradients_and_values!(gradients::AbstractArray, values::AbstractArray, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape function gradients and values of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>values</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L189-L194">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_hessians_gradients_and_values!" href="#Ferrite.reference_shape_hessians_gradients_and_values!"><code>Ferrite.reference_shape_hessians_gradients_and_values!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_hessians_gradients_and_values!(hessians::AbstractVector, gradients::AbstractVector, values::AbstractVector, ip::Interpolation, ξ::Vec)</code></pre><p>Evaluate all shape function hessians, gradients and values of <code>ip</code> at once at the reference point <code>ξ</code> and store them in <code>hessians</code>, <code>gradients</code>, and <code>values</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L204-L209">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_type-Union{Tuple{T}, Tuple{Interpolation, Type{T}}} where T<:Number" href="#Ferrite.shape_value_type-Union{Tuple{T}, Tuple{Interpolation, Type{T}}} where T<:Number"><code>Ferrite.shape_value_type</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_type(ip::Interpolation, ::Type{T}) where T<:Number</code></pre><p>Return the type of <code>shape_value(ip::Interpolation, ξ::Vec, ib::Int)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L60-L64">source</a></section></article><h3 id="Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element"><a class="docs-heading-anchor" href="#Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element">Required methods to implement for all subtypes of <code>Interpolation</code> to define a new finite element</a><a id="Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element-1"></a><a class="docs-heading-anchor-permalink" href="#Required-methods-to-implement-for-all-subtypes-of-Interpolation-to-define-a-new-finite-element" title="Permalink"></a></h3><p>Depending on the dimension of the reference element the following functions have to be implemented</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}" href="#Ferrite.reference_shape_value-Tuple{Interpolation, Vec, Int64}"><code>Ferrite.reference_shape_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_shape_value(ip::Interpolation, ξ::Vec, i::Int)</code></pre><p>Evaluate the value of the <code>i</code>th shape function of the interpolation <code>ip</code> at a point <code>ξ</code> on the reference element. The index <code>i</code> must match the index in <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices(::Interpolation)</code></a>, <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Interpolation)</code></a> and <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Interpolation)</code></a>.</p><p>For nodal interpolations the indices also must match the indices of <a href="#Ferrite.reference_coordinates-Tuple{Interpolation}"><code>reference_coordinates(::Interpolation)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L221-L231">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vertexdof_indices-Tuple{Interpolation}" href="#Ferrite.vertexdof_indices-Tuple{Interpolation}"><code>Ferrite.vertexdof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">vertexdof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective vertex in local enumeration on a cell defined by <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices(::Cell)</code></a>. The vertex enumeration must match the vertex enumeration of the corresponding geometrical cell.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be the 1, as vertex dofs are enumerated first.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L278-L288">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_vertexdof_indices-Tuple{Interpolation}" href="#Ferrite.dirichlet_vertexdof_indices-Tuple{Interpolation}"><code>Ferrite.dirichlet_vertexdof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_vertexdof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective vertex in local enumeration on a cell defined by <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices(::Cell)</code></a>. The vertex enumeration must match the vertex enumeration of the corresponding geometrical cell. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.vertexdof_indices-Tuple{Interpolation}"><code>vertexdof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be the 1, as vertex dofs are enumerated first.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L291-L302">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facedof_indices-Tuple{Interpolation}" href="#Ferrite.facedof_indices-Tuple{Interpolation}"><code>Ferrite.facedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of all local dof indices for the respective face in local enumeration on a cell defined by <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Cell)</code></a>. The face enumeration must match the face enumeration of the corresponding geometrical cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L344-L350">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_facedof_indices-Tuple{Interpolation}" href="#Ferrite.dirichlet_facedof_indices-Tuple{Interpolation}"><code>Ferrite.dirichlet_facedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_facedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of all local dof indices for the respective face in local enumeration on a cell defined by <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Cell)</code></a>. The face enumeration must match the face enumeration of the corresponding geometrical cell. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.facedof_indices-Tuple{Interpolation}"><code>facedof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L353-L360">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facedof_interior_indices-Tuple{Interpolation}" href="#Ferrite.facedof_interior_indices-Tuple{Interpolation}"><code>Ferrite.facedof_interior_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facedof_interior_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of the local dof indices on the interior of the respective face in local enumeration on a cell defined by <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces(::Cell)</code></a>. The face enumeration must match the face enumeration of the corresponding geometrical cell. Note that the vertex and edge dofs are included here.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be the computed via "last edge interior dof index + 1", if face dofs exist.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L363-L374">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.edgedof_indices-Tuple{Interpolation}" href="#Ferrite.edgedof_indices-Tuple{Interpolation}"><code>Ferrite.edgedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">edgedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective edge in local enumeration on a cell defined by <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Cell)</code></a>. The edge enumeration must match the edge enumeration of the corresponding geometrical cell.</p><p>The dofs are guaranteed to be aligned with the local ordering of the entities on the oriented edge. Here the first entries are the vertex dofs, followed by the edge interior dofs.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L305-L314">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dirichlet_edgedof_indices-Tuple{Interpolation}" href="#Ferrite.dirichlet_edgedof_indices-Tuple{Interpolation}"><code>Ferrite.dirichlet_edgedof_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dirichlet_edgedof_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of local dof indices for the respective edge in local enumeration on a cell defined by <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Cell)</code></a>. The edge enumeration must match the edge enumeration of the corresponding geometrical cell. Used internally in <a href="../../reference/boundary_conditions/#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> and defaults to <a href="#Ferrite.edgedof_indices-Tuple{Interpolation}"><code>edgedof_indices(ip::Interpolation)</code></a> for continuous interpolation.</p><p>The dofs are guaranteed to be aligned with the local ordering of the entities on the oriented edge. Here the first entries are the vertex dofs, followed by the edge interior dofs.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L317-L327">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.edgedof_interior_indices-Tuple{Interpolation}" href="#Ferrite.edgedof_interior_indices-Tuple{Interpolation}"><code>Ferrite.edgedof_interior_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">edgedof_interior_indices(ip::Interpolation)</code></pre><p>A tuple containing tuples of the local dof indices on the interior of the respective edge in local enumeration on a cell defined by <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges(::Cell)</code></a>. The edge enumeration must match the edge enumeration of the corresponding geometrical cell. Note that the vertex dofs are included here.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing! The first dof must be computed via "last vertex dof index + 1", if edge dofs exist.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L330-L341">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.volumedof_interior_indices-Tuple{Interpolation}" href="#Ferrite.volumedof_interior_indices-Tuple{Interpolation}"><code>Ferrite.volumedof_interior_indices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">volumedof_interior_indices(ip::Interpolation)</code></pre><p>Tuple containing the dof indices associated with the interior of a volume.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The dofs appearing in the tuple must be continuous and increasing, volumedofs are enumerated last.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L377-L385">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnbasefunctions-Tuple{Interpolation}" href="#Ferrite.getnbasefunctions-Tuple{Interpolation}"><code>Ferrite.getnbasefunctions</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getnbasefunctions(ip::Interpolation)</code></pre><p>Return the number of base functions for the interpolation <code>ip</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L148-L152">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_coordinates-Tuple{Interpolation}" href="#Ferrite.reference_coordinates-Tuple{Interpolation}"><code>Ferrite.reference_coordinates</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_coordinates(ip::Interpolation)</code></pre><p>Returns a vector of coordinates with length <a href="#Ferrite.getnbasefunctions-Tuple{Interpolation}"><code>getnbasefunctions(::Interpolation)</code></a> and indices corresponding to the indices of a dof in <a href="../elements/#Ferrite.vertices-Tuple{Ferrite.AbstractCell}"><code>vertices</code></a>, <a href="../elements/#Ferrite.faces-Tuple{Ferrite.AbstractCell}"><code>faces</code></a> and <a href="../elements/#Ferrite.edges-Tuple{Ferrite.AbstractCell}"><code>edges</code></a>.</p><pre><code class="nohighlight hljs">Only required for nodal interpolations.
-TODO: Separate nodal and non-nodal interpolations.</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L265-L275">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.is_discontinuous-Tuple{Interpolation}" href="#Ferrite.is_discontinuous-Tuple{Interpolation}"><code>Ferrite.is_discontinuous</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">is_discontinuous(::Interpolation)
-is_discontinuous(::Type{<:Interpolation})</code></pre><p>Checks whether the interpolation is discontinuous (i.e. <code>DiscontinuousLagrange</code>)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L419-L424">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.adjust_dofs_during_distribution-Tuple{Interpolation}" href="#Ferrite.adjust_dofs_during_distribution-Tuple{Interpolation}"><code>Ferrite.adjust_dofs_during_distribution</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">adjust_dofs_during_distribution(::Interpolation)</code></pre><p>This function must return <code>true</code> if the dofs should be adjusted (i.e. permuted) during dof distribution. This is in contrast to i) adjusting the dofs during <a href="../../reference/fevalues/#Ferrite.reinit!"><code>reinit!</code></a> in the assembly loop, or ii) not adjusting at all (which is not needed for low order interpolations, generally).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L73-L80">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.mapping_type" href="#Ferrite.mapping_type"><code>Ferrite.mapping_type</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">mapping_type(ip::Interpolation)</code></pre><p>Get the type of mapping from the reference cell to the real cell for an interpolation <code>ip</code>. Subtypes of <code>ScalarInterpolation</code> and <code>VectorizedInterpolation</code> return <code>IdentityMapping()</code>, but other non-scalar interpolations may request different mapping types.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L1765-L1772">source</a></section></article><p>for all entities which exist on that reference element. The dof functions default to having no dofs defined on a specific entity. Hence, not overloading of the dof functions will result in an element with zero dofs. Also, it should always be double checked that everything is consistent as specified in the docstring of the corresponding function, as inconsistent implementations can lead to bugs which are really difficult to track down.</p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+TODO: Separate nodal and non-nodal interpolations.</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L265-L275">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.is_discontinuous-Tuple{Interpolation}" href="#Ferrite.is_discontinuous-Tuple{Interpolation}"><code>Ferrite.is_discontinuous</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">is_discontinuous(::Interpolation)
+is_discontinuous(::Type{<:Interpolation})</code></pre><p>Checks whether the interpolation is discontinuous (i.e. <code>DiscontinuousLagrange</code>)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L419-L424">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.adjust_dofs_during_distribution-Tuple{Interpolation}" href="#Ferrite.adjust_dofs_during_distribution-Tuple{Interpolation}"><code>Ferrite.adjust_dofs_during_distribution</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">adjust_dofs_during_distribution(::Interpolation)</code></pre><p>This function must return <code>true</code> if the dofs should be adjusted (i.e. permuted) during dof distribution. This is in contrast to i) adjusting the dofs during <a href="../../reference/fevalues/#Ferrite.reinit!"><code>reinit!</code></a> in the assembly loop, or ii) not adjusting at all (which is not needed for low order interpolations, generally).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L73-L80">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.mapping_type" href="#Ferrite.mapping_type"><code>Ferrite.mapping_type</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">mapping_type(ip::Interpolation)</code></pre><p>Get the type of mapping from the reference cell to the real cell for an interpolation <code>ip</code>. Subtypes of <code>ScalarInterpolation</code> and <code>VectorizedInterpolation</code> return <code>IdentityMapping()</code>, but other non-scalar interpolations may request different mapping types.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L1765-L1772">source</a></section></article><p>for all entities which exist on that reference element. The dof functions default to having no dofs defined on a specific entity. Hence, not overloading of the dof functions will result in an element with zero dofs. Also, it should always be double checked that everything is consistent as specified in the docstring of the corresponding function, as inconsistent implementations can lead to bugs which are really difficult to track down.</p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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analysis</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/performance.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-performance"><a class="docs-heading-anchor" href="#devdocs-performance">Performance analysis</a><a id="devdocs-performance-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-performance" title="Permalink"></a></h1><p>In the benchmark folder we provide basic infrastructure to analyze the performance of Ferrite to help tracking down performance regression issues. Two basic tools can be directly executed via make: A basic benchmark for the current branch and a comparison between two commits. To execute the benchmark on the current branch only open a shell in the benchmark folder and call</p><pre><code class="nohighlight hljs">make benchmark</code></pre><p>whereas for the comparison of two commits simply call</p><pre><code class="nohighlight hljs">make compare target=<target-commit> baseline=<baseline-commit></code></pre><p>If you have a custom julia executable that is not accessible via the <code>julia</code> command, then you can pass the executable via</p><pre><code class="nohighlight hljs">JULIA_CMD=<path-to-julia-executable> make compare target=<target-commit> baseline=<baseline-commit></code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>For the performance comparison between two commits you must not have any uncommitted or untracked files in your Ferrite.jl folder! Otherwise the <code>PkgBenchmark.jl</code> will fail to setup the comparison.</p></div></div><p>For more fine grained control you can run subsets of the benchmarks via by appending <code>-<subset></code> to compare or benchmark, e.g.</p><pre><code class="nohighlight hljs">make benchmark-mesh</code></pre><p>to benchmark only the mesh functionality. The following subsets are currently available:</p><ul><li><code>assembly</code></li><li><code>boundary-conditions</code></li><li><code>dofs</code></li><li><code>mesh</code></li></ul><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>It is recommended to run all benchmarks before running subsets to get the correct tuning parameters for each benchmark.</p></div></div></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. 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analysis</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/performance.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="devdocs-performance"><a class="docs-heading-anchor" href="#devdocs-performance">Performance analysis</a><a id="devdocs-performance-1"></a><a class="docs-heading-anchor-permalink" href="#devdocs-performance" title="Permalink"></a></h1><p>In the benchmark folder we provide basic infrastructure to analyze the performance of Ferrite to help tracking down performance regression issues. Two basic tools can be directly executed via make: A basic benchmark for the current branch and a comparison between two commits. To execute the benchmark on the current branch only open a shell in the benchmark folder and call</p><pre><code class="nohighlight hljs">make benchmark</code></pre><p>whereas for the comparison of two commits simply call</p><pre><code class="nohighlight hljs">make compare target=<target-commit> baseline=<baseline-commit></code></pre><p>If you have a custom julia executable that is not accessible via the <code>julia</code> command, then you can pass the executable via</p><pre><code class="nohighlight hljs">JULIA_CMD=<path-to-julia-executable> make compare target=<target-commit> baseline=<baseline-commit></code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>For the performance comparison between two commits you must not have any uncommitted or untracked files in your Ferrite.jl folder! Otherwise the <code>PkgBenchmark.jl</code> will fail to setup the comparison.</p></div></div><p>For more fine grained control you can run subsets of the benchmarks via by appending <code>-<subset></code> to compare or benchmark, e.g.</p><pre><code class="nohighlight hljs">make benchmark-mesh</code></pre><p>to benchmark only the mesh functionality. The following subsets are currently available:</p><ul><li><code>assembly</code></li><li><code>boundary-conditions</code></li><li><code>dofs</code></li><li><code>mesh</code></li></ul><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>It is recommended to run all benchmarks before running subsets to get the correct tuning parameters for each benchmark.</p></div></div></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. 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cells</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/reference_cells.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Reference-cells"><a class="docs-heading-anchor" href="#Reference-cells">Reference cells</a><a id="Reference-cells-1"></a><a class="docs-heading-anchor-permalink" href="#Reference-cells" title="Permalink"></a></h1><p>The reference cells are used to i) define grid cells, ii) define shape functions, and iii) define quadrature rules. The numbering of vertices, edges, faces are visualized below. See also <a href="https://ferrite-fem.github.io/FerriteViz.jl/dev/api/#FerriteViz.elementinfo"><code>FerriteViz.elementinfo</code></a>.</p><h3 id="AbstractRefShape-subtypes"><a class="docs-heading-anchor" href="#AbstractRefShape-subtypes"><code>AbstractRefShape</code> subtypes</a><a id="AbstractRefShape-subtypes-1"></a><a class="docs-heading-anchor-permalink" href="#AbstractRefShape-subtypes" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.AbstractRefShape" href="#Ferrite.AbstractRefShape"><code>Ferrite.AbstractRefShape</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">AbstractRefShape{refdim}</code></pre><p>Supertype for all reference shapes, with reference dimension <code>refdim</code>. Reference shapes are used to define grid cells, shape functions, and quadrature rules. Currently existing reference shapes are: <a href="#Ferrite.RefLine"><code>RefLine</code></a>, <a href="#Ferrite.RefTriangle"><code>RefTriangle</code></a>, <a href="#Ferrite.RefQuadrilateral"><code>RefQuadrilateral</code></a>, <a href="#Ferrite.RefTetrahedron"><code>RefTetrahedron</code></a>, <a href="#Ferrite.RefHexahedron"><code>RefHexahedron</code></a>, <a href="#Ferrite.RefPrism"><code>RefPrism</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L35-L42">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefLine" href="#Ferrite.RefLine"><code>Ferrite.RefLine</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefLine <: AbstractRefShape{1}</code></pre><p>Reference line/interval, reference dimension 1.</p><pre><code class="nohighlight hljs">----------------+--------------------
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class="tocitem" href="../../howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../../gallery/">Code gallery</a></li><li><a class="tocitem" href="../">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Reference cells</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Reference cells</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/devdocs/reference_cells.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Reference-cells"><a class="docs-heading-anchor" href="#Reference-cells">Reference cells</a><a id="Reference-cells-1"></a><a class="docs-heading-anchor-permalink" href="#Reference-cells" title="Permalink"></a></h1><p>The reference cells are used to i) define grid cells, ii) define shape functions, and iii) define quadrature rules. The numbering of vertices, edges, faces are visualized below. See also <a href="https://ferrite-fem.github.io/FerriteViz.jl/dev/api/#FerriteViz.elementinfo"><code>FerriteViz.elementinfo</code></a>.</p><h3 id="AbstractRefShape-subtypes"><a class="docs-heading-anchor" href="#AbstractRefShape-subtypes"><code>AbstractRefShape</code> subtypes</a><a id="AbstractRefShape-subtypes-1"></a><a class="docs-heading-anchor-permalink" href="#AbstractRefShape-subtypes" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.AbstractRefShape" href="#Ferrite.AbstractRefShape"><code>Ferrite.AbstractRefShape</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">AbstractRefShape{refdim}</code></pre><p>Supertype for all reference shapes, with reference dimension <code>refdim</code>. Reference shapes are used to define grid cells, shape functions, and quadrature rules. Currently existing reference shapes are: <a href="#Ferrite.RefLine"><code>RefLine</code></a>, <a href="#Ferrite.RefTriangle"><code>RefTriangle</code></a>, <a href="#Ferrite.RefQuadrilateral"><code>RefQuadrilateral</code></a>, <a href="#Ferrite.RefTetrahedron"><code>RefTetrahedron</code></a>, <a href="#Ferrite.RefHexahedron"><code>RefHexahedron</code></a>, <a href="#Ferrite.RefPrism"><code>RefPrism</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L35-L42">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefLine" href="#Ferrite.RefLine"><code>Ferrite.RefLine</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefLine <: AbstractRefShape{1}</code></pre><p>Reference line/interval, reference dimension 1.</p><pre><code class="nohighlight hljs">----------------+--------------------
Vertex numbers: | Vertex coordinates:
1-------2 | v1: 𝛏 = (-1.0,)
--> ξ₁ | v2: 𝛏 = ( 1.0,)
----------------+--------------------
Edge numbers: | Edge identifiers:
+---1---+ | e1: (v1, v2)
-----------------+--------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/docs.jl#L5-L19">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefTriangle" href="#Ferrite.RefTriangle"><code>Ferrite.RefTriangle</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefTriangle <: AbstractRefShape{2}</code></pre><p>Reference triangle, reference dimension 2.</p><pre><code class="nohighlight hljs">----------------+--------------------
+----------------+--------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/docs.jl#L5-L19">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefTriangle" href="#Ferrite.RefTriangle"><code>Ferrite.RefTriangle</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefTriangle <: AbstractRefShape{2}</code></pre><p>Reference triangle, reference dimension 2.</p><pre><code class="nohighlight hljs">----------------+--------------------
Vertex numbers: | Vertex coordinates:
2 |
| \ | v1: 𝛏 = (1.0, 0.0)
@@ -28,7 +28,7 @@
| \ | f1: (v1, v2, v3)
| 1 \ |
+-------+ |
-----------------+--------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/docs.jl#L22-L51">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefQuadrilateral" href="#Ferrite.RefQuadrilateral"><code>Ferrite.RefQuadrilateral</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefQuadrilateral <: AbstractRefShape{2}</code></pre><p>Reference quadrilateral, reference dimension 2.</p><pre><code class="nohighlight hljs">----------------+---------------------
+----------------+--------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/docs.jl#L22-L51">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefQuadrilateral" href="#Ferrite.RefQuadrilateral"><code>Ferrite.RefQuadrilateral</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefQuadrilateral <: AbstractRefShape{2}</code></pre><p>Reference quadrilateral, reference dimension 2.</p><pre><code class="nohighlight hljs">----------------+---------------------
Vertex numbers: | Vertex coordinates:
4-------3 |
| | | v1: 𝛏 = (-1.0, -1.0)
@@ -50,7 +50,7 @@
| 1 | | f1: (v1, v2, v3, v4)
| | |
+-------+ |
-----------------+---------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/docs.jl#L54-L83">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefTetrahedron" href="#Ferrite.RefTetrahedron"><code>Ferrite.RefTetrahedron</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefTetrahedron <: AbstractRefShape{3}</code></pre><p>Reference tetrahedron, reference dimension 3.</p><pre><code class="nohighlight hljs">---------------------------------------+-------------------------
+----------------+---------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/docs.jl#L54-L83">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefTetrahedron" href="#Ferrite.RefTetrahedron"><code>Ferrite.RefTetrahedron</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefTetrahedron <: AbstractRefShape{3}</code></pre><p>Reference tetrahedron, reference dimension 3.</p><pre><code class="nohighlight hljs">---------------------------------------+-------------------------
Vertex numbers: | Vertex coordinates:
4 4 |
^ ξ₃ / \ /| \ | v1: 𝛏 = (0.0, 0.0, 0.0)
@@ -74,7 +74,7 @@
/ 3 \ /2 +___ \ | f3: (v2, v3, v4)
/ __--+ / / 1 __‾-+ | f4: (v1, v4, v3)
+ __--‾‾ +/__--‾‾ |
----------------------------------------+-------------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/docs.jl#L86-L117">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefHexahedron" href="#Ferrite.RefHexahedron"><code>Ferrite.RefHexahedron</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefHexahedron <: AbstractRefShape{3}</code></pre><p>Reference hexahedron, reference dimension 3.</p><pre><code class="nohighlight hljs">-----------------------------------------+----------------------------
+---------------------------------------+-------------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/docs.jl#L86-L117">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefHexahedron" href="#Ferrite.RefHexahedron"><code>Ferrite.RefHexahedron</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefHexahedron <: AbstractRefShape{3}</code></pre><p>Reference hexahedron, reference dimension 3.</p><pre><code class="nohighlight hljs">-----------------------------------------+----------------------------
Vertex numbers: | Vertex coordinates:
5--------8 5--------8 | v1: 𝛏 = (-1.0, -1.0, -1.0)
/ /| /| | | v2: 𝛏 = ( 1.0, -1.0, -1.0)
@@ -104,7 +104,7 @@
| 3 | / | / / | f5: (v1, v5, v8, v4)
| |/ |/ 1 / | f6: (v5, v6, v7, v8)
+--------+ +--------+ |
------------------------------------------+-----------------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/docs.jl#L120-L157">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefPrism" href="#Ferrite.RefPrism"><code>Ferrite.RefPrism</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefPrism <: AbstractRefShape{3}</code></pre><p>Reference prism, reference dimension 3.</p><pre><code class="nohighlight hljs">-----------------------------------------+----------------------------
+-----------------------------------------+-----------------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/docs.jl#L120-L157">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RefPrism" href="#Ferrite.RefPrism"><code>Ferrite.RefPrism</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RefPrism <: AbstractRefShape{3}</code></pre><p>Reference prism, reference dimension 3.</p><pre><code class="nohighlight hljs">-----------------------------------------+----------------------------
Vertex numbers: | Vertex coordinates:
4-------/6 4--------6 |
/ / | /| | | v1: 𝛏 = (0.0, 0.0, 0.0)
@@ -134,8 +134,8 @@
| / | / 1 / | f5: (v4, v5, v6)
| / |/ / |
+ / + / |
------------------------------------------+----------------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/docs.jl#L160-L197">source</a></section></article><h3 id="Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape"><a class="docs-heading-anchor" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape">Required methods to implement for all subtypes of <code>AbstractRefShape</code> to define a new reference shape</a><a id="Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape-1"></a><a class="docs-heading-anchor-permalink" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_vertices-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_vertices-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_vertices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_vertices(::Type{<:AbstractRefShape})
-reference_vertices(::AbstractCell)</code></pre><p>Returns a tuple of integers containing the local node indices corresponding to the vertices (i.e. corners or endpoints) of the cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L60-L66">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_edges-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_edges-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_edges</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_edges(::Type{<:AbstractRefShape})
-reference_edges(::AbstractCell)</code></pre><p>Returns a tuple of 2-tuples containing the ordered local node indices (corresponding to the vertices) that define an edge.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L78-L84">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_faces-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_faces-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_faces</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_faces(::Type{<:AbstractRefShape})
-reference_faces(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered local node indices (corresponding to the vertices) that define a face.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L98-L104">source</a></section></article><p>which automatically defines</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_facets-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_facets-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_facets</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.reference_facets(::Type{<:AbstractRefShape})
-Ferrite.reference_facets(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered local node indices (corresponding to the vertices) that define a facet.</p><p>See also <a href="../elements/#Ferrite.reference_vertices-Tuple{Ferrite.AbstractCell}"><code>reference_vertices</code></a>, <a href="../elements/#Ferrite.reference_edges-Tuple{Ferrite.AbstractCell}"><code>reference_edges</code></a>, and <a href="../elements/#Ferrite.reference_faces-Tuple{Ferrite.AbstractCell}"><code>reference_faces</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L136-L144">source</a></section></article><h3 id="Applicable-methods-to-AbstractRefShapes"><a class="docs-heading-anchor" href="#Applicable-methods-to-AbstractRefShapes">Applicable methods to <code>AbstractRefShape</code>s</a><a id="Applicable-methods-to-AbstractRefShapes-1"></a><a class="docs-heading-anchor-permalink" href="#Applicable-methods-to-AbstractRefShapes" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefdim-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.getrefdim-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.getrefdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefdim(RefShape::Type{<:AbstractRefShape})</code></pre><p>Get the dimension of the reference shape</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L56-L60">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+-----------------------------------------+----------------------------</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/docs.jl#L160-L197">source</a></section></article><h3 id="Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape"><a class="docs-heading-anchor" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape">Required methods to implement for all subtypes of <code>AbstractRefShape</code> to define a new reference shape</a><a id="Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape-1"></a><a class="docs-heading-anchor-permalink" href="#Required-methods-to-implement-for-all-subtypes-of-AbstractRefShape-to-define-a-new-reference-shape" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_vertices-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_vertices-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_vertices</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_vertices(::Type{<:AbstractRefShape})
+reference_vertices(::AbstractCell)</code></pre><p>Returns a tuple of integers containing the local node indices corresponding to the vertices (i.e. corners or endpoints) of the cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L60-L66">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_edges-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_edges-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_edges</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_edges(::Type{<:AbstractRefShape})
+reference_edges(::AbstractCell)</code></pre><p>Returns a tuple of 2-tuples containing the ordered local node indices (corresponding to the vertices) that define an edge.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L78-L84">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_faces-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_faces-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_faces</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reference_faces(::Type{<:AbstractRefShape})
+reference_faces(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered local node indices (corresponding to the vertices) that define a face.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L98-L104">source</a></section></article><p>which automatically defines</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reference_facets-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.reference_facets-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.reference_facets</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.reference_facets(::Type{<:AbstractRefShape})
+Ferrite.reference_facets(::AbstractCell)</code></pre><p>Returns a tuple of n-tuples containing the ordered local node indices (corresponding to the vertices) that define a facet.</p><p>See also <a href="../elements/#Ferrite.reference_vertices-Tuple{Ferrite.AbstractCell}"><code>reference_vertices</code></a>, <a href="../elements/#Ferrite.reference_edges-Tuple{Ferrite.AbstractCell}"><code>reference_edges</code></a>, and <a href="../elements/#Ferrite.reference_faces-Tuple{Ferrite.AbstractCell}"><code>reference_faces</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L136-L144">source</a></section></article><h3 id="Applicable-methods-to-AbstractRefShapes"><a class="docs-heading-anchor" href="#Applicable-methods-to-AbstractRefShapes">Applicable methods to <code>AbstractRefShape</code>s</a><a id="Applicable-methods-to-AbstractRefShapes-1"></a><a class="docs-heading-anchor-permalink" href="#Applicable-methods-to-AbstractRefShapes" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefdim-Tuple{Type{<:Ferrite.AbstractRefShape}}" href="#Ferrite.getrefdim-Tuple{Type{<:Ferrite.AbstractRefShape}}"><code>Ferrite.getrefdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefdim(RefShape::Type{<:AbstractRefShape})</code></pre><p>Get the dimension of the reference shape</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L56-L60">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/devdocs/special_datastructures/index.html b/dev/devdocs/special_datastructures/index.html
index 237d2ce710..46824e89e1 100644
--- a/dev/devdocs/special_datastructures/index.html
+++ b/dev/devdocs/special_datastructures/index.html
@@ -3,4 +3,4 @@
for (ind, val) in some_data
push_at_index!(buffer, val, ind)
end
-end</code></pre><p><code>sizehint</code> tells how much space to allocate for the index <code>ind</code> if no <code>val</code> has been added to that index before, or how much more space to allocate in case all previously allocated space for <code>ind</code> has been used up.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/CollectionsOfViews.jl#L85-L104">source</a></section><section><div><pre><code class="language-julia hljs">ArrayOfVectorViews(b::CollectionsOfViews.ConstructionBuffer)</code></pre><p>Creates the <code>ArrayOfVectorViews</code> directly from the <code>ConstructionBuffer</code> that was manually created and filled.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/CollectionsOfViews.jl#L112-L116">source</a></section><section><div><pre><code class="language-julia hljs">ArrayOfVectorViews(indices::Vector{Int}, data::Vector{T}, lin_idx::LinearIndices{N}; checkargs = true)</code></pre><p>Creates the <code>ArrayOfVectorViews</code> directly where the user is responsible for having the correct input data. Checking of the argument dimensions can be elided by setting <code>checkargs = false</code>, but incorrect dimensions may lead to illegal out of bounds access later.</p><p><code>data</code> is indexed by <code>indices[i]:indices[i+1]</code>, where <code>i = lin_idx[idx...]</code> and <code>idx...</code> are the user-provided indices to the <code>ArrayOfVectorViews</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/CollectionsOfViews.jl#L137-L146">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CollectionsOfViews.ConstructionBuffer" href="#Ferrite.CollectionsOfViews.ConstructionBuffer"><code>Ferrite.CollectionsOfViews.ConstructionBuffer</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ConstructionBuffer(data::Vector, dims::NTuple{N, Int}, sizehint)</code></pre><p>Create a buffer for creating an <a href="#ArrayOfVectorViews"><code>ArrayOfVectorViews</code></a>, representing an array with <code>N</code> axes. <code>sizehint</code> sets the number of elements in <code>data</code> allocated when a new index is added via <code>push_at_index!</code>, or when the current storage for the index is full, how much many additional elements are reserved for that index. Any content in <code>data</code> is overwritten, but performance is improved by pre-allocating it to a reasonable size or by <code>sizehint!</code>ing it.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/CollectionsOfViews.jl#L19-L27">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CollectionsOfViews.push_at_index!" href="#Ferrite.CollectionsOfViews.push_at_index!"><code>Ferrite.CollectionsOfViews.push_at_index!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">push_at_index!(b::ConstructionBuffer, val, indices::Int...)</code></pre><p><code>push!</code> the value <code>val</code> to the <code>Vector</code> view at the index given by <code>indices</code>, typically called inside the <a href="#ArrayOfVectorViews"><code>ArrayOfVectorViews</code></a> constructor do-block. But can also be used when manually creating a <code>ConstructionBuffer</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/CollectionsOfViews.jl#L33-L39">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><p><code>sizehint</code> tells how much space to allocate for the index <code>ind</code> if no <code>val</code> has been added to that index before, or how much more space to allocate in case all previously allocated space for <code>ind</code> has been used up.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/CollectionsOfViews.jl#L85-L104">source</a></section><section><div><pre><code class="language-julia hljs">ArrayOfVectorViews(b::CollectionsOfViews.ConstructionBuffer)</code></pre><p>Creates the <code>ArrayOfVectorViews</code> directly from the <code>ConstructionBuffer</code> that was manually created and filled.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/CollectionsOfViews.jl#L112-L116">source</a></section><section><div><pre><code class="language-julia hljs">ArrayOfVectorViews(indices::Vector{Int}, data::Vector{T}, lin_idx::LinearIndices{N}; checkargs = true)</code></pre><p>Creates the <code>ArrayOfVectorViews</code> directly where the user is responsible for having the correct input data. Checking of the argument dimensions can be elided by setting <code>checkargs = false</code>, but incorrect dimensions may lead to illegal out of bounds access later.</p><p><code>data</code> is indexed by <code>indices[i]:indices[i+1]</code>, where <code>i = lin_idx[idx...]</code> and <code>idx...</code> are the user-provided indices to the <code>ArrayOfVectorViews</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/CollectionsOfViews.jl#L137-L146">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CollectionsOfViews.ConstructionBuffer" href="#Ferrite.CollectionsOfViews.ConstructionBuffer"><code>Ferrite.CollectionsOfViews.ConstructionBuffer</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ConstructionBuffer(data::Vector, dims::NTuple{N, Int}, sizehint)</code></pre><p>Create a buffer for creating an <a href="#ArrayOfVectorViews"><code>ArrayOfVectorViews</code></a>, representing an array with <code>N</code> axes. <code>sizehint</code> sets the number of elements in <code>data</code> allocated when a new index is added via <code>push_at_index!</code>, or when the current storage for the index is full, how much many additional elements are reserved for that index. Any content in <code>data</code> is overwritten, but performance is improved by pre-allocating it to a reasonable size or by <code>sizehint!</code>ing it.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/CollectionsOfViews.jl#L19-L27">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CollectionsOfViews.push_at_index!" href="#Ferrite.CollectionsOfViews.push_at_index!"><code>Ferrite.CollectionsOfViews.push_at_index!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">push_at_index!(b::ConstructionBuffer, val, indices::Int...)</code></pre><p><code>push!</code> the value <code>val</code> to the <code>Vector</code> view at the index given by <code>indices</code>, typically called inside the <a href="#ArrayOfVectorViews"><code>ArrayOfVectorViews</code></a> constructor do-block. But can also be used when manually creating a <code>ConstructionBuffer</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/CollectionsOfViews.jl#L33-L39">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/gallery/helmholtz/index.html b/dev/gallery/helmholtz/index.html
index a112aaf6c6..e614a039d3 100644
--- a/dev/gallery/helmholtz/index.html
+++ b/dev/gallery/helmholtz/index.html
@@ -108,4 +108,4 @@
vtk = VTKGridFile("helmholtz", dh)
write_solution(vtk, dh, u)
close(vtk)
-println("Helmholtz successful")</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Helmholtz successful</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+println("Helmholtz successful")</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Helmholtz successful</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/gallery/index.html b/dev/gallery/index.html
index 950750ac95..a4329ffa24 100644
--- a/dev/gallery/index.html
+++ b/dev/gallery/index.html
@@ -1,2 +1,2 @@
<!DOCTYPE html>
-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Code gallery · Ferrite.jl</title><meta name="title" content="Code gallery · Ferrite.jl"/><meta property="og:title" content="Code gallery · Ferrite.jl"/><meta property="twitter:title" content="Code gallery · Ferrite.jl"/><meta name="description" content="Documentation for Ferrite.jl."/><meta property="og:description" content="Documentation for Ferrite.jl."/><meta property="twitter:description" content="Documentation for Ferrite.jl."/><meta property="og:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/gallery/"/><meta property="twitter:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/gallery/"/><link rel="canonical" href="https://ferrite-fem.github.io/Ferrite.jl/stable/gallery/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" 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literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Code gallery</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Code gallery</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/gallery/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Code-gallery"><a class="docs-heading-anchor" href="#Code-gallery">Code gallery</a><a id="Code-gallery-1"></a><a class="docs-heading-anchor-permalink" href="#Code-gallery" title="Permalink"></a></h1><p>This page gives an overview of the code gallery. Compared to the tutorials, these programs do not focus on teaching Ferrite, but rather focus on showing how Ferrite can be used "in the wild".</p><div class="admonition is-info"><header class="admonition-header">Contribute to the gallery!</header><div class="admonition-body"><p>Most of the gallery is user contributed. If you use Ferrite, and have something you want to share, please contribute to the gallery! This could, for example, be your research code for a published paper, some interesting application, or just some nice trick.</p></div></div><hr/><h4 id="[Helmholtz-equation](helmholtz.md)"><a class="docs-heading-anchor" href="#[Helmholtz-equation](helmholtz.md)"><a href="helmholtz/">Helmholtz equation</a></a><a id="[Helmholtz-equation](helmholtz.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Helmholtz-equation](helmholtz.md)" title="Permalink"></a></h4><p>Solves the Helmholtz equation on the unit square using a combination of Dirichlet and Neumann boundary conditions and the method of manufactured solutions.</p><p><em>Contributed by</em>: Kristoffer Carlsson (<a href="https://github.com/KristofferC">@KristofferC</a>).</p><hr/><h4 id="[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)"><a class="docs-heading-anchor" href="#[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)"><a href="quasi_incompressible_hyperelasticity/">Nearly incompressible hyperelasticity</a></a><a id="[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)" title="Permalink"></a></h4><p>This program combines the ideas from <a href="../tutorials/incompressible_elasticity/">Tutorial 3: Incompressible elasticity</a> and <a href="../tutorials/incompressible_elasticity/">Tutorial 4: Hyperelasticity</a> to construct a mixed element solving three-dimensional displacement-pressure equations.</p><p><em>Contributed by</em>: Bhavesh Shrimali (<a href="https://github.com/bhaveshshrimali">@bhaveshshrimali</a>).</p><hr/><h4 id="[Ginzburg-Landau-model-energy-minimization](landau.md)"><a class="docs-heading-anchor" href="#[Ginzburg-Landau-model-energy-minimization](landau.md)"><a href="landau/">Ginzburg-Landau model energy minimization</a></a><a id="[Ginzburg-Landau-model-energy-minimization](landau.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Ginzburg-Landau-model-energy-minimization](landau.md)" title="Permalink"></a></h4><p>A basic Ginzburg-Landau model is solved. <a href="https://github.com/JuliaDiff/ForwardDiff.jl">ForwardDiff.jl</a> is used to compute the gradient and hessian of the energy function. Multi-threading is used to parallelize the assembly procedure.</p><p><em>Contributed by</em>: Louis Ponet (<a href="https://github.com/louisponet">@louisponet</a>).</p><hr/><h4 id="[Topology-optimization](topology_optimization.md)"><a class="docs-heading-anchor" href="#[Topology-optimization](topology_optimization.md)"><a href="topology_optimization/">Topology optimization</a></a><a id="[Topology-optimization](topology_optimization.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Topology-optimization](topology_optimization.md)" title="Permalink"></a></h4><p>Topology optimization is shown for the bending problem by using a SIMP material model. To avoid numerical instabilities, a regularization scheme requiring the calculation of the Laplacian is imposed, which is done by using the grid topology functionalities.</p><p><em>Contributed by</em>: Mischa Blaszczyk (<a href="https://github.com/blaszm">@blaszm</a>).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../howto/threaded_assembly/">« Multi-threaded assembly</a><a class="docs-footer-nextpage" href="../devdocs/">Developer documentation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Code gallery · Ferrite.jl</title><meta name="title" content="Code gallery · Ferrite.jl"/><meta property="og:title" content="Code gallery · Ferrite.jl"/><meta property="twitter:title" content="Code gallery · Ferrite.jl"/><meta name="description" content="Documentation for Ferrite.jl."/><meta property="og:description" content="Documentation for Ferrite.jl."/><meta property="twitter:description" content="Documentation for Ferrite.jl."/><meta property="og:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/gallery/"/><meta property="twitter:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/gallery/"/><link rel="canonical" href="https://ferrite-fem.github.io/Ferrite.jl/stable/gallery/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" 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literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Code gallery</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Code gallery</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/gallery/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Code-gallery"><a class="docs-heading-anchor" href="#Code-gallery">Code gallery</a><a id="Code-gallery-1"></a><a class="docs-heading-anchor-permalink" href="#Code-gallery" title="Permalink"></a></h1><p>This page gives an overview of the code gallery. Compared to the tutorials, these programs do not focus on teaching Ferrite, but rather focus on showing how Ferrite can be used "in the wild".</p><div class="admonition is-info"><header class="admonition-header">Contribute to the gallery!</header><div class="admonition-body"><p>Most of the gallery is user contributed. If you use Ferrite, and have something you want to share, please contribute to the gallery! This could, for example, be your research code for a published paper, some interesting application, or just some nice trick.</p></div></div><hr/><h4 id="[Helmholtz-equation](helmholtz.md)"><a class="docs-heading-anchor" href="#[Helmholtz-equation](helmholtz.md)"><a href="helmholtz/">Helmholtz equation</a></a><a id="[Helmholtz-equation](helmholtz.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Helmholtz-equation](helmholtz.md)" title="Permalink"></a></h4><p>Solves the Helmholtz equation on the unit square using a combination of Dirichlet and Neumann boundary conditions and the method of manufactured solutions.</p><p><em>Contributed by</em>: Kristoffer Carlsson (<a href="https://github.com/KristofferC">@KristofferC</a>).</p><hr/><h4 id="[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)"><a class="docs-heading-anchor" href="#[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)"><a href="quasi_incompressible_hyperelasticity/">Nearly incompressible hyperelasticity</a></a><a id="[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Nearly-incompressible-hyperelasticity](quasi_incompressible_hyperelasticity.md)" title="Permalink"></a></h4><p>This program combines the ideas from <a href="../tutorials/incompressible_elasticity/">Tutorial 3: Incompressible elasticity</a> and <a href="../tutorials/incompressible_elasticity/">Tutorial 4: Hyperelasticity</a> to construct a mixed element solving three-dimensional displacement-pressure equations.</p><p><em>Contributed by</em>: Bhavesh Shrimali (<a href="https://github.com/bhaveshshrimali">@bhaveshshrimali</a>).</p><hr/><h4 id="[Ginzburg-Landau-model-energy-minimization](landau.md)"><a class="docs-heading-anchor" href="#[Ginzburg-Landau-model-energy-minimization](landau.md)"><a href="landau/">Ginzburg-Landau model energy minimization</a></a><a id="[Ginzburg-Landau-model-energy-minimization](landau.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Ginzburg-Landau-model-energy-minimization](landau.md)" title="Permalink"></a></h4><p>A basic Ginzburg-Landau model is solved. <a href="https://github.com/JuliaDiff/ForwardDiff.jl">ForwardDiff.jl</a> is used to compute the gradient and hessian of the energy function. Multi-threading is used to parallelize the assembly procedure.</p><p><em>Contributed by</em>: Louis Ponet (<a href="https://github.com/louisponet">@louisponet</a>).</p><hr/><h4 id="[Topology-optimization](topology_optimization.md)"><a class="docs-heading-anchor" href="#[Topology-optimization](topology_optimization.md)"><a href="topology_optimization/">Topology optimization</a></a><a id="[Topology-optimization](topology_optimization.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Topology-optimization](topology_optimization.md)" title="Permalink"></a></h4><p>Topology optimization is shown for the bending problem by using a SIMP material model. To avoid numerical instabilities, a regularization scheme requiring the calculation of the Laplacian is imposed, which is done by using the grid topology functionalities.</p><p><em>Contributed by</em>: Mischa Blaszczyk (<a href="https://github.com/blaszm">@blaszm</a>).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../howto/threaded_assembly/">« Multi-threaded assembly</a><a class="docs-footer-nextpage" href="../devdocs/">Developer documentation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/gallery/landau.ipynb b/dev/gallery/landau.ipynb
index d4eb4d1721..0adc03cd97 100644
--- a/dev/gallery/landau.ipynb
+++ b/dev/gallery/landau.ipynb
@@ -596,32 +596,32 @@
"text": [
"Iter Function value Gradient norm \n",
" 0 2.127588e+06 3.597094e+02\n",
- " * time: 0.028956890106201172\n",
+ " * time: 0.029977083206176758\n",
" 1 3.786155e+05 1.047687e+02\n",
- " * time: 3.771064043045044\n",
+ " * time: 3.7992539405822754\n",
" 2 5.306125e+04 2.978953e+01\n",
- " * time: 6.721739053726196\n",
+ " * time: 6.779293060302734\n",
" 3 -2.642320e+03 7.943136e+00\n",
- " * time: 9.63821005821228\n",
+ " * time: 9.712316036224365\n",
" 4 -1.027484e+04 1.752693e+00\n",
- " * time: 12.550831079483032\n",
+ " * time: 12.650713920593262\n",
" 5 -1.084925e+04 2.157295e-01\n",
- " * time: 15.484035968780518\n",
+ " * time: 15.602653980255127\n",
" 6 -1.085880e+04 5.288877e-03\n",
- " * time: 18.406095027923584\n",
+ " * time: 18.560922861099243\n",
" 7 -1.085881e+04 3.478176e-06\n",
- " * time: 21.31130290031433\n",
+ " * time: 21.508105039596558\n",
" 8 -1.085881e+04 1.596091e-12\n",
- " * time: 24.253534078598022\n",
+ " * time: 24.4543399810791\n",
" 9 -1.085881e+04 1.444882e-12\n",
- " * time: 27.229179859161377\n",
+ " * time: 27.474772930145264\n",
" 10 -1.085881e+04 1.548831e-13\n",
- " * time: 30.17466902732849\n",
+ " * time: 30.436681985855103\n",
" 11 -1.085881e+04 1.548831e-13\n",
- " * time: 33.20905804634094\n",
+ " * time: 33.468302965164185\n",
" 12 -1.085881e+04 1.508030e-13\n",
- " * time: 33.658751010894775\n",
- " 40.847445 seconds (14.89 M allocations: 4.060 GiB, 1.29% gc time, 12.96% compilation time)\n"
+ " * time: 33.90928888320923\n",
+ " 41.380651 seconds (14.89 M allocations: 4.060 GiB, 1.29% gc time, 13.21% compilation time)\n"
]
}
],
diff --git a/dev/gallery/landau/index.html b/dev/gallery/landau/index.html
index 721f029e8c..07fb2b99c0 100644
--- a/dev/gallery/landau/index.html
+++ b/dev/gallery/landau/index.html
@@ -190,29 +190,29 @@
@time minimize!(model)
save_landau("landaufinal", model)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Iter Function value Gradient norm
0 2.127588e+06 3.597094e+02
- * time: 7.581710815429688e-5
+ * time: 8.296966552734375e-5
1 3.786155e+05 1.047687e+02
- * time: 3.3353970050811768
+ * time: 2.9563701152801514
2 5.306125e+04 2.978953e+01
- * time: 6.266424894332886
+ * time: 5.893932104110718
3 -2.642320e+03 7.943136e+00
- * time: 9.223273992538452
+ * time: 8.82431697845459
4 -1.027484e+04 1.752693e+00
- * time: 12.1903657913208
+ * time: 11.74088191986084
5 -1.084925e+04 2.157295e-01
- * time: 15.144420862197876
+ * time: 14.664075136184692
6 -1.085880e+04 5.288877e-03
- * time: 18.095075845718384
+ * time: 17.596476078033447
7 -1.085881e+04 3.478176e-06
- * time: 21.055737018585205
+ * time: 20.54066514968872
8 -1.085881e+04 1.596091e-12
- * time: 24.023859977722168
+ * time: 23.463698148727417
9 -1.085881e+04 1.444882e-12
- * time: 27.008771896362305
+ * time: 26.4148371219635
10 -1.085881e+04 1.548831e-13
- * time: 29.970186948776245
+ * time: 29.3373019695282
11 -1.085881e+04 1.548831e-13
- * time: 33.00416588783264
+ * time: 32.33782601356506
12 -1.085881e+04 1.508030e-13
- * time: 33.470629930496216
- 39.441095 seconds (11.21 M allocations: 3.880 GiB, 1.38% gc time, 7.97% compilation time)</code></pre><p>as we can see this runs very quickly even for relatively large gridsizes. The key to get high performance like this is to minimize the allocations inside the threaded loops, ideally to 0.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ * time: 32.7883460521698
+ 39.308007 seconds (11.21 M allocations: 3.880 GiB, 1.34% gc time, 8.63% compilation time)</code></pre><p>as we can see this runs very quickly even for relatively large gridsizes. The key to get high performance like this is to minimize the allocations inside the threaded loops, ideally to 0.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/gallery/quasi_incompressible_hyperelasticity/index.html b/dev/gallery/quasi_incompressible_hyperelasticity/index.html
index 737daa6d66..43a3011de0 100644
--- a/dev/gallery/quasi_incompressible_hyperelasticity/index.html
+++ b/dev/gallery/quasi_incompressible_hyperelasticity/index.html
@@ -485,4 +485,4 @@
quadratic_u = Lagrange{RefTetrahedron, 2}()^3
linear_p = Lagrange{RefTetrahedron, 1}()
-vol_def = solve(quadratic_u, linear_p)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+vol_def = solve(quadratic_u, linear_p)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/gallery/topology_optimization.ipynb b/dev/gallery/topology_optimization.ipynb
index 5e5bd38b94..685dba1589 100644
--- a/dev/gallery/topology_optimization.ipynb
+++ b/dev/gallery/topology_optimization.ipynb
@@ -827,7 +827,7 @@
" Starting Newton iterations\n",
"Converged at iteration number: 65\n",
"Rel. stiffness: 4.8466 \n",
- " 4.635604 seconds (2.45 M allocations: 2.016 GiB, 1.94% gc time, 6.47% compilation time)\n"
+ " 4.590804 seconds (2.45 M allocations: 2.016 GiB, 1.95% gc time, 6.62% compilation time)\n"
]
}
],
diff --git a/dev/gallery/topology_optimization/index.html b/dev/gallery/topology_optimization/index.html
index c80a06cfd5..70800aa298 100644
--- a/dev/gallery/topology_optimization/index.html
+++ b/dev/gallery/topology_optimization/index.html
@@ -365,7 +365,7 @@
Starting Newton iterations
Converged at iteration number: 65
Rel. stiffness: 4.8466
- 4.437066 seconds (2.24 M allocations: 2.005 GiB, 2.10% gc time, 1.95% compilation time)</code></pre><p>We observe, that the stiffness for the lower value of <span>$ra$</span> is higher, but also requires more iterations until convergence and finer structures to be manufactured, as can be seen in Figure 2:</p><p><img src="../bending.png" alt/></p><p><em>Figure 2</em>: Optimization results of the bending beam for smaller (left) and larger (right) value of the regularization parameter <span>$\beta$</span>.</p><p>To prove mesh independence, the user could vary the mesh resolution and compare the results.</p><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><div class="citation noncanonical"><dl><dt>[14]</dt><dd><div>D. R. Jantos, K. Hackl and P. Junker. <a href="https://doi.org/10.1002/nme.5988"><em>An accurate and fast regularization approach to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1002/nme.5988">International Journal for Numerical Methods in Engineering <strong>117</strong>, 991–1017</a> (2019).</div></dd><dt>[15]</dt><dd><div>M. Blaszczyk, D. R. Jantos and P. Junker. <a href="https://doi.org/10.1016/j.cma.2022.114698"><em>Application of Taylor series combined with the weighted least square method to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1016/j.cma.2022.114698">Computer Methods in Applied Mechanics and Engineering <strong>393</strong>, 114698</a> (2022).</div></dd></dl></div><h2 id="topology_optimization-plain-program"><a class="docs-heading-anchor" href="#topology_optimization-plain-program">Plain program</a><a id="topology_optimization-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#topology_optimization-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../topology_optimization.jl"><code>topology_optimization.jl</code></a>.</p><pre><code class="language-julia hljs">using Ferrite, SparseArrays, LinearAlgebra, Tensors, Printf
+ 4.456553 seconds (2.24 M allocations: 2.005 GiB, 2.18% gc time, 1.83% compilation time)</code></pre><p>We observe, that the stiffness for the lower value of <span>$ra$</span> is higher, but also requires more iterations until convergence and finer structures to be manufactured, as can be seen in Figure 2:</p><p><img src="../bending.png" alt/></p><p><em>Figure 2</em>: Optimization results of the bending beam for smaller (left) and larger (right) value of the regularization parameter <span>$\beta$</span>.</p><p>To prove mesh independence, the user could vary the mesh resolution and compare the results.</p><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><div class="citation noncanonical"><dl><dt>[14]</dt><dd><div>D. R. Jantos, K. Hackl and P. Junker. <a href="https://doi.org/10.1002/nme.5988"><em>An accurate and fast regularization approach to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1002/nme.5988">International Journal for Numerical Methods in Engineering <strong>117</strong>, 991–1017</a> (2019).</div></dd><dt>[15]</dt><dd><div>M. Blaszczyk, D. R. Jantos and P. Junker. <a href="https://doi.org/10.1016/j.cma.2022.114698"><em>Application of Taylor series combined with the weighted least square method to thermodynamic topology optimization</em></a>. <a href="https://doi.org/10.1016/j.cma.2022.114698">Computer Methods in Applied Mechanics and Engineering <strong>393</strong>, 114698</a> (2022).</div></dd></dl></div><h2 id="topology_optimization-plain-program"><a class="docs-heading-anchor" href="#topology_optimization-plain-program">Plain program</a><a id="topology_optimization-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#topology_optimization-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../topology_optimization.jl"><code>topology_optimization.jl</code></a>.</p><pre><code class="language-julia hljs">using Ferrite, SparseArrays, LinearAlgebra, Tensors, Printf
function create_grid(n)
corners = [
@@ -755,4 +755,4 @@
end
@time topopt(0.03, 0.5, 60, "large_radius"; output = :false);
-#topopt(0.02, 0.5, 60, "topopt_animation"; output=:true); # can be used to create animations</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+#topopt(0.02, 0.5, 60, "topopt_animation"; output=:true); # can be used to create animations</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/howto/index.html b/dev/howto/index.html
index 14e11c13e5..4ac32618c0 100644
--- a/dev/howto/index.html
+++ b/dev/howto/index.html
@@ -1,2 +1,2 @@
<!DOCTYPE html>
-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>How-to guide overview · Ferrite.jl</title><meta name="title" content="How-to guide overview · Ferrite.jl"/><meta property="og:title" content="How-to guide overview · Ferrite.jl"/><meta property="twitter:title" content="How-to guide overview · Ferrite.jl"/><meta name="description" content="Documentation for Ferrite.jl."/><meta property="og:description" content="Documentation for Ferrite.jl."/><meta property="twitter:description" content="Documentation for Ferrite.jl."/><meta property="og:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/howto/"/><meta property="twitter:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/howto/"/><link rel="canonical" href="https://ferrite-fem.github.io/Ferrite.jl/stable/howto/"/><script data-outdated-warner src="../assets/warner.js"></script><link 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GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/howto/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="How-to-guides"><a class="docs-heading-anchor" href="#How-to-guides">How-to guides</a><a id="How-to-guides-1"></a><a class="docs-heading-anchor-permalink" href="#How-to-guides" title="Permalink"></a></h1><p>This page gives an overview of the <em>how-to guides</em>. How-to guides address various common tasks one might want to do in a finite element program. Many of the guides are extensions, or build on top of, the tutorials and, therefore, some familiarity with Ferrite is assumed.</p><hr/><h4 id="[Post-processing-and-visualization](postprocessing.md)"><a class="docs-heading-anchor" href="#[Post-processing-and-visualization](postprocessing.md)"><a href="postprocessing/">Post processing and visualization</a></a><a id="[Post-processing-and-visualization](postprocessing.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Post-processing-and-visualization](postprocessing.md)" title="Permalink"></a></h4><p>This guide builds on top of <a href="../tutorials/heat_equation/">Tutorial 1: Heat equation</a> and discusses various post processsing techniques with the goal of visualizing primary fields (the finite element solution) and secondary quantities (e.g. fluxes, stresses, etc.). Concretely, this guide answers:</p><ul><li>How to visualize data from quadrature points?</li><li>How to evaluate the finite element solution, or secondary quantities, in arbitrary points of the domain?</li></ul><hr/><h4 id="[Multi-threaded-assembly](threaded_assembly.md)"><a class="docs-heading-anchor" href="#[Multi-threaded-assembly](threaded_assembly.md)"><a href="threaded_assembly/">Multi-threaded assembly</a></a><a id="[Multi-threaded-assembly](threaded_assembly.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Multi-threaded-assembly](threaded_assembly.md)" title="Permalink"></a></h4><p>This guide modifies <a href="../tutorials/linear_elasticity/">Tutorial 2: Linear elasticity</a> such that the program is using multi-threading to parallelize the assembly procedure. Concretely this shows how to use grid coloring and "scratch values" in order to use multi-threading without running into race-conditions.</p><hr/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reference/utils/">« Development utility functions</a><a class="docs-footer-nextpage" href="postprocessing/">Post processing and visualization »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. 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href="../reference/assembly/">Assembly</a></li><li><a class="tocitem" href="../reference/boundary_conditions/">Boundary conditions</a></li><li><a class="tocitem" href="../reference/grid/">Grid & AbstractGrid</a></li><li><a class="tocitem" href="../reference/export/">Postprocessing</a></li><li><a class="tocitem" href="../reference/utils/">Development utility functions</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-6" type="checkbox" checked/><label class="tocitem" for="menuitem-6"><span class="docs-label">How-to guides</span><i class="docs-chevron"></i></label><ul class="collapsed"><li class="is-active"><a class="tocitem" href>How-to guide overview</a></li><li><a class="tocitem" href="postprocessing/">Post processing and visualization</a></li><li><a class="tocitem" href="threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../gallery/">Code gallery</a></li><li><a class="tocitem" href="../devdocs/">Developer 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GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/howto/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="How-to-guides"><a class="docs-heading-anchor" href="#How-to-guides">How-to guides</a><a id="How-to-guides-1"></a><a class="docs-heading-anchor-permalink" href="#How-to-guides" title="Permalink"></a></h1><p>This page gives an overview of the <em>how-to guides</em>. How-to guides address various common tasks one might want to do in a finite element program. Many of the guides are extensions, or build on top of, the tutorials and, therefore, some familiarity with Ferrite is assumed.</p><hr/><h4 id="[Post-processing-and-visualization](postprocessing.md)"><a class="docs-heading-anchor" href="#[Post-processing-and-visualization](postprocessing.md)"><a href="postprocessing/">Post processing and visualization</a></a><a id="[Post-processing-and-visualization](postprocessing.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Post-processing-and-visualization](postprocessing.md)" title="Permalink"></a></h4><p>This guide builds on top of <a href="../tutorials/heat_equation/">Tutorial 1: Heat equation</a> and discusses various post processsing techniques with the goal of visualizing primary fields (the finite element solution) and secondary quantities (e.g. fluxes, stresses, etc.). Concretely, this guide answers:</p><ul><li>How to visualize data from quadrature points?</li><li>How to evaluate the finite element solution, or secondary quantities, in arbitrary points of the domain?</li></ul><hr/><h4 id="[Multi-threaded-assembly](threaded_assembly.md)"><a class="docs-heading-anchor" href="#[Multi-threaded-assembly](threaded_assembly.md)"><a href="threaded_assembly/">Multi-threaded assembly</a></a><a id="[Multi-threaded-assembly](threaded_assembly.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Multi-threaded-assembly](threaded_assembly.md)" title="Permalink"></a></h4><p>This guide modifies <a href="../tutorials/linear_elasticity/">Tutorial 2: Linear elasticity</a> such that the program is using multi-threading to parallelize the assembly procedure. Concretely this shows how to use grid coloring and "scratch values" in order to use multi-threading without running into race-conditions.</p><hr/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reference/utils/">« Development utility functions</a><a class="docs-footer-nextpage" href="postprocessing/">Post processing and visualization »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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diff --git a/dev/howto/postprocessing/a13d7c95.svg b/dev/howto/postprocessing/b5acc34e.svg
similarity index 83%
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similarity index 85%
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diff --git a/dev/howto/postprocessing/index.html b/dev/howto/postprocessing/index.html
index e701472aee..20697bd631 100644
--- a/dev/howto/postprocessing/index.html
+++ b/dev/howto/postprocessing/index.html
@@ -22,7 +22,7 @@
return q
end</code></pre><p>Now call the function to get all the fluxes.</p><pre><code class="language-julia hljs">q_gp = compute_heat_fluxes(cellvalues, dh, u);</code></pre><p>Next, create an <a href="../../reference/export/#Ferrite.L2Projector-Tuple{Ferrite.AbstractGrid}"><code>L2Projector</code></a> using the same interpolation as was used to approximate the temperature field. On instantiation, the projector assembles the coefficient matrix <code>M</code> and computes the Cholesky factorization of it. By doing so, the projector can be reused without having to invert <code>M</code> every time.</p><pre><code class="language-julia hljs">projector = L2Projector(ip, grid);</code></pre><p>Project the integration point values to the nodal values</p><pre><code class="language-julia hljs">q_projected = project(projector, q_gp, qr);</code></pre><h2 id="Exporting-to-VTK"><a class="docs-heading-anchor" href="#Exporting-to-VTK">Exporting to VTK</a><a id="Exporting-to-VTK-1"></a><a class="docs-heading-anchor-permalink" href="#Exporting-to-VTK" title="Permalink"></a></h2><p>To visualize the heat flux, we export the projected field <code>q_projected</code> to a VTK-file, which can be viewed in e.g. <a href="https://www.paraview.org/">ParaView</a>. The result is also visualized in <em>Figure 1</em>.</p><pre><code class="language-julia hljs">VTKGridFile("heat_equation_flux", grid) do vtk
write_projection(vtk, projector, q_projected, "q")
-end;</code></pre><h2 id="Point-evaluation"><a class="docs-heading-anchor" href="#Point-evaluation">Point evaluation</a><a id="Point-evaluation-1"></a><a class="docs-heading-anchor-permalink" href="#Point-evaluation" title="Permalink"></a></h2><p><img src="../heat_square_pointevaluation.png" alt/></p><p><em>Figure 2</em>: Visualization of the cut line where we want to compute the temperature and heat flux.</p><p>Consider a cut-line through the domain like the black line in <em>Figure 2</em> above. We will evaluate the temperature and the heat flux distribution along a horizontal line.</p><pre><code class="language-julia hljs">points = [Vec((x, 0.75)) for x in range(-1.0, 1.0, length = 101)];</code></pre><p>First, we need to generate a <code>PointEvalHandler</code>. This will find and store the cells containing the input points.</p><pre><code class="language-julia hljs">ph = PointEvalHandler(grid, points);</code></pre><p>After the L2-Projection, the heat fluxes <code>q_projected</code> are stored in the DoF-ordering determined by the projector's internal DoFHandler, so to evaluate the flux <code>q</code> at our points we give the <code>PointEvalHandler</code>, the <code>L2Projector</code> and the values <code>q_projected</code>.</p><pre><code class="language-julia hljs">q_points = evaluate_at_points(ph, projector, q_projected);</code></pre><p>We can also extract the field values, here the temperature, right away from the result vector of the simulation, that is stored in <code>u</code>. These values are stored in the order of our initial DofHandler so the input is not the <code>PointEvalHandler</code>, the original <code>DofHandler</code>, the dof-vector <code>u</code>, and (optionally for single-field problems) the name of the field. From the <code>L2Projection</code>, the values are stored in the order of the degrees of freedom.</p><pre><code class="language-julia hljs">u_points = evaluate_at_points(ph, dh, u, :u);</code></pre><p>Now, we can plot the temperature and flux values with the help of any plotting library, e.g. Plots.jl. To do this, we need to import the package:</p><pre><code class="language-julia hljs">import Plots</code></pre><p>Firstly, we are going to plot the temperature values along the given line.</p><pre><code class="language-julia hljs">Plots.plot(getindex.(points, 1), u_points, xlabel = "x (coordinate)", ylabel = "u (temperature)", label = nothing)</code></pre><img src="d671bea3.svg" alt="Example block output"/><p><em>Figure 3</em>: Temperature along the cut line from <em>Figure 2</em>.</p><p>Secondly, the horizontal heat flux (i.e. the first component of the heat flux vector) is plotted.</p><pre><code class="language-julia hljs">Plots.plot(getindex.(points, 1), getindex.(q_points, 1), xlabel = "x (coordinate)", ylabel = "q_x (flux in x-direction)", label = nothing)</code></pre><img src="a13d7c95.svg" alt="Example block output"/><p><em>Figure 4</em>: <span>$x$</span>-component of the flux along the cut line from <em>Figure 2</em>.</p><h2 id="postprocessing-plain-program"><a class="docs-heading-anchor" href="#postprocessing-plain-program">Plain program</a><a id="postprocessing-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#postprocessing-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../postprocessing.jl"><code>postprocessing.jl</code></a>.</p><pre><code class="language-julia hljs">include("../tutorials/heat_equation.jl");
+end;</code></pre><h2 id="Point-evaluation"><a class="docs-heading-anchor" href="#Point-evaluation">Point evaluation</a><a id="Point-evaluation-1"></a><a class="docs-heading-anchor-permalink" href="#Point-evaluation" title="Permalink"></a></h2><p><img src="../heat_square_pointevaluation.png" alt/></p><p><em>Figure 2</em>: Visualization of the cut line where we want to compute the temperature and heat flux.</p><p>Consider a cut-line through the domain like the black line in <em>Figure 2</em> above. We will evaluate the temperature and the heat flux distribution along a horizontal line.</p><pre><code class="language-julia hljs">points = [Vec((x, 0.75)) for x in range(-1.0, 1.0, length = 101)];</code></pre><p>First, we need to generate a <code>PointEvalHandler</code>. This will find and store the cells containing the input points.</p><pre><code class="language-julia hljs">ph = PointEvalHandler(grid, points);</code></pre><p>After the L2-Projection, the heat fluxes <code>q_projected</code> are stored in the DoF-ordering determined by the projector's internal DoFHandler, so to evaluate the flux <code>q</code> at our points we give the <code>PointEvalHandler</code>, the <code>L2Projector</code> and the values <code>q_projected</code>.</p><pre><code class="language-julia hljs">q_points = evaluate_at_points(ph, projector, q_projected);</code></pre><p>We can also extract the field values, here the temperature, right away from the result vector of the simulation, that is stored in <code>u</code>. These values are stored in the order of our initial DofHandler so the input is not the <code>PointEvalHandler</code>, the original <code>DofHandler</code>, the dof-vector <code>u</code>, and (optionally for single-field problems) the name of the field. From the <code>L2Projection</code>, the values are stored in the order of the degrees of freedom.</p><pre><code class="language-julia hljs">u_points = evaluate_at_points(ph, dh, u, :u);</code></pre><p>Now, we can plot the temperature and flux values with the help of any plotting library, e.g. Plots.jl. To do this, we need to import the package:</p><pre><code class="language-julia hljs">import Plots</code></pre><p>Firstly, we are going to plot the temperature values along the given line.</p><pre><code class="language-julia hljs">Plots.plot(getindex.(points, 1), u_points, xlabel = "x (coordinate)", ylabel = "u (temperature)", label = nothing)</code></pre><img src="f282e318.svg" alt="Example block output"/><p><em>Figure 3</em>: Temperature along the cut line from <em>Figure 2</em>.</p><p>Secondly, the horizontal heat flux (i.e. the first component of the heat flux vector) is plotted.</p><pre><code class="language-julia hljs">Plots.plot(getindex.(points, 1), getindex.(q_points, 1), xlabel = "x (coordinate)", ylabel = "q_x (flux in x-direction)", label = nothing)</code></pre><img src="b5acc34e.svg" alt="Example block output"/><p><em>Figure 4</em>: <span>$x$</span>-component of the flux along the cut line from <em>Figure 2</em>.</p><h2 id="postprocessing-plain-program"><a class="docs-heading-anchor" href="#postprocessing-plain-program">Plain program</a><a id="postprocessing-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#postprocessing-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../postprocessing.jl"><code>postprocessing.jl</code></a>.</p><pre><code class="language-julia hljs">include("../tutorials/heat_equation.jl");
function compute_heat_fluxes(cellvalues::CellValues, dh::DofHandler, a::AbstractVector{T}) where {T}
@@ -69,4 +69,4 @@
Plots.plot(getindex.(points, 1), u_points, xlabel = "x (coordinate)", ylabel = "u (temperature)", label = nothing)
-Plots.plot(getindex.(points, 1), getindex.(q_points, 1), xlabel = "x (coordinate)", ylabel = "q_x (flux in x-direction)", label = nothing)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« How-to guide overview</a><a class="docs-footer-nextpage" href="../threaded_assembly/">Multi-threaded assembly »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+Plots.plot(getindex.(points, 1), getindex.(q_points, 1), xlabel = "x (coordinate)", ylabel = "q_x (flux in x-direction)", label = nothing)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« How-to guide overview</a><a class="docs-footer-nextpage" href="../threaded_assembly/">Multi-threaded assembly »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/howto/threaded_assembly/index.html b/dev/howto/threaded_assembly/index.html
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@time assemble_global!(K, f, dh, colors, cellvalues; ntasks = ntasks)
return
end
-nothing # hide</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../postprocessing/">« Post processing and visualization</a><a class="docs-footer-nextpage" href="../../gallery/">Code gallery »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+nothing # hide</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../postprocessing/">« Post processing and visualization</a><a class="docs-footer-nextpage" href="../../gallery/">Code gallery »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/index.html b/dev/index.html
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-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · Ferrite.jl</title><meta name="title" content="Home · Ferrite.jl"/><meta property="og:title" content="Home · Ferrite.jl"/><meta property="twitter:title" content="Home · Ferrite.jl"/><meta name="description" content="Documentation for Ferrite.jl."/><meta property="og:description" content="Documentation for Ferrite.jl."/><meta property="twitter:description" content="Documentation for Ferrite.jl."/><meta property="og:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/"/><meta property="twitter:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/"/><link rel="canonical" href="https://ferrite-fem.github.io/Ferrite.jl/stable/"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link 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rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href><img src="assets/logo.svg" alt="Ferrite.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href>Ferrite.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#How-the-documentation-is-organized"><span>How the documentation is organized</span></a></li><li><a class="tocitem" href="#Getting-started"><span>Getting started</span></a></li><li><a class="tocitem" href="#Contributing-to-Ferrite"><span>Contributing to Ferrite</span></a></li></ul></li><li><input class="collapse-toggle" id="menuitem-3" type="checkbox"/><label class="tocitem" for="menuitem-3"><span class="docs-label">Tutorials</span><i 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DifferentialEquations.jl</a></li><li><a class="tocitem" href="tutorials/reactive_surface/">Reactive surface</a></li><li><a class="tocitem" href="tutorials/linear_shell/">Linear shell</a></li><li><a class="tocitem" href="tutorials/dg_heat_equation/">Discontinuous Galerkin heat equation</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-4" type="checkbox"/><label class="tocitem" for="menuitem-4"><span class="docs-label">Topic guides</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="topics/">Topic guide overview</a></li><li><a class="tocitem" href="topics/fe_intro/">Introduction to FEM</a></li><li><a class="tocitem" href="topics/reference_shapes/">Reference shapes</a></li><li><a class="tocitem" href="topics/FEValues/">FEValues</a></li><li><a class="tocitem" href="topics/degrees_of_freedom/">Degrees of Freedom</a></li><li><a class="tocitem" href="topics/sparse_matrix/">Sparsity pattern and sparse matrices</a></li><li><a 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and sparse matrices</a></li><li><a class="tocitem" href="reference/assembly/">Assembly</a></li><li><a class="tocitem" href="reference/boundary_conditions/">Boundary conditions</a></li><li><a class="tocitem" href="reference/grid/">Grid & AbstractGrid</a></li><li><a class="tocitem" href="reference/export/">Postprocessing</a></li><li><a class="tocitem" href="reference/utils/">Development utility functions</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-6" type="checkbox"/><label class="tocitem" for="menuitem-6"><span class="docs-label">How-to guides</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="howto/">How-to guide overview</a></li><li><a class="tocitem" href="howto/postprocessing/">Post processing and visualization</a></li><li><a class="tocitem" href="howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="gallery/">Code gallery</a></li><li><a class="tocitem" href="devdocs/">Developer documentation</a></li><li><a class="tocitem" href="cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Ferrite.jl"><a class="docs-heading-anchor" href="#Ferrite.jl">Ferrite.jl</a><a id="Ferrite.jl-1"></a><a class="docs-heading-anchor-permalink" href="#Ferrite.jl" title="Permalink"></a></h1><p>Welcome to the documentation for Ferrite.jl! Ferrite is a finite element toolbox that provides functionalities to implement finite element analysis in <a href="https://github.com/JuliaLang/julia">Julia</a>. The aim is to be i) general, ii) performant, and iii) to keep mathematical abstractions.</p><div class="admonition is-info"><header class="admonition-header">Upgrading code from version 0.3.x to version 1.0</header><div class="admonition-body"><p>Ferrite version 1.0 contains a number of breaking changes compared to version 0.3.x. The <a href="changelog/">Changelog</a> documents all changes and there is also a section specifically for <a href="changelog/#Upgrading-code-from-Ferrite-0.3-to-1.0">Upgrading code from Ferrite 0.3 to 1.0</a>.</p></div></div><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Please help improve this documentation – if something confuses you, chances are you're not alone. It's easy to do as you read along: just click on the "Edit on GitHub" link at the top of each page, and then <a href="https://help.github.com/articles/editing-files-in-another-user-s-repository/">edit the files directly in your browser</a>. Your changes will be vetted by developers before becoming permanent, so don't worry about whether you might say something wrong. See also <a href="#Contributing-to-Ferrite">Contributing to Ferrite</a> for more details.</p></div></div><h2 id="How-the-documentation-is-organized"><a class="docs-heading-anchor" href="#How-the-documentation-is-organized">How the documentation is organized</a><a id="How-the-documentation-is-organized-1"></a><a class="docs-heading-anchor-permalink" href="#How-the-documentation-is-organized" title="Permalink"></a></h2><p>This high level view of the documentation structure will help you find what you are looking for. The document is organized as follows<sup class="footnote-reference"><a id="citeref-1" href="#footnote-1">[1]</a></sup>:</p><ul><li><a href="tutorials/"><strong>Tutorials</strong></a> are thoroughly documented examples which guides you through the process of solving partial differential equations using Ferrite.</li><li><a href="topics/"><strong>Topic guides</strong></a> contains more in-depth explanations and discussions about finite element programming concepts and ideas, and specifically how these are realized in Ferrite.</li><li><a href="reference/"><strong>Reference</strong></a> contains the technical API reference of functions and methods (e.g. the documentation strings).</li><li><a href="howto/"><strong>How-to guides</strong></a> will guide you through the steps involved in addressing common tasks and use-cases. These usually build on top of the tutorials and thus assume basic knowledge of how Ferrite works.</li></ul><p>The four sections above form the main user-facing parts of the documentation. In addition, the document also contain the following sections:</p><ul><li><a href="gallery/"><strong>Code gallery</strong></a> contain user contributed example programs showcasing what can be done with Ferrite.</li><li><a href="changelog/"><strong>Changelog</strong></a> contain release notes and information about how to upgrade between releases.</li><li><a href="devdocs/"><strong>Developer documentation</strong></a> contain documentation of Ferrite internal code and is mainly targeted at developers of Ferrite.</li></ul><h2 id="Getting-started"><a class="docs-heading-anchor" href="#Getting-started">Getting started</a><a id="Getting-started-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-started" title="Permalink"></a></h2><p>As a new user of Ferrite it is suggested to start working with the tutorials before using Ferrite to tackle the specific equation you ultimately want to solve. The tutorials start with explaining the basic concepts and then increase in complexity. Understanding the first tutorial program, <a href="tutorials/heat_equation/#tutorial-heat-equation">solving the heat equation</a>, is essential in order to understand how Ferrite works. Already this rather simple program discusses many of the important concepts. See the <a href="tutorials/#Tutorials">tutorials overview</a> for suggestion on how to progress to more advanced usage.</p><h3 id="Getting-help"><a class="docs-heading-anchor" href="#Getting-help">Getting help</a><a id="Getting-help-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-help" title="Permalink"></a></h3><p>If you have questions about Ferrite it is suggested to use the <code>#ferrite-fem</code> channel on the <a href="https://julialang.org/slack/">Julia Slack</a>, or the <code>#Ferrite.jl</code> stream on <a href="https://julialang.zulipchat.com/">Zulip</a>. Alternatively you can use the <a href="https://github.com/Ferrite-FEM/Ferrite.jl/discussions">discussion forum</a> on the GitHub repository.</p><h3 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h3><p>To use Ferrite you first need to install Julia, see <a href="https://julialang.org/">https://julialang.org/</a> for details. Installing Ferrite can then be done from the Pkg REPL; press <code>]</code> at the <code>julia></code> promp to enter <code>pkg></code> mode:</p><pre><code class="nohighlight hljs">pkg> add Ferrite</code></pre><p>This will install Ferrite and all necessary dependencies. Press backspace to get back to the <code>julia></code> prompt. (See the <a href="https://pkgdocs.julialang.org/">documentation for Pkg</a>, Julia's package manager, for more help regarding package installation and project management.)</p><p>Finally, to load Ferrite, use</p><pre><code class="language-julia hljs">using Ferrite</code></pre><p>You are now all set to start using Ferrite!</p><h2 id="Contributing-to-Ferrite"><a class="docs-heading-anchor" href="#Contributing-to-Ferrite">Contributing to Ferrite</a><a id="Contributing-to-Ferrite-1"></a><a class="docs-heading-anchor-permalink" href="#Contributing-to-Ferrite" title="Permalink"></a></h2><p>Ferrite is still under active development. If you find a bug, or have ideas for improvements, you are encouraged to interact with the developers on the <a href="https://github.com/Ferrite-FEM/Ferrite.jl">Ferrite GitHub repository</a>. There is also a thorough contributor guide which can be found in <a href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/CONTRIBUTING.md">CONTRIBUTING.md</a>.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>The organization of the document follows the <a href="https://diataxis.fr">Diátaxis Framework</a>.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="changelog/">Changelog »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. 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href="devdocs/">Developer documentation</a></li><li><a class="tocitem" href="cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Ferrite.jl"><a class="docs-heading-anchor" href="#Ferrite.jl">Ferrite.jl</a><a id="Ferrite.jl-1"></a><a class="docs-heading-anchor-permalink" href="#Ferrite.jl" title="Permalink"></a></h1><p>Welcome to the documentation for Ferrite.jl! Ferrite is a finite element toolbox that provides functionalities to implement finite element analysis in <a href="https://github.com/JuliaLang/julia">Julia</a>. The aim is to be i) general, ii) performant, and iii) to keep mathematical abstractions.</p><div class="admonition is-info"><header class="admonition-header">Upgrading code from version 0.3.x to version 1.0</header><div class="admonition-body"><p>Ferrite version 1.0 contains a number of breaking changes compared to version 0.3.x. The <a href="changelog/">Changelog</a> documents all changes and there is also a section specifically for <a href="changelog/#Upgrading-code-from-Ferrite-0.3-to-1.0">Upgrading code from Ferrite 0.3 to 1.0</a>.</p></div></div><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Please help improve this documentation – if something confuses you, chances are you're not alone. It's easy to do as you read along: just click on the "Edit on GitHub" link at the top of each page, and then <a href="https://help.github.com/articles/editing-files-in-another-user-s-repository/">edit the files directly in your browser</a>. Your changes will be vetted by developers before becoming permanent, so don't worry about whether you might say something wrong. See also <a href="#Contributing-to-Ferrite">Contributing to Ferrite</a> for more details.</p></div></div><h2 id="How-the-documentation-is-organized"><a class="docs-heading-anchor" href="#How-the-documentation-is-organized">How the documentation is organized</a><a id="How-the-documentation-is-organized-1"></a><a class="docs-heading-anchor-permalink" href="#How-the-documentation-is-organized" title="Permalink"></a></h2><p>This high level view of the documentation structure will help you find what you are looking for. The document is organized as follows<sup class="footnote-reference"><a id="citeref-1" href="#footnote-1">[1]</a></sup>:</p><ul><li><a href="tutorials/"><strong>Tutorials</strong></a> are thoroughly documented examples which guides you through the process of solving partial differential equations using Ferrite.</li><li><a href="topics/"><strong>Topic guides</strong></a> contains more in-depth explanations and discussions about finite element programming concepts and ideas, and specifically how these are realized in Ferrite.</li><li><a href="reference/"><strong>Reference</strong></a> contains the technical API reference of functions and methods (e.g. the documentation strings).</li><li><a href="howto/"><strong>How-to guides</strong></a> will guide you through the steps involved in addressing common tasks and use-cases. These usually build on top of the tutorials and thus assume basic knowledge of how Ferrite works.</li></ul><p>The four sections above form the main user-facing parts of the documentation. In addition, the document also contain the following sections:</p><ul><li><a href="gallery/"><strong>Code gallery</strong></a> contain user contributed example programs showcasing what can be done with Ferrite.</li><li><a href="changelog/"><strong>Changelog</strong></a> contain release notes and information about how to upgrade between releases.</li><li><a href="devdocs/"><strong>Developer documentation</strong></a> contain documentation of Ferrite internal code and is mainly targeted at developers of Ferrite.</li></ul><h2 id="Getting-started"><a class="docs-heading-anchor" href="#Getting-started">Getting started</a><a id="Getting-started-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-started" title="Permalink"></a></h2><p>As a new user of Ferrite it is suggested to start working with the tutorials before using Ferrite to tackle the specific equation you ultimately want to solve. The tutorials start with explaining the basic concepts and then increase in complexity. Understanding the first tutorial program, <a href="tutorials/heat_equation/#tutorial-heat-equation">solving the heat equation</a>, is essential in order to understand how Ferrite works. Already this rather simple program discusses many of the important concepts. See the <a href="tutorials/#Tutorials">tutorials overview</a> for suggestion on how to progress to more advanced usage.</p><h3 id="Getting-help"><a class="docs-heading-anchor" href="#Getting-help">Getting help</a><a id="Getting-help-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-help" title="Permalink"></a></h3><p>If you have questions about Ferrite it is suggested to use the <code>#ferrite-fem</code> channel on the <a href="https://julialang.org/slack/">Julia Slack</a>, or the <code>#Ferrite.jl</code> stream on <a href="https://julialang.zulipchat.com/">Zulip</a>. Alternatively you can use the <a href="https://github.com/Ferrite-FEM/Ferrite.jl/discussions">discussion forum</a> on the GitHub repository.</p><h3 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h3><p>To use Ferrite you first need to install Julia, see <a href="https://julialang.org/">https://julialang.org/</a> for details. Installing Ferrite can then be done from the Pkg REPL; press <code>]</code> at the <code>julia></code> promp to enter <code>pkg></code> mode:</p><pre><code class="nohighlight hljs">pkg> add Ferrite</code></pre><p>This will install Ferrite and all necessary dependencies. Press backspace to get back to the <code>julia></code> prompt. (See the <a href="https://pkgdocs.julialang.org/">documentation for Pkg</a>, Julia's package manager, for more help regarding package installation and project management.)</p><p>Finally, to load Ferrite, use</p><pre><code class="language-julia hljs">using Ferrite</code></pre><p>You are now all set to start using Ferrite!</p><h2 id="Contributing-to-Ferrite"><a class="docs-heading-anchor" href="#Contributing-to-Ferrite">Contributing to Ferrite</a><a id="Contributing-to-Ferrite-1"></a><a class="docs-heading-anchor-permalink" href="#Contributing-to-Ferrite" title="Permalink"></a></h2><p>Ferrite is still under active development. If you find a bug, or have ideas for improvements, you are encouraged to interact with the developers on the <a href="https://github.com/Ferrite-FEM/Ferrite.jl">Ferrite GitHub repository</a>. There is also a thorough contributor guide which can be found in <a href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/CONTRIBUTING.md">CONTRIBUTING.md</a>.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>The organization of the document follows the <a href="https://diataxis.fr">Diátaxis Framework</a>.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="changelog/">Changelog »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. 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class="tocitem" href="../../devdocs/">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">API reference</a></li><li class="is-active"><a href>Assembly</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Assembly</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/assembly.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Assembly"><a class="docs-heading-anchor" href="#Assembly">Assembly</a><a id="Assembly-1"></a><a class="docs-heading-anchor-permalink" href="#Assembly" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.start_assemble" href="#Ferrite.start_assemble"><code>Ferrite.start_assemble</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">start_assemble(K::AbstractSparseMatrixCSC; fillzero::Bool=true) -> CSCAssembler
start_assemble(K::AbstractSparseMatrixCSC, f::Vector; fillzero::Bool=true) -> CSCAssembler</code></pre><p>Create a <code>CSCAssembler</code> from the matrix <code>K</code> and optional vector <code>f</code>.</p><pre><code class="nohighlight hljs">start_assemble(K::Symmetric{AbstractSparseMatrixCSC}; fillzero::Bool=true) -> SymmetricCSCAssembler
-start_assemble(K::Symmetric{AbstractSparseMatrixCSC}, f::Vector=Td[]; fillzero::Bool=true) -> SymmetricCSCAssembler</code></pre><p>Create a <code>SymmetricCSCAssembler</code> from the matrix <code>K</code> and optional vector <code>f</code>.</p><p><code>CSCAssembler</code> and <code>SymmetricCSCAssembler</code> allocate workspace necessary for efficient matrix assembly. To assemble the contribution from an element, use <a href="#Ferrite.assemble!"><code>assemble!</code></a>.</p><p>The keyword argument <code>fillzero</code> can be set to <code>false</code> if <code>K</code> and <code>f</code> should not be zeroed out, but instead keep their current values.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L207-L224">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.assemble!" href="#Ferrite.assemble!"><code>Ferrite.assemble!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">assemble!(a::COOAssembler, dofs, Ke)
-assemble!(a::COOAssembler, dofs, Ke, fe)</code></pre><p>Assembles the element matrix <code>Ke</code> and element vector <code>fe</code> into <code>a</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L70-L75">source</a></section><section><div><pre><code class="language-julia hljs">assemble!(a::COOAssembler, rowdofs, coldofs, Ke)</code></pre><p>Assembles the matrix <code>Ke</code> into <code>a</code> according to the dofs specified by <code>rowdofs</code> and <code>coldofs</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L99-L103">source</a></section><section><div><pre><code class="language-julia hljs">assemble!(g, dofs, ge)</code></pre><p>Assembles the element residual <code>ge</code> into the global residual vector <code>g</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L149-L153">source</a></section><section><div><pre><code class="language-julia hljs">assemble!(A::AbstractAssembler, dofs::AbstractVector{Int}, Ke::AbstractMatrix)
-assemble!(A::AbstractAssembler, dofs::AbstractVector{Int}, Ke::AbstractMatrix, fe::AbstractVector)</code></pre><p>Assemble the element stiffness matrix <code>Ke</code> (and optional force vector <code>fe</code>) into the global stiffness (and force) in <code>A</code>, given the element degrees of freedom <code>dofs</code>.</p><p>This is equivalent to <code>K[dofs, dofs] += Ke</code> and <code>f[dofs] += fe</code>, where <code>K</code> is the global stiffness matrix and <code>f</code> the global force/residual vector, but more efficient.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L240-L249">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.finish_assemble" href="#Ferrite.finish_assemble"><code>Ferrite.finish_assemble</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">finish_assemble(a::COOAssembler) -> K, f</code></pre><p>Finalize the assembly and return the sparse matrix <code>K::SparseMatrixCSC</code> and vector <code>f::Vector</code>. If the assembler have not been used for vector assembly, <code>f</code> is an empty vector.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L121-L127">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sparsity_pattern/">« Sparsity pattern and sparse matrices</a><a class="docs-footer-nextpage" href="../boundary_conditions/">Boundary conditions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+start_assemble(K::Symmetric{AbstractSparseMatrixCSC}, f::Vector=Td[]; fillzero::Bool=true) -> SymmetricCSCAssembler</code></pre><p>Create a <code>SymmetricCSCAssembler</code> from the matrix <code>K</code> and optional vector <code>f</code>.</p><p><code>CSCAssembler</code> and <code>SymmetricCSCAssembler</code> allocate workspace necessary for efficient matrix assembly. To assemble the contribution from an element, use <a href="#Ferrite.assemble!"><code>assemble!</code></a>.</p><p>The keyword argument <code>fillzero</code> can be set to <code>false</code> if <code>K</code> and <code>f</code> should not be zeroed out, but instead keep their current values.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L207-L224">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.assemble!" href="#Ferrite.assemble!"><code>Ferrite.assemble!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">assemble!(a::COOAssembler, dofs, Ke)
+assemble!(a::COOAssembler, dofs, Ke, fe)</code></pre><p>Assembles the element matrix <code>Ke</code> and element vector <code>fe</code> into <code>a</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L70-L75">source</a></section><section><div><pre><code class="language-julia hljs">assemble!(a::COOAssembler, rowdofs, coldofs, Ke)</code></pre><p>Assembles the matrix <code>Ke</code> into <code>a</code> according to the dofs specified by <code>rowdofs</code> and <code>coldofs</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L99-L103">source</a></section><section><div><pre><code class="language-julia hljs">assemble!(g, dofs, ge)</code></pre><p>Assembles the element residual <code>ge</code> into the global residual vector <code>g</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L149-L153">source</a></section><section><div><pre><code class="language-julia hljs">assemble!(A::AbstractAssembler, dofs::AbstractVector{Int}, Ke::AbstractMatrix)
+assemble!(A::AbstractAssembler, dofs::AbstractVector{Int}, Ke::AbstractMatrix, fe::AbstractVector)</code></pre><p>Assemble the element stiffness matrix <code>Ke</code> (and optional force vector <code>fe</code>) into the global stiffness (and force) in <code>A</code>, given the element degrees of freedom <code>dofs</code>.</p><p>This is equivalent to <code>K[dofs, dofs] += Ke</code> and <code>f[dofs] += fe</code>, where <code>K</code> is the global stiffness matrix and <code>f</code> the global force/residual vector, but more efficient.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L240-L249">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.finish_assemble" href="#Ferrite.finish_assemble"><code>Ferrite.finish_assemble</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">finish_assemble(a::COOAssembler) -> K, f</code></pre><p>Finalize the assembly and return the sparse matrix <code>K::SparseMatrixCSC</code> and vector <code>f::Vector</code>. If the assembler have not been used for vector assembly, <code>f</code> is an empty vector.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L121-L127">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sparsity_pattern/">« Sparsity pattern and sparse matrices</a><a class="docs-footer-nextpage" href="../boundary_conditions/">Boundary conditions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="is-active"><a href>Boundary conditions</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/boundary_conditions.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Boundary-conditions"><a class="docs-heading-anchor" href="#Boundary-conditions">Boundary conditions</a><a id="Boundary-conditions-1"></a><a class="docs-heading-anchor-permalink" href="#Boundary-conditions" title="Permalink"></a></h1><ul><li><a href="#Ferrite.ConstraintHandler"><code>Ferrite.ConstraintHandler</code></a></li><li><a href="#Ferrite.Dirichlet"><code>Ferrite.Dirichlet</code></a></li><li><a href="#Ferrite.PeriodicDirichlet"><code>Ferrite.PeriodicDirichlet</code></a></li><li><a href="#Ferrite.RHSData"><code>Ferrite.RHSData</code></a></li><li><a href="#Ferrite.add!"><code>Ferrite.add!</code></a></li><li><a href="#Ferrite.apply!"><code>Ferrite.apply!</code></a></li><li><a href="#Ferrite.apply_analytical!"><code>Ferrite.apply_analytical!</code></a></li><li><a href="#Ferrite.apply_assemble!"><code>Ferrite.apply_assemble!</code></a></li><li><a href="#Ferrite.apply_local!"><code>Ferrite.apply_local!</code></a></li><li><a href="#Ferrite.apply_rhs!"><code>Ferrite.apply_rhs!</code></a></li><li><a href="#Ferrite.apply_zero!"><code>Ferrite.apply_zero!</code></a></li><li><a href="#Ferrite.close!"><code>Ferrite.close!</code></a></li><li><a href="#Ferrite.collect_periodic_facets"><code>Ferrite.collect_periodic_facets</code></a></li><li><a href="#Ferrite.collect_periodic_facets!"><code>Ferrite.collect_periodic_facets!</code></a></li><li><a href="#Ferrite.get_rhs_data"><code>Ferrite.get_rhs_data</code></a></li><li><a href="#Ferrite.update!"><code>Ferrite.update!</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ConstraintHandler" href="#Ferrite.ConstraintHandler"><code>Ferrite.ConstraintHandler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ConstraintHandler([T=Float64], dh::AbstractDofHandler)</code></pre><p>A collection of constraints associated with the dof handler <code>dh</code>. <code>T</code> is the numeric type for stored values.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L78-L83">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Dirichlet" href="#Ferrite.Dirichlet"><code>Ferrite.Dirichlet</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Dirichlet(u::Symbol, ∂Ω::AbstractVecOrSet, f::Function, components=nothing)</code></pre><p>Create a Dirichlet boundary condition on <code>u</code> on the <code>∂Ω</code> part of the boundary. <code>f</code> is a function of the form <code>f(x)</code> or <code>f(x, t)</code> where <code>x</code> is the spatial coordinate and <code>t</code> is the current time, and returns the prescribed value. <code>components</code> specify the components of <code>u</code> that are prescribed by this condition. By default all components of <code>u</code> are prescribed.</p><p>The set, <code>∂Ω</code>, can be an <code>AbstractSet</code> or <code>AbstractVector</code> with elements of type <a href="../grid/#Ferrite.FacetIndex"><code>FacetIndex</code></a>, <a href="../grid/#Ferrite.FaceIndex"><code>FaceIndex</code></a>, <a href="../grid/#Ferrite.EdgeIndex"><code>EdgeIndex</code></a>, <a href="../grid/#Ferrite.VertexIndex"><code>VertexIndex</code></a>, or <code>Int</code>. For most cases, the element type is <code>FacetIndex</code>, as shown below. To constrain a single point, using <code>VertexIndex</code> is recommended, but it is also possible to constrain a specific nodes by giving the node numbers via <code>Int</code> elements. To constrain e.g. an edge in 3d <code>EdgeIndex</code> elements can be given.</p><p>For example, here we create a Dirichlet condition for the <code>:u</code> field, on the facetset called <code>∂Ω</code> and the value given by the <code>sin</code> function:</p><p><em>Examples</em></p><pre><code class="language-julia hljs"># Obtain the facetset from the grid
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class="is-active"><a href>Boundary conditions</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/boundary_conditions.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Boundary-conditions"><a class="docs-heading-anchor" href="#Boundary-conditions">Boundary conditions</a><a id="Boundary-conditions-1"></a><a class="docs-heading-anchor-permalink" href="#Boundary-conditions" title="Permalink"></a></h1><ul><li><a href="#Ferrite.ConstraintHandler"><code>Ferrite.ConstraintHandler</code></a></li><li><a href="#Ferrite.Dirichlet"><code>Ferrite.Dirichlet</code></a></li><li><a href="#Ferrite.PeriodicDirichlet"><code>Ferrite.PeriodicDirichlet</code></a></li><li><a href="#Ferrite.RHSData"><code>Ferrite.RHSData</code></a></li><li><a href="#Ferrite.add!"><code>Ferrite.add!</code></a></li><li><a href="#Ferrite.apply!"><code>Ferrite.apply!</code></a></li><li><a href="#Ferrite.apply_analytical!"><code>Ferrite.apply_analytical!</code></a></li><li><a href="#Ferrite.apply_assemble!"><code>Ferrite.apply_assemble!</code></a></li><li><a href="#Ferrite.apply_local!"><code>Ferrite.apply_local!</code></a></li><li><a href="#Ferrite.apply_rhs!"><code>Ferrite.apply_rhs!</code></a></li><li><a href="#Ferrite.apply_zero!"><code>Ferrite.apply_zero!</code></a></li><li><a href="#Ferrite.close!"><code>Ferrite.close!</code></a></li><li><a href="#Ferrite.collect_periodic_facets"><code>Ferrite.collect_periodic_facets</code></a></li><li><a href="#Ferrite.collect_periodic_facets!"><code>Ferrite.collect_periodic_facets!</code></a></li><li><a href="#Ferrite.get_rhs_data"><code>Ferrite.get_rhs_data</code></a></li><li><a href="#Ferrite.update!"><code>Ferrite.update!</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ConstraintHandler" href="#Ferrite.ConstraintHandler"><code>Ferrite.ConstraintHandler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ConstraintHandler([T=Float64], dh::AbstractDofHandler)</code></pre><p>A collection of constraints associated with the dof handler <code>dh</code>. <code>T</code> is the numeric type for stored values.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L78-L83">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Dirichlet" href="#Ferrite.Dirichlet"><code>Ferrite.Dirichlet</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Dirichlet(u::Symbol, ∂Ω::AbstractVecOrSet, f::Function, components=nothing)</code></pre><p>Create a Dirichlet boundary condition on <code>u</code> on the <code>∂Ω</code> part of the boundary. <code>f</code> is a function of the form <code>f(x)</code> or <code>f(x, t)</code> where <code>x</code> is the spatial coordinate and <code>t</code> is the current time, and returns the prescribed value. <code>components</code> specify the components of <code>u</code> that are prescribed by this condition. By default all components of <code>u</code> are prescribed.</p><p>The set, <code>∂Ω</code>, can be an <code>AbstractSet</code> or <code>AbstractVector</code> with elements of type <a href="../grid/#Ferrite.FacetIndex"><code>FacetIndex</code></a>, <a href="../grid/#Ferrite.FaceIndex"><code>FaceIndex</code></a>, <a href="../grid/#Ferrite.EdgeIndex"><code>EdgeIndex</code></a>, <a href="../grid/#Ferrite.VertexIndex"><code>VertexIndex</code></a>, or <code>Int</code>. For most cases, the element type is <code>FacetIndex</code>, as shown below. To constrain a single point, using <code>VertexIndex</code> is recommended, but it is also possible to constrain a specific nodes by giving the node numbers via <code>Int</code> elements. To constrain e.g. an edge in 3d <code>EdgeIndex</code> elements can be given.</p><p>For example, here we create a Dirichlet condition for the <code>:u</code> field, on the facetset called <code>∂Ω</code> and the value given by the <code>sin</code> function:</p><p><em>Examples</em></p><pre><code class="language-julia hljs"># Obtain the facetset from the grid
∂Ω = getfacetset(grid, "boundary-1")
# Prescribe scalar field :s on ∂Ω to sin(t)
@@ -9,26 +9,26 @@
dbc = Dirichlet(:v, ∂Ω, x -> 0 * x)
# Prescribe component 2 and 3 of vector field :v on ∂Ω to [sin(t), cos(t)]
-dbc = Dirichlet(:v, ∂Ω, (x, t) -> [sin(t), cos(t)], [2, 3])</code></pre><p><code>Dirichlet</code> boundary conditions are added to a <a href="#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> which applies the condition via <a href="#Ferrite.apply!"><code>apply!</code></a> and/or <a href="#Ferrite.apply_zero!"><code>apply_zero!</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L2-L40">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PeriodicDirichlet" href="#Ferrite.PeriodicDirichlet"><code>Ferrite.PeriodicDirichlet</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PeriodicDirichlet(u::Symbol, facet_mapping, components=nothing)
+dbc = Dirichlet(:v, ∂Ω, (x, t) -> [sin(t), cos(t)], [2, 3])</code></pre><p><code>Dirichlet</code> boundary conditions are added to a <a href="#Ferrite.ConstraintHandler"><code>ConstraintHandler</code></a> which applies the condition via <a href="#Ferrite.apply!"><code>apply!</code></a> and/or <a href="#Ferrite.apply_zero!"><code>apply_zero!</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L2-L40">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PeriodicDirichlet" href="#Ferrite.PeriodicDirichlet"><code>Ferrite.PeriodicDirichlet</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PeriodicDirichlet(u::Symbol, facet_mapping, components=nothing)
PeriodicDirichlet(u::Symbol, facet_mapping, R::AbstractMatrix, components=nothing)
-PeriodicDirichlet(u::Symbol, facet_mapping, f::Function, components=nothing)</code></pre><p>Create a periodic Dirichlet boundary condition for the field <code>u</code> on the facet-pairs given in <code>facet_mapping</code>. The mapping can be computed with <a href="#Ferrite.collect_periodic_facets"><code>collect_periodic_facets</code></a>. The constraint ensures that degrees-of-freedom on the mirror facet are constrained to the corresponding degrees-of-freedom on the image facet. <code>components</code> specify the components of <code>u</code> that are prescribed by this condition. By default all components of <code>u</code> are prescribed.</p><p>If the mapping is not aligned with the coordinate axis (e.g. rotated) a rotation matrix <code>R</code> should be passed to the constructor. This matrix rotates dofs on the mirror facet to the image facet. Note that this is only applicable for vector-valued problems.</p><p>To construct an inhomogeneous periodic constraint it is possible to pass a function <code>f</code>. Note that this is currently only supported when the periodicity is aligned with the coordinate axes.</p><p>See the manual section on <a href="../../topics/boundary_conditions/#Periodic-boundary-conditions">Periodic boundary conditions</a> for more information.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L896-L916">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.collect_periodic_facets" href="#Ferrite.collect_periodic_facets"><code>Ferrite.collect_periodic_facets</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">collect_periodic_facets(grid::Grid, mset, iset, transform::Union{Function,Nothing}=nothing; tol=1e-12)</code></pre><p>Match all mirror facets in <code>mset</code> with a corresponding image facet in <code>iset</code>. Return a dictionary which maps each mirror facet to a image facet. The result can then be passed to <a href="#Ferrite.PeriodicDirichlet"><code>PeriodicDirichlet</code></a>.</p><p><code>mset</code> and <code>iset</code> can be given as a <code>String</code> (an existing facet set in the grid) or as a <code>AbstractSet{FacetIndex}</code> directly.</p><p>By default this function looks for a matching facet in the directions of the coordinate system. For other types of periodicities the <code>transform</code> function can be used. The <code>transform</code> function is applied on the coordinates of the image facet, and is expected to transform the coordinates to the matching locations in the mirror set.</p><p>The keyword <code>tol</code> specifies the tolerance (i.e. distance and deviation in facet-normals) between a image-facet and mirror-facet, for them to be considered matched.</p><p>See also: <a href="#Ferrite.collect_periodic_facets!"><code>collect_periodic_facets!</code></a>, <a href="#Ferrite.PeriodicDirichlet"><code>PeriodicDirichlet</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L1258-L1277">source</a></section><section><div><pre><code class="language-julia hljs">collect_periodic_facets(grid::Grid, all_facets::Union{AbstractSet{FacetIndex},String,Nothing}=nothing; tol=1e-12)</code></pre><p>Split all facets in <code>all_facets</code> into image and mirror sets. For each matching pair, the facet located further along the vector <code>(1, 1, 1)</code> becomes the image facet.</p><p>If no set is given, all facets on the outer boundary of the grid (i.e. all facets that do not have a neighbor) is used.</p><p>See also: <a href="#Ferrite.collect_periodic_facets!"><code>collect_periodic_facets!</code></a>, <a href="#Ferrite.PeriodicDirichlet"><code>PeriodicDirichlet</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L1282-L1292">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.collect_periodic_facets!" href="#Ferrite.collect_periodic_facets!"><code>Ferrite.collect_periodic_facets!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">collect_periodic_facets!(facet_map::Vector{PeriodicFacetPair}, grid::Grid, mset, iset, transform::Union{Function,Nothing}; tol=1e-12)</code></pre><p>Same as <a href="#Ferrite.collect_periodic_facets"><code>collect_periodic_facets</code></a> but adds all matches to the existing <code>facet_map</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L1298-L1302">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!" href="#Ferrite.add!"><code>Ferrite.add!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(sdh::SubDofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the SubDofHandler <code>sdh</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L259-L263">source</a></section><section><div><pre><code class="language-julia hljs">add!(dh::DofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the DofHandler <code>dh</code>.</p><p>The field is added to all cells of the underlying grid, use <a href="../dofhandler/#Ferrite.SubDofHandler"><code>SubDofHandler</code></a>s if the grid contains multiple cell types, or to add the field to subset of all the cells.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L298-L306">source</a></section><section><div><pre><code class="language-julia hljs">add!(ch::ConstraintHandler, ac::AffineConstraint)</code></pre><p>Add the <code>AffineConstraint</code> to the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L265-L269">source</a></section><section><div><pre><code class="language-julia hljs">add!(ch::ConstraintHandler, dbc::Dirichlet)</code></pre><p>Add a <code>Dirichlet</code> boundary condition to the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L818-L822">source</a></section><section><div><pre><code class="language-julia hljs">add!(proj::L2Projector, set::AbstractVecOrSet{Int}, ip::Interpolation;
- qr_rhs, [qr_lhs])</code></pre><p>Add an interpolation <code>ip</code> on the cells in <code>set</code> to the <code>L2Projector</code> <code>proj</code>.</p><ul><li><code>qr_rhs</code> sets the quadrature rule used to later integrate the right-hand-side of the projection equation, when calling <a href="../export/#Ferrite.project"><code>project</code></a>. It should match the quadrature points used when creating the quadrature-point variables to project.</li><li>The <em>optional</em> <code>qr_lhs</code> sets the quadrature rule used to integrate the left-hand-side of the projection equation, and defaults to a quadrature rule that integrates the mass-matrix exactly for the given interpolation <code>ip</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/L2_projection.jl#L94-L106">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.close!" href="#Ferrite.close!"><code>Ferrite.close!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">close!(dh::AbstractDofHandler)</code></pre><p>Closes <code>dh</code> and creates degrees of freedom for each cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L328-L332">source</a></section><section><div><pre><code class="language-julia hljs">close!(ch::ConstraintHandler)</code></pre><p>Close and finalize the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L206-L210">source</a></section><section><div><pre><code class="language-julia hljs">close!(proj::L2Projector)</code></pre><p>Close <code>proj</code> which assembles and calculates the left-hand-side of the projection equation, before doing a Cholesky factorization of the mass-matrix.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/L2_projection.jl#L126-L131">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.update!" href="#Ferrite.update!"><code>Ferrite.update!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">update!(ch::ConstraintHandler, time::Real=0.0)</code></pre><p>Update time-dependent inhomogeneities for the new time. This calls <code>f(x)</code> or <code>f(x, t)</code> when applicable, where <code>f</code> is the function(s) corresponding to the constraints in the handler, to compute the inhomogeneities.</p><p>Note that this is called implicitly in <code>close!(::ConstraintHandler)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L397-L405">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply!" href="#Ferrite.apply!"><code>Ferrite.apply!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply!(K::SparseMatrixCSC, rhs::AbstractVector, ch::ConstraintHandler)</code></pre><p>Adjust the matrix <code>K</code> and right hand side <code>rhs</code> to account for the Dirichlet boundary conditions specified in <code>ch</code> such that <code>K \ rhs</code> gives the expected solution.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p><code>apply!(K, rhs, ch)</code> essentially calculates</p><pre><code class="language-julia hljs">rhs[free] = rhs[free] - K[constrained, constrained] * a[constrained]</code></pre><p>where <code>a[constrained]</code> are the inhomogeneities. Consequently, the sign of <code>rhs</code> matters (in contrast with <code>apply_zero!</code>).</p></div></div><pre><code class="language-julia hljs">apply!(v::AbstractVector, ch::ConstraintHandler)</code></pre><p>Apply Dirichlet boundary conditions and affine constraints, specified in <code>ch</code>, to the solution vector <code>v</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">K, f = assemble_system(...) # Assemble system
+PeriodicDirichlet(u::Symbol, facet_mapping, f::Function, components=nothing)</code></pre><p>Create a periodic Dirichlet boundary condition for the field <code>u</code> on the facet-pairs given in <code>facet_mapping</code>. The mapping can be computed with <a href="#Ferrite.collect_periodic_facets"><code>collect_periodic_facets</code></a>. The constraint ensures that degrees-of-freedom on the mirror facet are constrained to the corresponding degrees-of-freedom on the image facet. <code>components</code> specify the components of <code>u</code> that are prescribed by this condition. By default all components of <code>u</code> are prescribed.</p><p>If the mapping is not aligned with the coordinate axis (e.g. rotated) a rotation matrix <code>R</code> should be passed to the constructor. This matrix rotates dofs on the mirror facet to the image facet. Note that this is only applicable for vector-valued problems.</p><p>To construct an inhomogeneous periodic constraint it is possible to pass a function <code>f</code>. Note that this is currently only supported when the periodicity is aligned with the coordinate axes.</p><p>See the manual section on <a href="../../topics/boundary_conditions/#Periodic-boundary-conditions">Periodic boundary conditions</a> for more information.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L896-L916">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.collect_periodic_facets" href="#Ferrite.collect_periodic_facets"><code>Ferrite.collect_periodic_facets</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">collect_periodic_facets(grid::Grid, mset, iset, transform::Union{Function,Nothing}=nothing; tol=1e-12)</code></pre><p>Match all mirror facets in <code>mset</code> with a corresponding image facet in <code>iset</code>. Return a dictionary which maps each mirror facet to a image facet. The result can then be passed to <a href="#Ferrite.PeriodicDirichlet"><code>PeriodicDirichlet</code></a>.</p><p><code>mset</code> and <code>iset</code> can be given as a <code>String</code> (an existing facet set in the grid) or as a <code>AbstractSet{FacetIndex}</code> directly.</p><p>By default this function looks for a matching facet in the directions of the coordinate system. For other types of periodicities the <code>transform</code> function can be used. The <code>transform</code> function is applied on the coordinates of the image facet, and is expected to transform the coordinates to the matching locations in the mirror set.</p><p>The keyword <code>tol</code> specifies the tolerance (i.e. distance and deviation in facet-normals) between a image-facet and mirror-facet, for them to be considered matched.</p><p>See also: <a href="#Ferrite.collect_periodic_facets!"><code>collect_periodic_facets!</code></a>, <a href="#Ferrite.PeriodicDirichlet"><code>PeriodicDirichlet</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L1258-L1277">source</a></section><section><div><pre><code class="language-julia hljs">collect_periodic_facets(grid::Grid, all_facets::Union{AbstractSet{FacetIndex},String,Nothing}=nothing; tol=1e-12)</code></pre><p>Split all facets in <code>all_facets</code> into image and mirror sets. For each matching pair, the facet located further along the vector <code>(1, 1, 1)</code> becomes the image facet.</p><p>If no set is given, all facets on the outer boundary of the grid (i.e. all facets that do not have a neighbor) is used.</p><p>See also: <a href="#Ferrite.collect_periodic_facets!"><code>collect_periodic_facets!</code></a>, <a href="#Ferrite.PeriodicDirichlet"><code>PeriodicDirichlet</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L1282-L1292">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.collect_periodic_facets!" href="#Ferrite.collect_periodic_facets!"><code>Ferrite.collect_periodic_facets!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">collect_periodic_facets!(facet_map::Vector{PeriodicFacetPair}, grid::Grid, mset, iset, transform::Union{Function,Nothing}; tol=1e-12)</code></pre><p>Same as <a href="#Ferrite.collect_periodic_facets"><code>collect_periodic_facets</code></a> but adds all matches to the existing <code>facet_map</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L1298-L1302">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!" href="#Ferrite.add!"><code>Ferrite.add!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(sdh::SubDofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the SubDofHandler <code>sdh</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L259-L263">source</a></section><section><div><pre><code class="language-julia hljs">add!(dh::DofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the DofHandler <code>dh</code>.</p><p>The field is added to all cells of the underlying grid, use <a href="../dofhandler/#Ferrite.SubDofHandler"><code>SubDofHandler</code></a>s if the grid contains multiple cell types, or to add the field to subset of all the cells.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L298-L306">source</a></section><section><div><pre><code class="language-julia hljs">add!(ch::ConstraintHandler, ac::AffineConstraint)</code></pre><p>Add the <code>AffineConstraint</code> to the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L265-L269">source</a></section><section><div><pre><code class="language-julia hljs">add!(ch::ConstraintHandler, dbc::Dirichlet)</code></pre><p>Add a <code>Dirichlet</code> boundary condition to the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L818-L822">source</a></section><section><div><pre><code class="language-julia hljs">add!(proj::L2Projector, set::AbstractVecOrSet{Int}, ip::Interpolation;
+ qr_rhs, [qr_lhs])</code></pre><p>Add an interpolation <code>ip</code> on the cells in <code>set</code> to the <code>L2Projector</code> <code>proj</code>.</p><ul><li><code>qr_rhs</code> sets the quadrature rule used to later integrate the right-hand-side of the projection equation, when calling <a href="../export/#Ferrite.project"><code>project</code></a>. It should match the quadrature points used when creating the quadrature-point variables to project.</li><li>The <em>optional</em> <code>qr_lhs</code> sets the quadrature rule used to integrate the left-hand-side of the projection equation, and defaults to a quadrature rule that integrates the mass-matrix exactly for the given interpolation <code>ip</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/L2_projection.jl#L94-L106">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.close!" href="#Ferrite.close!"><code>Ferrite.close!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">close!(dh::AbstractDofHandler)</code></pre><p>Closes <code>dh</code> and creates degrees of freedom for each cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L328-L332">source</a></section><section><div><pre><code class="language-julia hljs">close!(ch::ConstraintHandler)</code></pre><p>Close and finalize the <code>ConstraintHandler</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L206-L210">source</a></section><section><div><pre><code class="language-julia hljs">close!(proj::L2Projector)</code></pre><p>Close <code>proj</code> which assembles and calculates the left-hand-side of the projection equation, before doing a Cholesky factorization of the mass-matrix.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/L2_projection.jl#L126-L131">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.update!" href="#Ferrite.update!"><code>Ferrite.update!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">update!(ch::ConstraintHandler, time::Real=0.0)</code></pre><p>Update time-dependent inhomogeneities for the new time. This calls <code>f(x)</code> or <code>f(x, t)</code> when applicable, where <code>f</code> is the function(s) corresponding to the constraints in the handler, to compute the inhomogeneities.</p><p>Note that this is called implicitly in <code>close!(::ConstraintHandler)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L397-L405">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply!" href="#Ferrite.apply!"><code>Ferrite.apply!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply!(K::SparseMatrixCSC, rhs::AbstractVector, ch::ConstraintHandler)</code></pre><p>Adjust the matrix <code>K</code> and right hand side <code>rhs</code> to account for the Dirichlet boundary conditions specified in <code>ch</code> such that <code>K \ rhs</code> gives the expected solution.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p><code>apply!(K, rhs, ch)</code> essentially calculates</p><pre><code class="language-julia hljs">rhs[free] = rhs[free] - K[constrained, constrained] * a[constrained]</code></pre><p>where <code>a[constrained]</code> are the inhomogeneities. Consequently, the sign of <code>rhs</code> matters (in contrast with <code>apply_zero!</code>).</p></div></div><pre><code class="language-julia hljs">apply!(v::AbstractVector, ch::ConstraintHandler)</code></pre><p>Apply Dirichlet boundary conditions and affine constraints, specified in <code>ch</code>, to the solution vector <code>v</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">K, f = assemble_system(...) # Assemble system
apply!(K, f, ch) # Adjust K and f to account for boundary conditions
u = K \ f # Solve the system, u should be "approximately correct"
-apply!(u, ch) # Explicitly make sure bcs are correct</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The last operation is not strictly necessary since the boundary conditions should already be fulfilled after <code>apply!(K, f, ch)</code>. However, solvers of linear systems are not exact, and thus <code>apply!(u, ch)</code> can be used to make sure the boundary conditions are fulfilled exactly.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L507-L542">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_zero!" href="#Ferrite.apply_zero!"><code>Ferrite.apply_zero!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_zero!(K::SparseMatrixCSC, rhs::AbstractVector, ch::ConstraintHandler)</code></pre><p>Adjust the matrix <code>K</code> and the right hand side <code>rhs</code> to account for prescribed Dirichlet boundary conditions and affine constraints such that <code>du = K \ rhs</code> gives the expected result (e.g. <code>du</code> zero for all prescribed degrees of freedom).</p><pre><code class="nohighlight hljs">apply_zero!(v::AbstractVector, ch::ConstraintHandler)</code></pre><p>Zero-out values in <code>v</code> corresponding to prescribed degrees of freedom and update values prescribed by affine constraints, such that if <code>a</code> fulfills the constraints, <code>a ± v</code> also will.</p><p>These methods are typically used in e.g. a Newton solver where the increment, <code>du</code>, should be prescribed to zero even for non-homogeneouos boundary conditions.</p><p>See also: <a href="#Ferrite.apply!"><code>apply!</code></a>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">u = un + Δu # Current guess
+apply!(u, ch) # Explicitly make sure bcs are correct</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The last operation is not strictly necessary since the boundary conditions should already be fulfilled after <code>apply!(K, f, ch)</code>. However, solvers of linear systems are not exact, and thus <code>apply!(u, ch)</code> can be used to make sure the boundary conditions are fulfilled exactly.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L507-L542">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_zero!" href="#Ferrite.apply_zero!"><code>Ferrite.apply_zero!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_zero!(K::SparseMatrixCSC, rhs::AbstractVector, ch::ConstraintHandler)</code></pre><p>Adjust the matrix <code>K</code> and the right hand side <code>rhs</code> to account for prescribed Dirichlet boundary conditions and affine constraints such that <code>du = K \ rhs</code> gives the expected result (e.g. <code>du</code> zero for all prescribed degrees of freedom).</p><pre><code class="nohighlight hljs">apply_zero!(v::AbstractVector, ch::ConstraintHandler)</code></pre><p>Zero-out values in <code>v</code> corresponding to prescribed degrees of freedom and update values prescribed by affine constraints, such that if <code>a</code> fulfills the constraints, <code>a ± v</code> also will.</p><p>These methods are typically used in e.g. a Newton solver where the increment, <code>du</code>, should be prescribed to zero even for non-homogeneouos boundary conditions.</p><p>See also: <a href="#Ferrite.apply!"><code>apply!</code></a>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">u = un + Δu # Current guess
K, g = assemble_system(...) # Assemble residual and tangent for current guess
apply_zero!(K, g, ch) # Adjust tangent and residual to take prescribed values into account
ΔΔu = K \ g # Compute the (negative) increment, prescribed values are "approximately" zero
apply_zero!(ΔΔu, ch) # Make sure values are exactly zero
-Δu .-= ΔΔu # Update current guess</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The last call to <code>apply_zero!</code> is only strictly necessary for affine constraints. However, even if the Dirichlet boundary conditions should be fulfilled after <code>apply!(K, g, ch)</code>, solvers of linear systems are not exact. <code>apply!(ΔΔu, ch)</code> can be used to make sure the values for the prescribed degrees of freedom are fulfilled exactly.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L545-L579">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_local!" href="#Ferrite.apply_local!"><code>Ferrite.apply_local!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_local!(
+Δu .-= ΔΔu # Update current guess</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The last call to <code>apply_zero!</code> is only strictly necessary for affine constraints. However, even if the Dirichlet boundary conditions should be fulfilled after <code>apply!(K, g, ch)</code>, solvers of linear systems are not exact. <code>apply!(ΔΔu, ch)</code> can be used to make sure the values for the prescribed degrees of freedom are fulfilled exactly.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L545-L579">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_local!" href="#Ferrite.apply_local!"><code>Ferrite.apply_local!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_local!(
local_matrix::AbstractMatrix, local_vector::AbstractVector,
global_dofs::AbstractVector, ch::ConstraintHandler;
apply_zero::Bool = false
-)</code></pre><p>Similar to <a href="#Ferrite.apply!"><code>apply!</code></a> but perform condensation of constrained degrees-of-freedom locally in <code>local_matrix</code> and <code>local_vector</code> <em>before</em> they are to be assembled into the global system.</p><p>When the keyword argument <code>apply_zero</code> is <code>true</code> all inhomogeneities are set to <code>0</code> (cf. <a href="#Ferrite.apply!"><code>apply!</code></a> vs <a href="#Ferrite.apply_zero!"><code>apply_zero!</code></a>).</p><p>This method can only be used if all constraints are "local", i.e. no constraint couples with dofs outside of the element dofs (<code>global_dofs</code>) since condensation of such constraints requires writing to entries in the global matrix/vector. For such a case, <a href="#Ferrite.apply_assemble!"><code>apply_assemble!</code></a> can be used instead.</p><p>Note that this method is destructive since it, by definition, modifies <code>local_matrix</code> and <code>local_vector</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L1582-L1603">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_assemble!" href="#Ferrite.apply_assemble!"><code>Ferrite.apply_assemble!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_assemble!(
+)</code></pre><p>Similar to <a href="#Ferrite.apply!"><code>apply!</code></a> but perform condensation of constrained degrees-of-freedom locally in <code>local_matrix</code> and <code>local_vector</code> <em>before</em> they are to be assembled into the global system.</p><p>When the keyword argument <code>apply_zero</code> is <code>true</code> all inhomogeneities are set to <code>0</code> (cf. <a href="#Ferrite.apply!"><code>apply!</code></a> vs <a href="#Ferrite.apply_zero!"><code>apply_zero!</code></a>).</p><p>This method can only be used if all constraints are "local", i.e. no constraint couples with dofs outside of the element dofs (<code>global_dofs</code>) since condensation of such constraints requires writing to entries in the global matrix/vector. For such a case, <a href="#Ferrite.apply_assemble!"><code>apply_assemble!</code></a> can be used instead.</p><p>Note that this method is destructive since it, by definition, modifies <code>local_matrix</code> and <code>local_vector</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L1582-L1603">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_assemble!" href="#Ferrite.apply_assemble!"><code>Ferrite.apply_assemble!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_assemble!(
assembler::AbstractAssembler, ch::ConstraintHandler,
global_dofs::AbstractVector{Int},
local_matrix::AbstractMatrix, local_vector::AbstractVector;
apply_zero::Bool = false
-)</code></pre><p>Assemble <code>local_matrix</code> and <code>local_vector</code> into the global system in <code>assembler</code> by first doing constraint condensation using <a href="#Ferrite.apply_local!"><code>apply_local!</code></a>.</p><p>This is similar to using <a href="#Ferrite.apply_local!"><code>apply_local!</code></a> followed by <a href="../assembly/#Ferrite.assemble!"><code>assemble!</code></a> with the advantage that non-local constraints can be handled, since this method can write to entries of the global matrix and vector outside of the indices in <code>global_dofs</code>.</p><p>When the keyword argument <code>apply_zero</code> is <code>true</code> all inhomogeneities are set to <code>0</code> (cf. <a href="#Ferrite.apply!"><code>apply!</code></a> vs <a href="#Ferrite.apply_zero!"><code>apply_zero!</code></a>).</p><p>Note that this method is destructive since it modifies <code>local_matrix</code> and <code>local_vector</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/assembler.jl#L345-L364">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_rhs_data" href="#Ferrite.get_rhs_data"><code>Ferrite.get_rhs_data</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_rhs_data(ch::ConstraintHandler, A::SparseMatrixCSC) -> RHSData</code></pre><p>Returns the needed <a href="#Ferrite.RHSData"><code>RHSData</code></a> for <a href="#Ferrite.apply_rhs!"><code>apply_rhs!</code></a>.</p><p>This must be used when the same stiffness matrix is reused for multiple steps, for example when timestepping, with different non-homogeneouos Dirichlet boundary conditions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L121-L129">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_rhs!" href="#Ferrite.apply_rhs!"><code>Ferrite.apply_rhs!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_rhs!(data::RHSData, f::AbstractVector, ch::ConstraintHandler, applyzero::Bool=false)</code></pre><p>Applies the boundary condition to the right-hand-side vector without modifying the stiffness matrix.</p><p>See also: <a href="#Ferrite.get_rhs_data"><code>get_rhs_data</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L136-L142">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RHSData" href="#Ferrite.RHSData"><code>Ferrite.RHSData</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RHSData</code></pre><p>Stores the constrained columns and mean of the diagonal of stiffness matrix <code>A</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/ConstraintHandler.jl#L111-L115">source</a></section></article><h1 id="Initial-conditions"><a class="docs-heading-anchor" href="#Initial-conditions">Initial conditions</a><a id="Initial-conditions-1"></a><a class="docs-heading-anchor-permalink" href="#Initial-conditions" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_analytical!" href="#Ferrite.apply_analytical!"><code>Ferrite.apply_analytical!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_analytical!(
+)</code></pre><p>Assemble <code>local_matrix</code> and <code>local_vector</code> into the global system in <code>assembler</code> by first doing constraint condensation using <a href="#Ferrite.apply_local!"><code>apply_local!</code></a>.</p><p>This is similar to using <a href="#Ferrite.apply_local!"><code>apply_local!</code></a> followed by <a href="../assembly/#Ferrite.assemble!"><code>assemble!</code></a> with the advantage that non-local constraints can be handled, since this method can write to entries of the global matrix and vector outside of the indices in <code>global_dofs</code>.</p><p>When the keyword argument <code>apply_zero</code> is <code>true</code> all inhomogeneities are set to <code>0</code> (cf. <a href="#Ferrite.apply!"><code>apply!</code></a> vs <a href="#Ferrite.apply_zero!"><code>apply_zero!</code></a>).</p><p>Note that this method is destructive since it modifies <code>local_matrix</code> and <code>local_vector</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/assembler.jl#L345-L364">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_rhs_data" href="#Ferrite.get_rhs_data"><code>Ferrite.get_rhs_data</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_rhs_data(ch::ConstraintHandler, A::SparseMatrixCSC) -> RHSData</code></pre><p>Returns the needed <a href="#Ferrite.RHSData"><code>RHSData</code></a> for <a href="#Ferrite.apply_rhs!"><code>apply_rhs!</code></a>.</p><p>This must be used when the same stiffness matrix is reused for multiple steps, for example when timestepping, with different non-homogeneouos Dirichlet boundary conditions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L121-L129">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_rhs!" href="#Ferrite.apply_rhs!"><code>Ferrite.apply_rhs!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_rhs!(data::RHSData, f::AbstractVector, ch::ConstraintHandler, applyzero::Bool=false)</code></pre><p>Applies the boundary condition to the right-hand-side vector without modifying the stiffness matrix.</p><p>See also: <a href="#Ferrite.get_rhs_data"><code>get_rhs_data</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L136-L142">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RHSData" href="#Ferrite.RHSData"><code>Ferrite.RHSData</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RHSData</code></pre><p>Stores the constrained columns and mean of the diagonal of stiffness matrix <code>A</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/ConstraintHandler.jl#L111-L115">source</a></section></article><h1 id="Initial-conditions"><a class="docs-heading-anchor" href="#Initial-conditions">Initial conditions</a><a id="Initial-conditions-1"></a><a class="docs-heading-anchor-permalink" href="#Initial-conditions" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.apply_analytical!" href="#Ferrite.apply_analytical!"><code>Ferrite.apply_analytical!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">apply_analytical!(
a::AbstractVector, dh::AbstractDofHandler, fieldname::Symbol,
- f::Function, cellset=1:getncells(get_grid(dh)))</code></pre><p>Apply a solution <code>f(x)</code> by modifying the values in the degree of freedom vector <code>a</code> pertaining to the field <code>fieldname</code> for all cells in <code>cellset</code>. The function <code>f(x)</code> are given the spatial coordinate of the degree of freedom. For scalar fields, <code>f(x)::Number</code>, and for vector fields with dimension <code>dim</code>, <code>f(x)::Vec{dim}</code>.</p><p>This function can be used to apply initial conditions for time dependent problems.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This function only works for standard nodal finite element interpolations when the function value at the (algebraic) node is equal to the corresponding degree of freedom value. This holds for e.g. Lagrange and Serendipity interpolations, including sub- and superparametric elements.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/apply_analytical.jl#L7-L27">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../assembly/">« Assembly</a><a class="docs-footer-nextpage" href="../grid/">Grid & AbstractGrid »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ f::Function, cellset=1:getncells(get_grid(dh)))</code></pre><p>Apply a solution <code>f(x)</code> by modifying the values in the degree of freedom vector <code>a</code> pertaining to the field <code>fieldname</code> for all cells in <code>cellset</code>. The function <code>f(x)</code> are given the spatial coordinate of the degree of freedom. For scalar fields, <code>f(x)::Number</code>, and for vector fields with dimension <code>dim</code>, <code>f(x)::Vec{dim}</code>.</p><p>This function can be used to apply initial conditions for time dependent problems.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This function only works for standard nodal finite element interpolations when the function value at the (algebraic) node is equal to the corresponding degree of freedom value. This holds for e.g. Lagrange and Serendipity interpolations, including sub- and superparametric elements.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/apply_analytical.jl#L7-L27">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../assembly/">« Assembly</a><a class="docs-footer-nextpage" href="../grid/">Grid & AbstractGrid »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/reference/dofhandler/index.html b/dev/reference/dofhandler/index.html
index 6c40fc547e..bbbc1acf76 100644
--- a/dev/reference/dofhandler/index.html
+++ b/dev/reference/dofhandler/index.html
@@ -4,7 +4,7 @@
ip_p = Lagrange{RefTriangle, 1}() # scalar interpolation for a field p
add!(dh, :u, ip_u)
add!(dh, :p, ip_p)
-close!(dh)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L111-L132">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SubDofHandler" href="#Ferrite.SubDofHandler"><code>Ferrite.SubDofHandler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SubDofHandler(dh::AbstractDofHandler, cellset::AbstractVecOrSet{Int})</code></pre><p>Create an <code>sdh::SubDofHandler</code> from the parent <code>dh</code>, pertaining to the cells in <code>cellset</code>. This allows you to add fields to parts of the domain, or using different interpolations or cell types (e.g. <code>Triangles</code> and <code>Quadrilaterals</code>). All fields and cell types must be the same in one <code>SubDofHandler</code>.</p><p>After construction any number of discrete fields can be added to the SubDofHandler using <a href="../boundary_conditions/#Ferrite.add!"><code>add!</code></a>. Construction is finalized by calling <a href="../boundary_conditions/#Ferrite.close!"><code>close!</code></a> on the parent <code>dh</code>.</p><p><strong>Examples</strong></p><p>We assume we have a <code>grid</code> containing "Triangle" and "Quadrilateral" cells, including the cellsets "triangles" and "quadilaterals" for to these cells.</p><pre><code class="language-julia hljs">dh = DofHandler(grid)
+close!(dh)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L111-L132">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SubDofHandler" href="#Ferrite.SubDofHandler"><code>Ferrite.SubDofHandler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SubDofHandler(dh::AbstractDofHandler, cellset::AbstractVecOrSet{Int})</code></pre><p>Create an <code>sdh::SubDofHandler</code> from the parent <code>dh</code>, pertaining to the cells in <code>cellset</code>. This allows you to add fields to parts of the domain, or using different interpolations or cell types (e.g. <code>Triangles</code> and <code>Quadrilaterals</code>). All fields and cell types must be the same in one <code>SubDofHandler</code>.</p><p>After construction any number of discrete fields can be added to the SubDofHandler using <a href="../boundary_conditions/#Ferrite.add!"><code>add!</code></a>. Construction is finalized by calling <a href="../boundary_conditions/#Ferrite.close!"><code>close!</code></a> on the parent <code>dh</code>.</p><p><strong>Examples</strong></p><p>We assume we have a <code>grid</code> containing "Triangle" and "Quadrilateral" cells, including the cellsets "triangles" and "quadilaterals" for to these cells.</p><pre><code class="language-julia hljs">dh = DofHandler(grid)
sdh_tri = SubDofHandler(dh, getcellset(grid, "triangles"))
ip_tri = Lagrange{RefTriangle, 2}()^2 # vector interpolation for a field u
@@ -14,10 +14,10 @@
ip_quad = Lagrange{RefQuadrilateral, 2}()^2 # vector interpolation for a field u
add!(sdh_quad, :u, ip_quad)
-close!(dh) # Finalize by closing the parent</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L28-L55">source</a></section></article><h2 id="Adding-fields-to-the-DofHandlers"><a class="docs-heading-anchor" href="#Adding-fields-to-the-DofHandlers">Adding fields to the DofHandlers</a><a id="Adding-fields-to-the-DofHandlers-1"></a><a class="docs-heading-anchor-permalink" href="#Adding-fields-to-the-DofHandlers" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!-Tuple{DofHandler, Symbol, Interpolation}" href="#Ferrite.add!-Tuple{DofHandler, Symbol, Interpolation}"><code>Ferrite.add!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(dh::DofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the DofHandler <code>dh</code>.</p><p>The field is added to all cells of the underlying grid, use <a href="#Ferrite.SubDofHandler"><code>SubDofHandler</code></a>s if the grid contains multiple cell types, or to add the field to subset of all the cells.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L298-L306">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!-Tuple{SubDofHandler, Symbol, Interpolation}" href="#Ferrite.add!-Tuple{SubDofHandler, Symbol, Interpolation}"><code>Ferrite.add!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(sdh::SubDofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the SubDofHandler <code>sdh</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L259-L263">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.close!-Tuple{DofHandler}" href="#Ferrite.close!-Tuple{DofHandler}"><code>Ferrite.close!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">close!(dh::AbstractDofHandler)</code></pre><p>Closes <code>dh</code> and creates degrees of freedom for each cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L328-L332">source</a></section></article><h2 id="Dof-renumbering"><a class="docs-heading-anchor" href="#Dof-renumbering">Dof renumbering</a><a id="Dof-renumbering-1"></a><a class="docs-heading-anchor-permalink" href="#Dof-renumbering" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.renumber!" href="#Ferrite.renumber!"><code>Ferrite.renumber!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">renumber!(dh::AbstractDofHandler, order)
-renumber!(dh::AbstractDofHandler, ch::ConstraintHandler, order)</code></pre><p>Renumber the degrees of freedom in the DofHandler and/or ConstraintHandler according to the ordering <code>order</code>.</p><p><code>order</code> can be given by one of the following options:</p><ul><li>A permutation vector <code>perm::AbstractVector{Int}</code> such that dof <code>i</code> is renumbered to <code>perm[i]</code>.</li><li><a href="#Ferrite.DofOrder.FieldWise"><code>DofOrder.FieldWise()</code></a> for renumbering dofs field wise.</li><li><a href="#Ferrite.DofOrder.ComponentWise"><code>DofOrder.ComponentWise()</code></a> for renumbering dofs component wise.</li><li><code>DofOrder.Ext{T}</code> for "external" renumber permutations, see documentation for <code>DofOrder.Ext</code> for details.</li></ul><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>The dof numbering in the DofHandler and ConstraintHandler <em>must always be consistent</em>. It is therefore necessary to either renumber <em>before</em> creating the ConstraintHandler in the first place, or to renumber the DofHandler and the ConstraintHandler <em>together</em>.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofRenumbering.jl#L42-L61">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.DofOrder.FieldWise" href="#Ferrite.DofOrder.FieldWise"><code>Ferrite.DofOrder.FieldWise</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DofOrder.FieldWise()
-DofOrder.FieldWise(target_blocks::Vector{Int})</code></pre><p>Dof order passed to <a href="#Ferrite.renumber!"><code>renumber!</code></a> to renumber global dofs field wise resulting in a globally blocked system.</p><p>The default behavior is to group dofs of each field into their own block, with the same order as in the DofHandler. This can be customized by passing a vector of the same length as the total number of fields in the DofHandler (see <code>getfieldnames(dh)</code>) that maps each field to a "target block": to renumber a DofHandler with three fields <code>:u</code>, <code>:v</code>, <code>:w</code> such that dofs for <code>:u</code> and <code>:w</code> end up in the first global block, and dofs for <code>:v</code> in the second global block use <code>DofOrder.FieldWise([1, 2, 1])</code>.</p><p>This renumbering is stable such that the original relative ordering of dofs within each target block is maintained.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofRenumbering.jl#L128-L144">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.DofOrder.ComponentWise" href="#Ferrite.DofOrder.ComponentWise"><code>Ferrite.DofOrder.ComponentWise</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DofOrder.ComponentWise()
-DofOrder.ComponentWise(target_blocks::Vector{Int})</code></pre><p>Dof order passed to <a href="#Ferrite.renumber!"><code>renumber!</code></a> to renumber global dofs component wise resulting in a globally blocked system.</p><p>The default behavior is to group dofs of each component into their own block, with the same order as in the DofHandler. This can be customized by passing a vector of length <code>ncomponents</code> that maps each component to a "target block" (see <a href="#Ferrite.DofOrder.FieldWise"><code>DofOrder.FieldWise</code></a> for details).</p><p>This renumbering is stable such that the original relative ordering of dofs within each target block is maintained.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofRenumbering.jl#L161-L175">source</a></section></article><h2 id="Common-methods"><a class="docs-heading-anchor" href="#Common-methods">Common methods</a><a id="Common-methods-1"></a><a class="docs-heading-anchor-permalink" href="#Common-methods" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ndofs" href="#Ferrite.ndofs"><code>Ferrite.ndofs</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ndofs(dh::AbstractDofHandler)</code></pre><p>Return the number of degrees of freedom in <code>dh</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L167-L171">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ndofs_per_cell" href="#Ferrite.ndofs_per_cell"><code>Ferrite.ndofs_per_cell</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ndofs_per_cell(dh::AbstractDofHandler[, cell::Int=1])</code></pre><p>Return the number of degrees of freedom for the cell with index <code>cell</code>.</p><p>See also <a href="#Ferrite.ndofs"><code>ndofs</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L174-L180">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dof_range" href="#Ferrite.dof_range"><code>Ferrite.dof_range</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dof_range(sdh::SubDofHandler, field_idx::Int)
+close!(dh) # Finalize by closing the parent</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L28-L55">source</a></section></article><h2 id="Adding-fields-to-the-DofHandlers"><a class="docs-heading-anchor" href="#Adding-fields-to-the-DofHandlers">Adding fields to the DofHandlers</a><a id="Adding-fields-to-the-DofHandlers-1"></a><a class="docs-heading-anchor-permalink" href="#Adding-fields-to-the-DofHandlers" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!-Tuple{DofHandler, Symbol, Interpolation}" href="#Ferrite.add!-Tuple{DofHandler, Symbol, Interpolation}"><code>Ferrite.add!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(dh::DofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the DofHandler <code>dh</code>.</p><p>The field is added to all cells of the underlying grid, use <a href="#Ferrite.SubDofHandler"><code>SubDofHandler</code></a>s if the grid contains multiple cell types, or to add the field to subset of all the cells.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L298-L306">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!-Tuple{SubDofHandler, Symbol, Interpolation}" href="#Ferrite.add!-Tuple{SubDofHandler, Symbol, Interpolation}"><code>Ferrite.add!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(sdh::SubDofHandler, name::Symbol, ip::Interpolation)</code></pre><p>Add a field called <code>name</code> approximated by <code>ip</code> to the SubDofHandler <code>sdh</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L259-L263">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.close!-Tuple{DofHandler}" href="#Ferrite.close!-Tuple{DofHandler}"><code>Ferrite.close!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">close!(dh::AbstractDofHandler)</code></pre><p>Closes <code>dh</code> and creates degrees of freedom for each cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L328-L332">source</a></section></article><h2 id="Dof-renumbering"><a class="docs-heading-anchor" href="#Dof-renumbering">Dof renumbering</a><a id="Dof-renumbering-1"></a><a class="docs-heading-anchor-permalink" href="#Dof-renumbering" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.renumber!" href="#Ferrite.renumber!"><code>Ferrite.renumber!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">renumber!(dh::AbstractDofHandler, order)
+renumber!(dh::AbstractDofHandler, ch::ConstraintHandler, order)</code></pre><p>Renumber the degrees of freedom in the DofHandler and/or ConstraintHandler according to the ordering <code>order</code>.</p><p><code>order</code> can be given by one of the following options:</p><ul><li>A permutation vector <code>perm::AbstractVector{Int}</code> such that dof <code>i</code> is renumbered to <code>perm[i]</code>.</li><li><a href="#Ferrite.DofOrder.FieldWise"><code>DofOrder.FieldWise()</code></a> for renumbering dofs field wise.</li><li><a href="#Ferrite.DofOrder.ComponentWise"><code>DofOrder.ComponentWise()</code></a> for renumbering dofs component wise.</li><li><code>DofOrder.Ext{T}</code> for "external" renumber permutations, see documentation for <code>DofOrder.Ext</code> for details.</li></ul><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>The dof numbering in the DofHandler and ConstraintHandler <em>must always be consistent</em>. It is therefore necessary to either renumber <em>before</em> creating the ConstraintHandler in the first place, or to renumber the DofHandler and the ConstraintHandler <em>together</em>.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofRenumbering.jl#L42-L61">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.DofOrder.FieldWise" href="#Ferrite.DofOrder.FieldWise"><code>Ferrite.DofOrder.FieldWise</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DofOrder.FieldWise()
+DofOrder.FieldWise(target_blocks::Vector{Int})</code></pre><p>Dof order passed to <a href="#Ferrite.renumber!"><code>renumber!</code></a> to renumber global dofs field wise resulting in a globally blocked system.</p><p>The default behavior is to group dofs of each field into their own block, with the same order as in the DofHandler. This can be customized by passing a vector of the same length as the total number of fields in the DofHandler (see <code>getfieldnames(dh)</code>) that maps each field to a "target block": to renumber a DofHandler with three fields <code>:u</code>, <code>:v</code>, <code>:w</code> such that dofs for <code>:u</code> and <code>:w</code> end up in the first global block, and dofs for <code>:v</code> in the second global block use <code>DofOrder.FieldWise([1, 2, 1])</code>.</p><p>This renumbering is stable such that the original relative ordering of dofs within each target block is maintained.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofRenumbering.jl#L128-L144">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.DofOrder.ComponentWise" href="#Ferrite.DofOrder.ComponentWise"><code>Ferrite.DofOrder.ComponentWise</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DofOrder.ComponentWise()
+DofOrder.ComponentWise(target_blocks::Vector{Int})</code></pre><p>Dof order passed to <a href="#Ferrite.renumber!"><code>renumber!</code></a> to renumber global dofs component wise resulting in a globally blocked system.</p><p>The default behavior is to group dofs of each component into their own block, with the same order as in the DofHandler. This can be customized by passing a vector of length <code>ncomponents</code> that maps each component to a "target block" (see <a href="#Ferrite.DofOrder.FieldWise"><code>DofOrder.FieldWise</code></a> for details).</p><p>This renumbering is stable such that the original relative ordering of dofs within each target block is maintained.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofRenumbering.jl#L161-L175">source</a></section></article><h2 id="Common-methods"><a class="docs-heading-anchor" href="#Common-methods">Common methods</a><a id="Common-methods-1"></a><a class="docs-heading-anchor-permalink" href="#Common-methods" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ndofs" href="#Ferrite.ndofs"><code>Ferrite.ndofs</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ndofs(dh::AbstractDofHandler)</code></pre><p>Return the number of degrees of freedom in <code>dh</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L167-L171">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ndofs_per_cell" href="#Ferrite.ndofs_per_cell"><code>Ferrite.ndofs_per_cell</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ndofs_per_cell(dh::AbstractDofHandler[, cell::Int=1])</code></pre><p>Return the number of degrees of freedom for the cell with index <code>cell</code>.</p><p>See also <a href="#Ferrite.ndofs"><code>ndofs</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L174-L180">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.dof_range" href="#Ferrite.dof_range"><code>Ferrite.dof_range</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">dof_range(sdh::SubDofHandler, field_idx::Int)
dof_range(sdh::SubDofHandler, field_name::Symbol)
dof_range(dh:DofHandler, field_name::Symbol)</code></pre><p>Return the local dof range for a given field. The field can be specified by its name or index, where <code>field_idx</code> represents the index of a field within a <code>SubDofHandler</code> and <code>field_idxs</code> is a tuple of the <code>SubDofHandler</code>-index within the <code>DofHandler</code> and the <code>field_idx</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The <code>dof_range</code> of a field can vary between different <code>SubDofHandler</code>s. Therefore, it is advised to use the <code>field_idxs</code> or refer to a given <code>SubDofHandler</code> directly in case several <code>SubDofHandler</code>s exist. Using the <code>field_name</code> will always refer to the first occurrence of <code>field</code> within the <code>DofHandler</code>.</p></div></div><p>Example:</p><pre><code class="language-julia-repl hljs">julia> grid = generate_grid(Triangle, (3, 3))
Grid{2, Triangle, Float64} with 18 Triangle cells and 16 nodes
@@ -34,19 +34,19 @@
1:9
julia> dof_range(dh.subdofhandlers[1], 2) # field :p
-10:12</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L850-L885">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.celldofs" href="#Ferrite.celldofs"><code>Ferrite.celldofs</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">celldofs(dh::AbstractDofHandler, i::Int)</code></pre><p>Return a vector with the degrees of freedom that belong to cell <code>i</code>.</p><p>See also <a href="#Ferrite.celldofs!"><code>celldofs!</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L214-L220">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.celldofs!" href="#Ferrite.celldofs!"><code>Ferrite.celldofs!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">celldofs!(global_dofs::Vector{Int}, dh::AbstractDofHandler, i::Int)</code></pre><p>Store the degrees of freedom that belong to cell <code>i</code> in <code>global_dofs</code>.</p><p>See also <a href="#Ferrite.celldofs"><code>celldofs</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L196-L202">source</a></section></article><h1 id="Grid-iterators"><a class="docs-heading-anchor" href="#Grid-iterators">Grid iterators</a><a id="Grid-iterators-1"></a><a class="docs-heading-anchor-permalink" href="#Grid-iterators" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellCache" href="#Ferrite.CellCache"><code>Ferrite.CellCache</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CellCache(grid::Grid)
-CellCache(dh::AbstractDofHandler)</code></pre><p>Create a cache object with pre-allocated memory for the nodes, coordinates, and dofs of a cell. The cache is updated for a new cell by calling <code>reinit!(cache, cellid)</code> where <code>cellid::Int</code> is the cell id.</p><p><strong>Methods with <code>CellCache</code></strong></p><ul><li><code>reinit!(cc, i)</code>: reinitialize the cache for cell <code>i</code></li><li><code>cellid(cc)</code>: get the cell id of the currently cached cell</li><li><code>getnodes(cc)</code>: get the global node ids of the cell</li><li><code>getcoordinates(cc)</code>: get the coordinates of the cell</li><li><code>celldofs(cc)</code>: get the global dof ids of the cell</li><li><code>reinit!(fev, cc)</code>: reinitialize <a href="../fevalues/#Ferrite.CellValues"><code>CellValues</code></a> or <a href="../fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a></li></ul><p>See also <a href="#Ferrite.CellIterator"><code>CellIterator</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/iterators.jl#L17-L34">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellIterator" href="#Ferrite.CellIterator"><code>Ferrite.CellIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CellIterator(grid::Grid, cellset=1:getncells(grid))
+10:12</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L850-L885">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.celldofs" href="#Ferrite.celldofs"><code>Ferrite.celldofs</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">celldofs(dh::AbstractDofHandler, i::Int)</code></pre><p>Return a vector with the degrees of freedom that belong to cell <code>i</code>.</p><p>See also <a href="#Ferrite.celldofs!"><code>celldofs!</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L214-L220">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.celldofs!" href="#Ferrite.celldofs!"><code>Ferrite.celldofs!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">celldofs!(global_dofs::Vector{Int}, dh::AbstractDofHandler, i::Int)</code></pre><p>Store the degrees of freedom that belong to cell <code>i</code> in <code>global_dofs</code>.</p><p>See also <a href="#Ferrite.celldofs"><code>celldofs</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L196-L202">source</a></section></article><h1 id="Grid-iterators"><a class="docs-heading-anchor" href="#Grid-iterators">Grid iterators</a><a id="Grid-iterators-1"></a><a class="docs-heading-anchor-permalink" href="#Grid-iterators" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellCache" href="#Ferrite.CellCache"><code>Ferrite.CellCache</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CellCache(grid::Grid)
+CellCache(dh::AbstractDofHandler)</code></pre><p>Create a cache object with pre-allocated memory for the nodes, coordinates, and dofs of a cell. The cache is updated for a new cell by calling <code>reinit!(cache, cellid)</code> where <code>cellid::Int</code> is the cell id.</p><p><strong>Methods with <code>CellCache</code></strong></p><ul><li><code>reinit!(cc, i)</code>: reinitialize the cache for cell <code>i</code></li><li><code>cellid(cc)</code>: get the cell id of the currently cached cell</li><li><code>getnodes(cc)</code>: get the global node ids of the cell</li><li><code>getcoordinates(cc)</code>: get the coordinates of the cell</li><li><code>celldofs(cc)</code>: get the global dof ids of the cell</li><li><code>reinit!(fev, cc)</code>: reinitialize <a href="../fevalues/#Ferrite.CellValues"><code>CellValues</code></a> or <a href="../fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a></li></ul><p>See also <a href="#Ferrite.CellIterator"><code>CellIterator</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/iterators.jl#L17-L34">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellIterator" href="#Ferrite.CellIterator"><code>Ferrite.CellIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CellIterator(grid::Grid, cellset=1:getncells(grid))
CellIterator(dh::AbstractDofHandler, cellset=1:getncells(dh))</code></pre><p>Create a <code>CellIterator</code> to conveniently iterate over all, or a subset, of the cells in a grid. The elements of the iterator are <a href="#Ferrite.CellCache"><code>CellCache</code></a>s which are properly <code>reinit!</code>ialized. See <a href="#Ferrite.CellCache"><code>CellCache</code></a> for more details.</p><p>Looping over a <code>CellIterator</code>, i.e.:</p><pre><code class="language-julia hljs">for cc in CellIterator(grid, cellset)
# ...
end</code></pre><p>is thus simply convenience for the following equivalent snippet:</p><pre><code class="language-julia hljs">cc = CellCache(grid)
for idx in cellset
reinit!(cc, idx)
# ...
-end</code></pre><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p><code>CellIterator</code> is stateful and should not be used for things other than <code>for</code>-looping (e.g. broadcasting over, or collecting the iterator may yield unexpected results).</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/iterators.jl#L213-L238">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetCache" href="#Ferrite.FacetCache"><code>Ferrite.FacetCache</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetCache(grid::Grid)
-FacetCache(dh::AbstractDofHandler)</code></pre><p>Create a cache object with pre-allocated memory for the nodes, coordinates, and dofs of a cell suitable for looping over <em>facets</em> in a grid. The cache is updated for a new facet by calling <code>reinit!(cache, fi::FacetIndex)</code>.</p><p><strong>Methods with <code>fc::FacetCache</code></strong></p><ul><li><code>reinit!(fc, fi)</code>: reinitialize the cache for facet <code>fi::FacetIndex</code></li><li><code>cellid(fc)</code>: get the current cellid</li><li><code>getnodes(fc)</code>: get the global node ids of the <em>cell</em></li><li><code>getcoordinates(fc)</code>: get the coordinates of the <em>cell</em></li><li><code>celldofs(fc)</code>: get the global dof ids of the <em>cell</em></li><li><code>reinit!(fv, fc)</code>: reinitialize <a href="../fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a></li></ul><p>See also <a href="#Ferrite.FacetIterator"><code>FacetIterator</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/iterators.jl#L100-L117">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetIterator" href="#Ferrite.FacetIterator"><code>Ferrite.FacetIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetIterator(gridordh::Union{Grid,AbstractDofHandler}, facetset::AbstractVecOrSet{FacetIndex})</code></pre><p>Create a <code>FacetIterator</code> to conveniently iterate over the faces in <code>facestet</code>. The elements of the iterator are <a href="#Ferrite.FacetCache"><code>FacetCache</code></a>s which are properly <code>reinit!</code>ialized. See <a href="#Ferrite.FacetCache"><code>FacetCache</code></a> for more details.</p><p>Looping over a <code>FacetIterator</code>, i.e.:</p><pre><code class="language-julia hljs">for fc in FacetIterator(grid, facetset)
+end</code></pre><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p><code>CellIterator</code> is stateful and should not be used for things other than <code>for</code>-looping (e.g. broadcasting over, or collecting the iterator may yield unexpected results).</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/iterators.jl#L213-L238">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetCache" href="#Ferrite.FacetCache"><code>Ferrite.FacetCache</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetCache(grid::Grid)
+FacetCache(dh::AbstractDofHandler)</code></pre><p>Create a cache object with pre-allocated memory for the nodes, coordinates, and dofs of a cell suitable for looping over <em>facets</em> in a grid. The cache is updated for a new facet by calling <code>reinit!(cache, fi::FacetIndex)</code>.</p><p><strong>Methods with <code>fc::FacetCache</code></strong></p><ul><li><code>reinit!(fc, fi)</code>: reinitialize the cache for facet <code>fi::FacetIndex</code></li><li><code>cellid(fc)</code>: get the current cellid</li><li><code>getnodes(fc)</code>: get the global node ids of the <em>cell</em></li><li><code>getcoordinates(fc)</code>: get the coordinates of the <em>cell</em></li><li><code>celldofs(fc)</code>: get the global dof ids of the <em>cell</em></li><li><code>reinit!(fv, fc)</code>: reinitialize <a href="../fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a></li></ul><p>See also <a href="#Ferrite.FacetIterator"><code>FacetIterator</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/iterators.jl#L100-L117">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetIterator" href="#Ferrite.FacetIterator"><code>Ferrite.FacetIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetIterator(gridordh::Union{Grid,AbstractDofHandler}, facetset::AbstractVecOrSet{FacetIndex})</code></pre><p>Create a <code>FacetIterator</code> to conveniently iterate over the faces in <code>facestet</code>. The elements of the iterator are <a href="#Ferrite.FacetCache"><code>FacetCache</code></a>s which are properly <code>reinit!</code>ialized. See <a href="#Ferrite.FacetCache"><code>FacetCache</code></a> for more details.</p><p>Looping over a <code>FacetIterator</code>, i.e.:</p><pre><code class="language-julia hljs">for fc in FacetIterator(grid, facetset)
# ...
-end</code></pre><p>is thus simply convenience for the following equivalent snippet: ```julia fc = FacetCache(grid) for faceindex in facetset reinit!(fc, faceindex) # ... end</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/iterators.jl#L275-L295">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceCache" href="#Ferrite.InterfaceCache"><code>Ferrite.InterfaceCache</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceCache(grid::Grid)
-InterfaceCache(dh::AbstractDofHandler)</code></pre><p>Create a cache object with pre-allocated memory for the nodes, coordinates, and dofs of an interface. The cache is updated for a new cell by calling <code>reinit!(cache, facet_a, facet_b)</code> where <code>facet_a::FacetIndex</code> and <code>facet_b::FacetIndex</code> are the two interface facets.</p><p><strong>Struct fields of <code>InterfaceCache</code></strong></p><ul><li><code>ic.a :: FacetCache</code>: facet cache for the first facet of the interface</li><li><code>ic.b :: FacetCache</code>: facet cache for the second facet of the interface</li><li><code>ic.dofs :: Vector{Int}</code>: global dof ids for the interface (union of <code>ic.a.dofs</code> and <code>ic.b.dofs</code>)</li></ul><p><strong>Methods with <code>InterfaceCache</code></strong></p><ul><li><code>reinit!(cache::InterfaceCache, facet_a::FacetIndex, facet_b::FacetIndex)</code>: reinitialize the cache for a new interface</li><li><code>interfacedofs(ic)</code>: get the global dof ids of the interface</li></ul><p>See also <a href="#Ferrite.InterfaceIterator"><code>InterfaceIterator</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/iterators.jl#L148-L166">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceIterator" href="#Ferrite.InterfaceIterator"><code>Ferrite.InterfaceIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceIterator(grid::Grid, [topology::ExclusiveTopology])
+end</code></pre><p>is thus simply convenience for the following equivalent snippet: ```julia fc = FacetCache(grid) for faceindex in facetset reinit!(fc, faceindex) # ... end</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/iterators.jl#L275-L295">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceCache" href="#Ferrite.InterfaceCache"><code>Ferrite.InterfaceCache</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceCache(grid::Grid)
+InterfaceCache(dh::AbstractDofHandler)</code></pre><p>Create a cache object with pre-allocated memory for the nodes, coordinates, and dofs of an interface. The cache is updated for a new cell by calling <code>reinit!(cache, facet_a, facet_b)</code> where <code>facet_a::FacetIndex</code> and <code>facet_b::FacetIndex</code> are the two interface facets.</p><p><strong>Struct fields of <code>InterfaceCache</code></strong></p><ul><li><code>ic.a :: FacetCache</code>: facet cache for the first facet of the interface</li><li><code>ic.b :: FacetCache</code>: facet cache for the second facet of the interface</li><li><code>ic.dofs :: Vector{Int}</code>: global dof ids for the interface (union of <code>ic.a.dofs</code> and <code>ic.b.dofs</code>)</li></ul><p><strong>Methods with <code>InterfaceCache</code></strong></p><ul><li><code>reinit!(cache::InterfaceCache, facet_a::FacetIndex, facet_b::FacetIndex)</code>: reinitialize the cache for a new interface</li><li><code>interfacedofs(ic)</code>: get the global dof ids of the interface</li></ul><p>See also <a href="#Ferrite.InterfaceIterator"><code>InterfaceIterator</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/iterators.jl#L148-L166">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceIterator" href="#Ferrite.InterfaceIterator"><code>Ferrite.InterfaceIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceIterator(grid::Grid, [topology::ExclusiveTopology])
InterfaceIterator(dh::AbstractDofHandler, [topology::ExclusiveTopology])</code></pre><p>Create an <code>InterfaceIterator</code> to conveniently iterate over all the interfaces in a grid. The elements of the iterator are <a href="#Ferrite.InterfaceCache"><code>InterfaceCache</code></a>s which are properly <code>reinit!</code>ialized. See <a href="#Ferrite.InterfaceCache"><code>InterfaceCache</code></a> for more details. Looping over an <code>InterfaceIterator</code>, i.e.:</p><pre><code class="language-julia hljs">for ic in InterfaceIterator(grid, topology)
# ...
end</code></pre><p>is thus simply convenience for the following equivalent snippet for grids of dimensions > 1:</p><pre><code class="language-julia hljs">ic = InterfaceCache(grid)
@@ -57,4 +57,4 @@
neighbor_facet = neighbors[1]
reinit!(ic, facet, neighbor_facet)
# ...
-end</code></pre><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p><code>InterfaceIterator</code> is stateful and should not be used for things other than <code>for</code>-looping (e.g. broadcasting over, or collecting the iterator may yield unexpected results).</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/iterators.jl#L316-L344">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fevalues/">« FEValues</a><a class="docs-footer-nextpage" href="../sparsity_pattern/">Sparsity pattern and sparse matrices »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p><code>InterfaceIterator</code> is stateful and should not be used for things other than <code>for</code>-looping (e.g. broadcasting over, or collecting the iterator may yield unexpected results).</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/iterators.jl#L316-L344">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fevalues/">« FEValues</a><a class="docs-footer-nextpage" href="../sparsity_pattern/">Sparsity pattern and sparse matrices »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/reference/export/index.html b/dev/reference/export/index.html
index 90f357cdd7..218570f861 100644
--- a/dev/reference/export/index.html
+++ b/dev/reference/export/index.html
@@ -15,8 +15,8 @@
end
end
-projected = project(proj, vals)</code></pre><p>where <code>projected</code> can be used in e.g. <code>evaluate_at_points</code> with the <a href="#Ferrite.PointEvalHandler"><code>PointEvalHandler</code></a>, or with <a href="#Ferrite.evaluate_at_grid_nodes"><code>evaluate_at_grid_nodes</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/L2_projection.jl#L28-L66">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!-Tuple{L2Projector, Union{AbstractSet{Int64}, AbstractVector{Int64}}, Interpolation}" href="#Ferrite.add!-Tuple{L2Projector, Union{AbstractSet{Int64}, AbstractVector{Int64}}, Interpolation}"><code>Ferrite.add!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(proj::L2Projector, set::AbstractVecOrSet{Int}, ip::Interpolation;
- qr_rhs, [qr_lhs])</code></pre><p>Add an interpolation <code>ip</code> on the cells in <code>set</code> to the <code>L2Projector</code> <code>proj</code>.</p><ul><li><code>qr_rhs</code> sets the quadrature rule used to later integrate the right-hand-side of the projection equation, when calling <a href="#Ferrite.project"><code>project</code></a>. It should match the quadrature points used when creating the quadrature-point variables to project.</li><li>The <em>optional</em> <code>qr_lhs</code> sets the quadrature rule used to integrate the left-hand-side of the projection equation, and defaults to a quadrature rule that integrates the mass-matrix exactly for the given interpolation <code>ip</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/L2_projection.jl#L94-L106">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.close!-Tuple{L2Projector}" href="#Ferrite.close!-Tuple{L2Projector}"><code>Ferrite.close!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">close!(proj::L2Projector)</code></pre><p>Close <code>proj</code> which assembles and calculates the left-hand-side of the projection equation, before doing a Cholesky factorization of the mass-matrix.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/L2_projection.jl#L126-L131">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.L2Projector-Tuple{Interpolation, Ferrite.AbstractGrid}" href="#Ferrite.L2Projector-Tuple{Interpolation, Ferrite.AbstractGrid}"><code>Ferrite.L2Projector</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">L2Projector(ip::Interpolation, grid::AbstractGrid; [qr_lhs], [set])</code></pre><p>A quick way to initiate an <code>L2Projector</code>, add an interpolation <code>ip</code> on the <code>set</code> to it, and then <code>close!</code> it so that it can be used to <code>project</code>. The optional keyword argument <code>set</code> defaults to all cells in the <code>grid</code>, while <code>qr_lhs</code> defaults to a quadrature rule that integrates the mass matrix exactly for the interpolation <code>ip</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/L2_projection.jl#L72-L79">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.project" href="#Ferrite.project"><code>Ferrite.project</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">project(proj::L2Projector, vals, [qr_rhs::QuadratureRule])</code></pre><p>Makes a L2 projection of data <code>vals</code> to the nodes of the grid using the projector <code>proj</code> (see <a href="#Ferrite.L2Projector-Tuple{Ferrite.AbstractGrid}"><code>L2Projector</code></a>).</p><p><code>project</code> integrates the right hand side, and solves the projection <span>$u$</span> from the following projection equation: Find projection <span>$u \in U_h(\Omega) \subset L_2(\Omega)$</span> such that</p><p class="math-container">\[\int v u \ \mathrm{d}\Omega = \int v f \ \mathrm{d}\Omega \quad \forall v \in U_h(\Omega),\]</p><p>where <span>$f \in L_2(\Omega)$</span> is the data to project. The function space <span>$U_h(\Omega)$</span> is the finite element approximation given by the interpolations in <code>proj</code>.</p><p>The data <code>vals</code> should be an <code>AbstractVector</code> or <code>AbstractDict</code> that is indexed by the cell number. Each index in <code>vals</code> should give an <code>AbstractVector</code> with one element for each cell quadrature point.</p><p>If <code>proj</code> was created by calling <code>L2Projector(ip, grid, set)</code>, <code>qr_rhs</code> must be given. Otherwise, this is added for each domain when calling <code>add!(proj, args...)</code>.</p><p>Alternatively, <code>vals</code> can be a matrix, with the column index referring the cell number, and the row index corresponding to quadrature point number. Example (scalar) input data:</p><pre><code class="language-julia hljs">vals = [
+projected = project(proj, vals)</code></pre><p>where <code>projected</code> can be used in e.g. <code>evaluate_at_points</code> with the <a href="#Ferrite.PointEvalHandler"><code>PointEvalHandler</code></a>, or with <a href="#Ferrite.evaluate_at_grid_nodes"><code>evaluate_at_grid_nodes</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/L2_projection.jl#L28-L66">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add!-Tuple{L2Projector, Union{AbstractSet{Int64}, AbstractVector{Int64}}, Interpolation}" href="#Ferrite.add!-Tuple{L2Projector, Union{AbstractSet{Int64}, AbstractVector{Int64}}, Interpolation}"><code>Ferrite.add!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add!(proj::L2Projector, set::AbstractVecOrSet{Int}, ip::Interpolation;
+ qr_rhs, [qr_lhs])</code></pre><p>Add an interpolation <code>ip</code> on the cells in <code>set</code> to the <code>L2Projector</code> <code>proj</code>.</p><ul><li><code>qr_rhs</code> sets the quadrature rule used to later integrate the right-hand-side of the projection equation, when calling <a href="#Ferrite.project"><code>project</code></a>. It should match the quadrature points used when creating the quadrature-point variables to project.</li><li>The <em>optional</em> <code>qr_lhs</code> sets the quadrature rule used to integrate the left-hand-side of the projection equation, and defaults to a quadrature rule that integrates the mass-matrix exactly for the given interpolation <code>ip</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/L2_projection.jl#L94-L106">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.close!-Tuple{L2Projector}" href="#Ferrite.close!-Tuple{L2Projector}"><code>Ferrite.close!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">close!(proj::L2Projector)</code></pre><p>Close <code>proj</code> which assembles and calculates the left-hand-side of the projection equation, before doing a Cholesky factorization of the mass-matrix.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/L2_projection.jl#L126-L131">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.L2Projector-Tuple{Interpolation, Ferrite.AbstractGrid}" href="#Ferrite.L2Projector-Tuple{Interpolation, Ferrite.AbstractGrid}"><code>Ferrite.L2Projector</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">L2Projector(ip::Interpolation, grid::AbstractGrid; [qr_lhs], [set])</code></pre><p>A quick way to initiate an <code>L2Projector</code>, add an interpolation <code>ip</code> on the <code>set</code> to it, and then <code>close!</code> it so that it can be used to <code>project</code>. The optional keyword argument <code>set</code> defaults to all cells in the <code>grid</code>, while <code>qr_lhs</code> defaults to a quadrature rule that integrates the mass matrix exactly for the interpolation <code>ip</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/L2_projection.jl#L72-L79">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.project" href="#Ferrite.project"><code>Ferrite.project</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">project(proj::L2Projector, vals, [qr_rhs::QuadratureRule])</code></pre><p>Makes a L2 projection of data <code>vals</code> to the nodes of the grid using the projector <code>proj</code> (see <a href="#Ferrite.L2Projector-Tuple{Ferrite.AbstractGrid}"><code>L2Projector</code></a>).</p><p><code>project</code> integrates the right hand side, and solves the projection <span>$u$</span> from the following projection equation: Find projection <span>$u \in U_h(\Omega) \subset L_2(\Omega)$</span> such that</p><p class="math-container">\[\int v u \ \mathrm{d}\Omega = \int v f \ \mathrm{d}\Omega \quad \forall v \in U_h(\Omega),\]</p><p>where <span>$f \in L_2(\Omega)$</span> is the data to project. The function space <span>$U_h(\Omega)$</span> is the finite element approximation given by the interpolations in <code>proj</code>.</p><p>The data <code>vals</code> should be an <code>AbstractVector</code> or <code>AbstractDict</code> that is indexed by the cell number. Each index in <code>vals</code> should give an <code>AbstractVector</code> with one element for each cell quadrature point.</p><p>If <code>proj</code> was created by calling <code>L2Projector(ip, grid, set)</code>, <code>qr_rhs</code> must be given. Otherwise, this is added for each domain when calling <code>add!(proj, args...)</code>.</p><p>Alternatively, <code>vals</code> can be a matrix, with the column index referring the cell number, and the row index corresponding to quadrature point number. Example (scalar) input data:</p><pre><code class="language-julia hljs">vals = [
[0.44, 0.98, 0.32], # data for quadrature point 1, 2, 3 of element 1
[0.29, 0.48, 0.55], # data for quadrature point 1, 2, 3 of element 2
# ...
@@ -24,19 +24,19 @@
0.44 0.29 # ...
0.98 0.48 # ...
0.32 0.55 # ...
-]</code></pre><p>Supported data types to project are <code>Number</code>s and <code>AbstractTensor</code>s.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The order of the returned data correspond to the order of the <code>L2Projector</code>'s internal <code>DofHandler</code>. The data can be further analyzed with <a href="#Ferrite.evaluate_at_points"><code>evaluate_at_points</code></a> and <a href="#Ferrite.evaluate_at_grid_nodes"><code>evaluate_at_grid_nodes</code></a>. Use <a href="#Ferrite.write_projection"><code>write_projection</code></a> to export the result.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/L2_projection.jl#L196-L241">source</a></section></article><h2 id="Evaluation-at-points"><a class="docs-heading-anchor" href="#Evaluation-at-points">Evaluation at points</a><a id="Evaluation-at-points-1"></a><a class="docs-heading-anchor-permalink" href="#Evaluation-at-points" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.evaluate_at_grid_nodes" href="#Ferrite.evaluate_at_grid_nodes"><code>Ferrite.evaluate_at_grid_nodes</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">evaluate_at_grid_nodes(dh::AbstractDofHandler, u::AbstractVector{T}, fieldname::Symbol) where T</code></pre><p>Evaluate the approximated solution for field <code>fieldname</code> at the node coordinates of the grid given the Dof handler <code>dh</code> and the solution vector <code>u</code>.</p><p>Return a vector of length <code>getnnodes(grid)</code> where entry <code>i</code> contains the evaluation of the approximation in the coordinate of node <code>i</code>. If the field does not live on parts of the grid, the corresponding values for those nodes will be returned as <code>NaN</code>s.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/DofHandler.jl#L918-L927">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointEvalHandler" href="#Ferrite.PointEvalHandler"><code>Ferrite.PointEvalHandler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointEvalHandler(grid::Grid, points::AbstractVector{Vec{dim,T}}; kwargs...) where {dim, T}</code></pre><p>The <code>PointEvalHandler</code> can be used for function evaluation in <em>arbitrary points</em> in the domain – not just in quadrature points or nodes.</p><p>The constructor takes a grid and a vector of coordinates for the points. The <code>PointEvalHandler</code> computes i) the corresponding cell, and ii) the (local) coordinate within the cell, for each point. The fields of the <code>PointEvalHandler</code> are:</p><ul><li><code>cells::Vector{Union{Int,Nothing}}</code>: vector with cell IDs for the points, with <code>nothing</code> for points that could not be found.</li><li><code>local_coords::Vector{Union{Vec,Nothing}}</code>: vector with the local coordinates (i.e. coordinates in the reference configuration) for the points, with <code>nothing</code> for points that could not be found.</li></ul><p>There are two ways to use the <code>PointEvalHandler</code> to evaluate functions:</p><ul><li><a href="#Ferrite.evaluate_at_points"><code>evaluate_at_points</code></a>: can be used when the function is described by i) a <code>dh::DofHandler</code> + <code>uh::Vector</code> (for example the FE-solution), or ii) a <code>p::L2Projector</code> + <code>ph::Vector</code> (for projected data).</li><li>Iteration with <a href="#Ferrite.PointIterator"><code>PointIterator</code></a> + <a href="#Ferrite.PointValues"><code>PointValues</code></a>: can be used for more flexible evaluation in the points, for example to compute gradients.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/PointEvalHandler.jl#L7-L29">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.evaluate_at_points" href="#Ferrite.evaluate_at_points"><code>Ferrite.evaluate_at_points</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">evaluate_at_points(ph::PointEvalHandler, dh::AbstractDofHandler, dof_values::Vector{T}, [fieldname::Symbol]) where T
-evaluate_at_points(ph::PointEvalHandler, proj::L2Projector, dof_values::Vector{T}) where T</code></pre><p>Return a <code>Vector{T}</code> (for a 1-dimensional field) or a <code>Vector{Vec{fielddim, T}}</code> (for a vector field) with the field values of field <code>fieldname</code> in the points of the <code>PointEvalHandler</code>. The <code>fieldname</code> can be omitted if only one field is stored in <code>dh</code>. The field values are computed based on the <code>dof_values</code> and interpolated to the local coordinates by the function interpolation of the corresponding <code>field</code> stored in the <code>AbstractDofHandler</code> or the <code>L2Projector</code>.</p><p>Points that could not be found in the domain when constructing the <code>PointEvalHandler</code> will have <code>NaN</code>s for the corresponding entries in the output vector.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/PointEvalHandler.jl#L205-L218">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointValues" href="#Ferrite.PointValues"><code>Ferrite.PointValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointValues(cv::CellValues)
-PointValues([::Type{T}], func_interpol::Interpolation, [geom_interpol::Interpolation])</code></pre><p>Similar to <code>CellValues</code> but with a single updateable "quadrature point". <code>PointValues</code> are used for evaluation of functions/gradients in arbitrary points of the domain together with a <a href="#Ferrite.PointEvalHandler"><code>PointEvalHandler</code></a>.</p><p><code>PointValues</code> can be created from <code>CellValues</code>, or from the interpolations directly.</p><p><code>PointValues</code> are reinitialized like other <code>CellValues</code>, but since the local reference coordinate of the "quadrature point" changes this needs to be passed to <a href="../fevalues/#Ferrite.reinit!"><code>reinit!</code></a>, in addition to the element coordinates: <code>reinit!(pv, coords, local_coord)</code>. Alternatively, it can be reinitialized with a <a href="#Ferrite.PointLocation"><code>PointLocation</code></a> when iterating a <code>PointEvalHandler</code> with a <a href="#Ferrite.PointIterator"><code>PointIterator</code></a>.</p><p>For function/gradient evaluation, <code>PointValues</code> are used in the same way as <code>CellValues</code>, i.e. by using <a href="../fevalues/#Ferrite.function_value"><code>function_value</code></a>, <a href="../fevalues/#Ferrite.function_gradient"><code>function_gradient</code></a>, etc, with the exception that there is no need to specify the quadrature point index (since <code>PointValues</code> only have 1, this is the default).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/PointValues.jl#L1-L21">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointIterator" href="#Ferrite.PointIterator"><code>Ferrite.PointIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointIterator(ph::PointEvalHandler)</code></pre><p>Create an iterator over the points in the <a href="#Ferrite.PointEvalHandler"><code>PointEvalHandler</code></a>. The elements of the iterator are either a <a href="#Ferrite.PointLocation"><code>PointLocation</code></a>, if the corresponding point could be found in the grid, or <code>nothing</code>, if the point was not found.</p><p>A <code>PointLocation</code> can be used to query the cell ID with the <code>cellid</code> function, and can be used to reinitialize <a href="#Ferrite.PointValues"><code>PointValues</code></a> with <a href="../fevalues/#Ferrite.reinit!"><code>reinit!</code></a>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">ph = PointEvalHandler(grid, points)
+]</code></pre><p>Supported data types to project are <code>Number</code>s and <code>AbstractTensor</code>s.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The order of the returned data correspond to the order of the <code>L2Projector</code>'s internal <code>DofHandler</code>. The data can be further analyzed with <a href="#Ferrite.evaluate_at_points"><code>evaluate_at_points</code></a> and <a href="#Ferrite.evaluate_at_grid_nodes"><code>evaluate_at_grid_nodes</code></a>. Use <a href="#Ferrite.write_projection"><code>write_projection</code></a> to export the result.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/L2_projection.jl#L196-L241">source</a></section></article><h2 id="Evaluation-at-points"><a class="docs-heading-anchor" href="#Evaluation-at-points">Evaluation at points</a><a id="Evaluation-at-points-1"></a><a class="docs-heading-anchor-permalink" href="#Evaluation-at-points" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.evaluate_at_grid_nodes" href="#Ferrite.evaluate_at_grid_nodes"><code>Ferrite.evaluate_at_grid_nodes</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">evaluate_at_grid_nodes(dh::AbstractDofHandler, u::AbstractVector{T}, fieldname::Symbol) where T</code></pre><p>Evaluate the approximated solution for field <code>fieldname</code> at the node coordinates of the grid given the Dof handler <code>dh</code> and the solution vector <code>u</code>.</p><p>Return a vector of length <code>getnnodes(grid)</code> where entry <code>i</code> contains the evaluation of the approximation in the coordinate of node <code>i</code>. If the field does not live on parts of the grid, the corresponding values for those nodes will be returned as <code>NaN</code>s.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/DofHandler.jl#L918-L927">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointEvalHandler" href="#Ferrite.PointEvalHandler"><code>Ferrite.PointEvalHandler</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointEvalHandler(grid::Grid, points::AbstractVector{Vec{dim,T}}; kwargs...) where {dim, T}</code></pre><p>The <code>PointEvalHandler</code> can be used for function evaluation in <em>arbitrary points</em> in the domain – not just in quadrature points or nodes.</p><p>The constructor takes a grid and a vector of coordinates for the points. The <code>PointEvalHandler</code> computes i) the corresponding cell, and ii) the (local) coordinate within the cell, for each point. The fields of the <code>PointEvalHandler</code> are:</p><ul><li><code>cells::Vector{Union{Int,Nothing}}</code>: vector with cell IDs for the points, with <code>nothing</code> for points that could not be found.</li><li><code>local_coords::Vector{Union{Vec,Nothing}}</code>: vector with the local coordinates (i.e. coordinates in the reference configuration) for the points, with <code>nothing</code> for points that could not be found.</li></ul><p>There are two ways to use the <code>PointEvalHandler</code> to evaluate functions:</p><ul><li><a href="#Ferrite.evaluate_at_points"><code>evaluate_at_points</code></a>: can be used when the function is described by i) a <code>dh::DofHandler</code> + <code>uh::Vector</code> (for example the FE-solution), or ii) a <code>p::L2Projector</code> + <code>ph::Vector</code> (for projected data).</li><li>Iteration with <a href="#Ferrite.PointIterator"><code>PointIterator</code></a> + <a href="#Ferrite.PointValues"><code>PointValues</code></a>: can be used for more flexible evaluation in the points, for example to compute gradients.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/PointEvalHandler.jl#L7-L29">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.evaluate_at_points" href="#Ferrite.evaluate_at_points"><code>Ferrite.evaluate_at_points</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">evaluate_at_points(ph::PointEvalHandler, dh::AbstractDofHandler, dof_values::Vector{T}, [fieldname::Symbol]) where T
+evaluate_at_points(ph::PointEvalHandler, proj::L2Projector, dof_values::Vector{T}) where T</code></pre><p>Return a <code>Vector{T}</code> (for a 1-dimensional field) or a <code>Vector{Vec{fielddim, T}}</code> (for a vector field) with the field values of field <code>fieldname</code> in the points of the <code>PointEvalHandler</code>. The <code>fieldname</code> can be omitted if only one field is stored in <code>dh</code>. The field values are computed based on the <code>dof_values</code> and interpolated to the local coordinates by the function interpolation of the corresponding <code>field</code> stored in the <code>AbstractDofHandler</code> or the <code>L2Projector</code>.</p><p>Points that could not be found in the domain when constructing the <code>PointEvalHandler</code> will have <code>NaN</code>s for the corresponding entries in the output vector.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/PointEvalHandler.jl#L205-L218">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointValues" href="#Ferrite.PointValues"><code>Ferrite.PointValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointValues(cv::CellValues)
+PointValues([::Type{T}], func_interpol::Interpolation, [geom_interpol::Interpolation])</code></pre><p>Similar to <code>CellValues</code> but with a single updateable "quadrature point". <code>PointValues</code> are used for evaluation of functions/gradients in arbitrary points of the domain together with a <a href="#Ferrite.PointEvalHandler"><code>PointEvalHandler</code></a>.</p><p><code>PointValues</code> can be created from <code>CellValues</code>, or from the interpolations directly.</p><p><code>PointValues</code> are reinitialized like other <code>CellValues</code>, but since the local reference coordinate of the "quadrature point" changes this needs to be passed to <a href="../fevalues/#Ferrite.reinit!"><code>reinit!</code></a>, in addition to the element coordinates: <code>reinit!(pv, coords, local_coord)</code>. Alternatively, it can be reinitialized with a <a href="#Ferrite.PointLocation"><code>PointLocation</code></a> when iterating a <code>PointEvalHandler</code> with a <a href="#Ferrite.PointIterator"><code>PointIterator</code></a>.</p><p>For function/gradient evaluation, <code>PointValues</code> are used in the same way as <code>CellValues</code>, i.e. by using <a href="../fevalues/#Ferrite.function_value"><code>function_value</code></a>, <a href="../fevalues/#Ferrite.function_gradient"><code>function_gradient</code></a>, etc, with the exception that there is no need to specify the quadrature point index (since <code>PointValues</code> only have 1, this is the default).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/PointValues.jl#L1-L21">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointIterator" href="#Ferrite.PointIterator"><code>Ferrite.PointIterator</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointIterator(ph::PointEvalHandler)</code></pre><p>Create an iterator over the points in the <a href="#Ferrite.PointEvalHandler"><code>PointEvalHandler</code></a>. The elements of the iterator are either a <a href="#Ferrite.PointLocation"><code>PointLocation</code></a>, if the corresponding point could be found in the grid, or <code>nothing</code>, if the point was not found.</p><p>A <code>PointLocation</code> can be used to query the cell ID with the <code>cellid</code> function, and can be used to reinitialize <a href="#Ferrite.PointValues"><code>PointValues</code></a> with <a href="../fevalues/#Ferrite.reinit!"><code>reinit!</code></a>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">ph = PointEvalHandler(grid, points)
for point in PointIterator(ph)
point === nothing && continue # Skip any points that weren't found
reinit!(pointvalues, point) # Update pointvalues
# ...
-end</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/PointEvalHandler.jl#L330-L350">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointLocation" href="#Ferrite.PointLocation"><code>Ferrite.PointLocation</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointLocation</code></pre><p>Element of a <a href="#Ferrite.PointIterator"><code>PointIterator</code></a>, typically used to reinitialize <a href="#Ferrite.PointValues"><code>PointValues</code></a>. Fields:</p><ul><li><code>cid::Int</code>: ID of the cell containing the point</li><li><code>local_coord::Vec</code>: the local (reference) coordinate of the point</li><li><code>coords::Vector{Vec}</code>: the coordinates of the cell</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/PointEvalHandler.jl#L364-L372">source</a></section></article><h2 id="VTK-export"><a class="docs-heading-anchor" href="#VTK-export">VTK export</a><a id="VTK-export-1"></a><a class="docs-heading-anchor-permalink" href="#VTK-export" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.VTKGridFile" href="#Ferrite.VTKGridFile"><code>Ferrite.VTKGridFile</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">VTKGridFile(filename::AbstractString, grid::AbstractGrid; kwargs...)
+end</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/PointEvalHandler.jl#L330-L350">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.PointLocation" href="#Ferrite.PointLocation"><code>Ferrite.PointLocation</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PointLocation</code></pre><p>Element of a <a href="#Ferrite.PointIterator"><code>PointIterator</code></a>, typically used to reinitialize <a href="#Ferrite.PointValues"><code>PointValues</code></a>. Fields:</p><ul><li><code>cid::Int</code>: ID of the cell containing the point</li><li><code>local_coord::Vec</code>: the local (reference) coordinate of the point</li><li><code>coords::Vector{Vec}</code>: the coordinates of the cell</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/PointEvalHandler.jl#L364-L372">source</a></section></article><h2 id="VTK-export"><a class="docs-heading-anchor" href="#VTK-export">VTK export</a><a id="VTK-export-1"></a><a class="docs-heading-anchor-permalink" href="#VTK-export" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.VTKGridFile" href="#Ferrite.VTKGridFile"><code>Ferrite.VTKGridFile</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">VTKGridFile(filename::AbstractString, grid::AbstractGrid; kwargs...)
VTKGridFile(filename::AbstractString, dh::DofHandler; kwargs...)</code></pre><p>Create a <code>VTKGridFile</code> that contains an unstructured VTK grid. The keyword arguments are forwarded to <code>WriteVTK.vtk_grid</code>, see <a href="https://juliavtk.github.io/WriteVTK.jl/stable/grids/syntax/#Data-formatting-options">Data Formatting Options</a></p><p>This file handler can be used to to write data with</p><ul><li><a href="#Ferrite.write_solution"><code>write_solution</code></a></li><li><a href="#Ferrite.write_cell_data"><code>write_cell_data</code></a></li><li><a href="#Ferrite.write_projection"><code>write_projection</code></a></li><li><a href="#Ferrite.write_node_data"><code>write_node_data</code></a>.</li><li><a href="#Ferrite.write_cellset"><code>Ferrite.write_cellset</code></a></li><li><a href="#Ferrite.write_nodeset"><code>Ferrite.write_nodeset</code></a></li><li><a href="#Ferrite.write_constraints"><code>Ferrite.write_constraints</code></a></li></ul><p>It is necessary to call <code>close(::VTKGridFile)</code> to save the data after writing to the file handler. Using the supported <code>do</code>-block does this automatically:</p><pre><code class="language-julia hljs">VTKGridFile(filename, grid) do vtk
write_solution(vtk, dh, u)
write_cell_data(vtk, celldata)
-end</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L1-L27">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_solution" href="#Ferrite.write_solution"><code>Ferrite.write_solution</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_solution(vtk::VTKGridFile, dh::AbstractDofHandler, u::Vector, suffix="")</code></pre><p>Save the values at the nodes in the degree of freedom vector <code>u</code> to <code>vtk</code>. Each field in <code>dh</code> will be saved separately, and <code>suffix</code> can be used to append to the fieldname.</p><p><code>u</code> can also contain tensorial values, but each entry in <code>u</code> must correspond to a degree of freedom in <code>dh</code>, see <a href="#Ferrite.write_node_data"><code>write_node_data</code></a> for details. Use <code>write_node_data</code> directly when exporting values that are already sorted by the nodes in the grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L177-L188">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_projection" href="#Ferrite.write_projection"><code>Ferrite.write_projection</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_projection(vtk::VTKGridFile, proj::L2Projector, vals::Vector, name::AbstractString)</code></pre><p>Project <code>vals</code> to the grid nodes with <code>proj</code> and save to <code>vtk</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L198-L202">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_cell_data" href="#Ferrite.write_cell_data"><code>Ferrite.write_cell_data</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_cell_data(vtk::VTKGridFile, celldata::AbstractVector, name::String)</code></pre><p>Write the <code>celldata</code> that is ordered by the cells in the grid to the vtk file.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L210-L214">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_node_data" href="#Ferrite.write_node_data"><code>Ferrite.write_node_data</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_node_data(vtk::VTKGridFile, nodedata::Vector{Real}, name)
-write_node_data(vtk::VTKGridFile, nodedata::Vector{<:AbstractTensor}, name)</code></pre><p>Write the <code>nodedata</code> that is ordered by the nodes in the grid to <code>vtk</code>.</p><p>When <code>nodedata</code> contains <code>Tensors.Vec</code>s, each component is exported. Two-dimensional vectors are padded with zeros.</p><p>When <code>nodedata</code> contains second order tensors, the index order, <code>[11, 22, 33, 23, 13, 12, 32, 31, 21]</code>, follows the default Voigt order in Tensors.jl.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L220-L231">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_cellset" href="#Ferrite.write_cellset"><code>Ferrite.write_cellset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_cellset(vtk, grid::AbstractGrid)
+end</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L1-L27">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_solution" href="#Ferrite.write_solution"><code>Ferrite.write_solution</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_solution(vtk::VTKGridFile, dh::AbstractDofHandler, u::Vector, suffix="")</code></pre><p>Save the values at the nodes in the degree of freedom vector <code>u</code> to <code>vtk</code>. Each field in <code>dh</code> will be saved separately, and <code>suffix</code> can be used to append to the fieldname.</p><p><code>u</code> can also contain tensorial values, but each entry in <code>u</code> must correspond to a degree of freedom in <code>dh</code>, see <a href="#Ferrite.write_node_data"><code>write_node_data</code></a> for details. Use <code>write_node_data</code> directly when exporting values that are already sorted by the nodes in the grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L177-L188">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_projection" href="#Ferrite.write_projection"><code>Ferrite.write_projection</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_projection(vtk::VTKGridFile, proj::L2Projector, vals::Vector, name::AbstractString)</code></pre><p>Project <code>vals</code> to the grid nodes with <code>proj</code> and save to <code>vtk</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L198-L202">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_cell_data" href="#Ferrite.write_cell_data"><code>Ferrite.write_cell_data</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_cell_data(vtk::VTKGridFile, celldata::AbstractVector, name::String)</code></pre><p>Write the <code>celldata</code> that is ordered by the cells in the grid to the vtk file.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L210-L214">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_node_data" href="#Ferrite.write_node_data"><code>Ferrite.write_node_data</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_node_data(vtk::VTKGridFile, nodedata::Vector{Real}, name)
+write_node_data(vtk::VTKGridFile, nodedata::Vector{<:AbstractTensor}, name)</code></pre><p>Write the <code>nodedata</code> that is ordered by the nodes in the grid to <code>vtk</code>.</p><p>When <code>nodedata</code> contains <code>Tensors.Vec</code>s, each component is exported. Two-dimensional vectors are padded with zeros.</p><p>When <code>nodedata</code> contains second order tensors, the index order, <code>[11, 22, 33, 23, 13, 12, 32, 31, 21]</code>, follows the default Voigt order in Tensors.jl.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L220-L231">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_cellset" href="#Ferrite.write_cellset"><code>Ferrite.write_cellset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_cellset(vtk, grid::AbstractGrid)
write_cellset(vtk, grid::AbstractGrid, cellset::String)
-write_cellset(vtk, grid::AbstractGrid, cellsets::Union{AbstractVector{String},AbstractSet{String})</code></pre><p>Write all cell sets in the grid with name according to their keys and celldata 1 if the cell is in the set, and 0 otherwise. It is also possible to only export a single <code>cellset</code>, or multiple <code>cellsets</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L250-L258">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_nodeset" href="#Ferrite.write_nodeset"><code>Ferrite.write_nodeset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_nodeset(vtk::VTKGridFile, grid::AbstractGrid, nodeset::String)</code></pre><p>Write nodal values of 1 for nodes in <code>nodeset</code>, and 0 otherwise</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L238-L242">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_constraints" href="#Ferrite.write_constraints"><code>Ferrite.write_constraints</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_constraints(vtk::VTKGridFile, ch::ConstraintHandler)</code></pre><p>Saves the dirichlet boundary conditions to a vtkfile. Values will have a 1 where bcs are active and 0 otherwise</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L270-L275">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_cell_colors" href="#Ferrite.write_cell_colors"><code>Ferrite.write_cell_colors</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_cell_colors(vtk::VTKGridFile, grid::AbstractGrid, cell_colors, name="coloring")</code></pre><p>Write cell colors (see <a href="../grid/#Ferrite.create_coloring"><code>create_coloring</code></a>) to a VTK file for visualization.</p><p>In case of coloring a subset, the cells which are not part of the subset are represented as color 0.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Export/VTK.jl#L310-L316">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../grid/">« Grid & AbstractGrid</a><a class="docs-footer-nextpage" href="../utils/">Development utility functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+write_cellset(vtk, grid::AbstractGrid, cellsets::Union{AbstractVector{String},AbstractSet{String})</code></pre><p>Write all cell sets in the grid with name according to their keys and celldata 1 if the cell is in the set, and 0 otherwise. It is also possible to only export a single <code>cellset</code>, or multiple <code>cellsets</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L250-L258">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_nodeset" href="#Ferrite.write_nodeset"><code>Ferrite.write_nodeset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_nodeset(vtk::VTKGridFile, grid::AbstractGrid, nodeset::String)</code></pre><p>Write nodal values of 1 for nodes in <code>nodeset</code>, and 0 otherwise</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L238-L242">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_constraints" href="#Ferrite.write_constraints"><code>Ferrite.write_constraints</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_constraints(vtk::VTKGridFile, ch::ConstraintHandler)</code></pre><p>Saves the dirichlet boundary conditions to a vtkfile. Values will have a 1 where bcs are active and 0 otherwise</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L270-L275">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.write_cell_colors" href="#Ferrite.write_cell_colors"><code>Ferrite.write_cell_colors</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">write_cell_colors(vtk::VTKGridFile, grid::AbstractGrid, cell_colors, name="coloring")</code></pre><p>Write cell colors (see <a href="../grid/#Ferrite.create_coloring"><code>create_coloring</code></a>) to a VTK file for visualization.</p><p>In case of coloring a subset, the cells which are not part of the subset are represented as color 0.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Export/VTK.jl#L310-L316">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../grid/">« Grid & AbstractGrid</a><a class="docs-footer-nextpage" href="../utils/">Development utility functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="is-disabled">API reference</a></li><li class="is-active"><a href>FEValues</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>FEValues</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/fevalues.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="FEValues"><a class="docs-heading-anchor" href="#FEValues">FEValues</a><a id="FEValues-1"></a><a class="docs-heading-anchor-permalink" href="#FEValues" title="Permalink"></a></h1><h2 id="Main-types"><a class="docs-heading-anchor" href="#Main-types">Main types</a><a id="Main-types-1"></a><a class="docs-heading-anchor-permalink" href="#Main-types" title="Permalink"></a></h2><p><a href="#Ferrite.CellValues"><code>CellValues</code></a> and <a href="#Ferrite.FacetValues"><code>FacetValues</code></a> are the most common subtypes of <code>Ferrite.AbstractValues</code>. For more details about how these work, please see the related <a href="../../topics/FEValues/#fevalues_topicguide">topic guide</a>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellValues" href="#Ferrite.CellValues"><code>Ferrite.CellValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CellValues([::Type{T},] quad_rule::QuadratureRule, func_interpol::Interpolation, [geom_interpol::Interpolation])</code></pre><p>A <code>CellValues</code> object facilitates the process of evaluating values of shape functions, gradients of shape functions, values of nodal functions, gradients and divergences of nodal functions etc. in the finite element cell.</p><p><strong>Arguments:</strong></p><ul><li><code>T</code>: an optional argument (default to <code>Float64</code>) to determine the type the internal data is stored as.</li><li><code>quad_rule</code>: an instance of a <a href="../quadrature/#Ferrite.QuadratureRule"><code>QuadratureRule</code></a></li><li><code>func_interpol</code>: an instance of an <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> used to interpolate the approximated function</li><li><code>geom_interpol</code>: an optional instance of a <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> which is used to interpolate the geometry. By default linear Lagrange interpolation is used. For embedded elements the geometric interpolations should be vectorized to the spatial dimension.</li></ul><p><strong>Keyword arguments:</strong> The following keyword arguments are experimental and may change in future minor releases</p><ul><li><code>update_gradients</code>: Specifies if the gradients of the shape functions should be updated (default true)</li><li><code>update_hessians</code>: Specifies if the hessians of the shape functions should be updated (default false)</li><li><code>update_detJdV</code>: Specifies if the volume associated with each quadrature point should be updated (default true)</li></ul><p><strong>Common methods:</strong></p><ul><li><p><a href="#Ferrite.reinit!"><code>reinit!</code></a></p></li><li><p><a href="#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></p></li><li><p><a href="#Ferrite.getdetJdV"><code>getdetJdV</code></a></p></li><li><p><a href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></p></li><li><p><a href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_symmetric_gradient"><code>shape_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_divergence"><code>shape_divergence</code></a></p></li><li><p><a href="#Ferrite.function_value"><code>function_value</code></a></p></li><li><p><a href="#Ferrite.function_gradient"><code>function_gradient</code></a></p></li><li><p><a href="#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.function_divergence"><code>function_divergence</code></a></p></li><li><p><a href="#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a></p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/CellValues.jl#L1-L36">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetValues" href="#Ferrite.FacetValues"><code>Ferrite.FacetValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetValues([::Type{T}], quad_rule::FacetQuadratureRule, func_interpol::Interpolation, [geom_interpol::Interpolation])</code></pre><p>A <code>FacetValues</code> object facilitates the process of evaluating values of shape functions, gradients of shape functions, values of nodal functions, gradients and divergences of nodal functions etc. on the facets of finite elements.</p><p><strong>Arguments:</strong></p><ul><li><code>T</code>: an optional argument (default to <code>Float64</code>) to determine the type the internal data is stored as.</li><li><code>quad_rule</code>: an instance of a <a href="../quadrature/#Ferrite.FacetQuadratureRule"><code>FacetQuadratureRule</code></a></li><li><code>func_interpol</code>: an instance of an <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> used to interpolate the approximated function</li><li><code>geom_interpol</code>: an optional instance of an <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> which is used to interpolate the geometry. By default linear Lagrange interpolation is used.</li></ul><p><strong>Keyword arguments:</strong> The following keyword arguments are experimental and may change in future minor releases</p><ul><li><code>update_gradients</code>: Specifies if the gradients of the shape functions should be updated (default true)</li><li><code>update_hessians</code>: Specifies if the hessians of the shape functions should be updated (default false)</li></ul><p><strong>Common methods:</strong></p><ul><li><p><a href="#Ferrite.reinit!"><code>reinit!</code></a></p></li><li><p><a href="#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></p></li><li><p><a href="#Ferrite.getdetJdV"><code>getdetJdV</code></a></p></li><li><p><a href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></p></li><li><p><a href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_symmetric_gradient"><code>shape_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_divergence"><code>shape_divergence</code></a></p></li><li><p><a href="#Ferrite.function_value"><code>function_value</code></a></p></li><li><p><a href="#Ferrite.function_gradient"><code>function_gradient</code></a></p></li><li><p><a href="#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.function_divergence"><code>function_divergence</code></a></p></li><li><p><a href="#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a></p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/FacetValues.jl#L1-L36">source</a></section></article><div class="admonition is-warning"><header class="admonition-header">Embedded API</header><div class="admonition-body"><p>Currently, embedded <code>FEValues</code> returns <code>SArray</code>s, which behave differently from the <code>Tensor</code>s for normal value. In the future, we expect to return an <code>AbstractTensor</code>, this change may happen in a minor release, and the API for embedded <code>FEValues</code> should therefore be considered experimental.</p></div></div><h2 id="Applicable-functions"><a class="docs-heading-anchor" href="#Applicable-functions">Applicable functions</a><a id="Applicable-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Applicable-functions" title="Permalink"></a></h2><p>The following functions are applicable to both <code>CellValues</code> and <code>FacetValues</code>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reinit!" href="#Ferrite.reinit!"><code>Ferrite.reinit!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reinit!(cv::CellValues, cell::AbstractCell, x::AbstractVector)
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class="is-disabled">API reference</a></li><li class="is-active"><a href>FEValues</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>FEValues</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/fevalues.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="FEValues"><a class="docs-heading-anchor" href="#FEValues">FEValues</a><a id="FEValues-1"></a><a class="docs-heading-anchor-permalink" href="#FEValues" title="Permalink"></a></h1><h2 id="Main-types"><a class="docs-heading-anchor" href="#Main-types">Main types</a><a id="Main-types-1"></a><a class="docs-heading-anchor-permalink" href="#Main-types" title="Permalink"></a></h2><p><a href="#Ferrite.CellValues"><code>CellValues</code></a> and <a href="#Ferrite.FacetValues"><code>FacetValues</code></a> are the most common subtypes of <code>Ferrite.AbstractValues</code>. For more details about how these work, please see the related <a href="../../topics/FEValues/#fevalues_topicguide">topic guide</a>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellValues" href="#Ferrite.CellValues"><code>Ferrite.CellValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CellValues([::Type{T},] quad_rule::QuadratureRule, func_interpol::Interpolation, [geom_interpol::Interpolation])</code></pre><p>A <code>CellValues</code> object facilitates the process of evaluating values of shape functions, gradients of shape functions, values of nodal functions, gradients and divergences of nodal functions etc. in the finite element cell.</p><p><strong>Arguments:</strong></p><ul><li><code>T</code>: an optional argument (default to <code>Float64</code>) to determine the type the internal data is stored as.</li><li><code>quad_rule</code>: an instance of a <a href="../quadrature/#Ferrite.QuadratureRule"><code>QuadratureRule</code></a></li><li><code>func_interpol</code>: an instance of an <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> used to interpolate the approximated function</li><li><code>geom_interpol</code>: an optional instance of a <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> which is used to interpolate the geometry. By default linear Lagrange interpolation is used. For embedded elements the geometric interpolations should be vectorized to the spatial dimension.</li></ul><p><strong>Keyword arguments:</strong> The following keyword arguments are experimental and may change in future minor releases</p><ul><li><code>update_gradients</code>: Specifies if the gradients of the shape functions should be updated (default true)</li><li><code>update_hessians</code>: Specifies if the hessians of the shape functions should be updated (default false)</li><li><code>update_detJdV</code>: Specifies if the volume associated with each quadrature point should be updated (default true)</li></ul><p><strong>Common methods:</strong></p><ul><li><p><a href="#Ferrite.reinit!"><code>reinit!</code></a></p></li><li><p><a href="#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></p></li><li><p><a href="#Ferrite.getdetJdV"><code>getdetJdV</code></a></p></li><li><p><a href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></p></li><li><p><a href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_symmetric_gradient"><code>shape_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_divergence"><code>shape_divergence</code></a></p></li><li><p><a href="#Ferrite.function_value"><code>function_value</code></a></p></li><li><p><a href="#Ferrite.function_gradient"><code>function_gradient</code></a></p></li><li><p><a href="#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.function_divergence"><code>function_divergence</code></a></p></li><li><p><a href="#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a></p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/CellValues.jl#L1-L36">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetValues" href="#Ferrite.FacetValues"><code>Ferrite.FacetValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetValues([::Type{T}], quad_rule::FacetQuadratureRule, func_interpol::Interpolation, [geom_interpol::Interpolation])</code></pre><p>A <code>FacetValues</code> object facilitates the process of evaluating values of shape functions, gradients of shape functions, values of nodal functions, gradients and divergences of nodal functions etc. on the facets of finite elements.</p><p><strong>Arguments:</strong></p><ul><li><code>T</code>: an optional argument (default to <code>Float64</code>) to determine the type the internal data is stored as.</li><li><code>quad_rule</code>: an instance of a <a href="../quadrature/#Ferrite.FacetQuadratureRule"><code>FacetQuadratureRule</code></a></li><li><code>func_interpol</code>: an instance of an <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> used to interpolate the approximated function</li><li><code>geom_interpol</code>: an optional instance of an <a href="../interpolations/#Ferrite.Interpolation"><code>Interpolation</code></a> which is used to interpolate the geometry. By default linear Lagrange interpolation is used.</li></ul><p><strong>Keyword arguments:</strong> The following keyword arguments are experimental and may change in future minor releases</p><ul><li><code>update_gradients</code>: Specifies if the gradients of the shape functions should be updated (default true)</li><li><code>update_hessians</code>: Specifies if the hessians of the shape functions should be updated (default false)</li></ul><p><strong>Common methods:</strong></p><ul><li><p><a href="#Ferrite.reinit!"><code>reinit!</code></a></p></li><li><p><a href="#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></p></li><li><p><a href="#Ferrite.getdetJdV"><code>getdetJdV</code></a></p></li><li><p><a href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></p></li><li><p><a href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_symmetric_gradient"><code>shape_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_divergence"><code>shape_divergence</code></a></p></li><li><p><a href="#Ferrite.function_value"><code>function_value</code></a></p></li><li><p><a href="#Ferrite.function_gradient"><code>function_gradient</code></a></p></li><li><p><a href="#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.function_divergence"><code>function_divergence</code></a></p></li><li><p><a href="#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a></p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/FacetValues.jl#L1-L36">source</a></section></article><div class="admonition is-warning"><header class="admonition-header">Embedded API</header><div class="admonition-body"><p>Currently, embedded <code>FEValues</code> returns <code>SArray</code>s, which behave differently from the <code>Tensor</code>s for normal value. In the future, we expect to return an <code>AbstractTensor</code>, this change may happen in a minor release, and the API for embedded <code>FEValues</code> should therefore be considered experimental.</p></div></div><h2 id="Applicable-functions"><a class="docs-heading-anchor" href="#Applicable-functions">Applicable functions</a><a id="Applicable-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Applicable-functions" title="Permalink"></a></h2><p>The following functions are applicable to both <code>CellValues</code> and <code>FacetValues</code>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.reinit!" href="#Ferrite.reinit!"><code>Ferrite.reinit!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reinit!(cv::CellValues, cell::AbstractCell, x::AbstractVector)
reinit!(cv::CellValues, x::AbstractVector)
reinit!(fv::FacetValues, cell::AbstractCell, x::AbstractVector, facet::Int)
-reinit!(fv::FacetValues, x::AbstractVector, function_gradient::Int)</code></pre><p>Update the <code>CellValues</code>/<code>FacetValues</code> object for a cell or facet with cell coordinates <code>x</code>. The derivatives of the shape functions, and the new integration weights are computed. For interpolations with non-identity mappings, the current <code>cell</code> is also required.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L46-L55">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnquadpoints" href="#Ferrite.getnquadpoints"><code>Ferrite.getnquadpoints</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnquadpoints(fe_v::AbstractValues)</code></pre><p>Return the number of quadrature points. For <code>FacetValues</code>, this is the number for the current facet.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L58-L63">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getdetJdV" href="#Ferrite.getdetJdV"><code>Ferrite.getdetJdV</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getdetJdV(fe_v::AbstractValues, q_point::Int)</code></pre><p>Return the product between the determinant of the Jacobian and the quadrature point weight for the given quadrature point: <span>$\det(J(\mathbf{x})) w_q$</span>.</p><p>This value is typically used when one integrates a function on a finite element cell or facet as</p><p><span>$\int\limits_\Omega f(\mathbf{x}) d \Omega \approx \sum\limits_{q = 1}^{n_q} f(\mathbf{x}_q) \det(J(\mathbf{x})) w_q$</span> <span>$\int\limits_\Gamma f(\mathbf{x}) d \Gamma \approx \sum\limits_{q = 1}^{n_q} f(\mathbf{x}_q) \det(J(\mathbf{x})) w_q$</span></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L66-L78">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}" href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>Ferrite.shape_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the value of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L81-L86">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}" href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>Ferrite.shape_gradient</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the gradient of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L98-L103">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_symmetric_gradient" href="#Ferrite.shape_symmetric_gradient"><code>Ferrite.shape_symmetric_gradient</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_symmetric_gradient(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the symmetric gradient of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L106-L111">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_divergence" href="#Ferrite.shape_divergence"><code>Ferrite.shape_divergence</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_divergence(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the divergence of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L114-L119">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_curl" href="#Ferrite.shape_curl"><code>Ferrite.shape_curl</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_curl(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the curl of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L126-L131">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.geometric_value" href="#Ferrite.geometric_value"><code>Ferrite.geometric_value</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">geometric_value(fe_v::AbstractValues, q_point, base_function::Int)</code></pre><p>Return the value of the geometric shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L89-L94">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_value" href="#Ferrite.function_value"><code>Ferrite.function_value</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_value(iv::InterfaceValues, q_point::Int, u; here::Bool)
-function_value(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there; here::Bool)</code></pre><p>Compute the value of the function in quadrature point <code>q_point</code> on the "here" (<code>here=true</code>) or "there" (<code>here=false</code>) side of the interface. <code>u_here</code> and <code>u_there</code> are the values of the degrees of freedom for the respective element.</p><p><code>u</code> is a vector of scalar values for the degrees of freedom. This function can be used with a single <code>u</code> vector containing the dofs of both elements of the interface or two vectors (<code>u_here</code> and <code>u_there</code>) which contain the dofs of each cell of the interface respectively.</p><p><code>here</code> determines which element to use for calculating function value. <code>true</code> uses the value on the first element's side of the interface, while <code>false</code> uses the value on the second element's side.</p><p>The value of a scalar valued function is computed as <span>$u(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) u_i$</span> where <span>$u_i$</span> are the value of <span>$u$</span> in the nodes. For a vector valued function the value is calculated as <span>$\mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L159-L178">source</a></section><section><div><pre><code class="language-julia hljs">function_value(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the value of the function in a quadrature point. <code>u</code> is a vector with values for the degrees of freedom. For a scalar valued function, <code>u</code> contains scalars. For a vector valued function, <code>u</code> can be a vector of scalars (for use of <code>VectorValues</code>) or <code>u</code> can be a vector of <code>Vec</code>s (for use with ScalarValues).</p><p>The value of a scalar valued function is computed as <span>$u(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) u_i$</span> where <span>$u_i$</span> are the value of <span>$u$</span> in the nodes. For a vector valued function the value is calculated as <span>$\mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L138-L150">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_gradient" href="#Ferrite.function_gradient"><code>Ferrite.function_gradient</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_gradient(iv::InterfaceValues, q_point::Int, u; here::Bool)
-function_gradient(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there; here::Bool)</code></pre><p>Compute the gradient of the function in a quadrature point. <code>u</code> is a vector of scalar values for the degrees of freedom. This function can be used with a single <code>u</code> vector containing the dofs of both elements of the interface or two vectors (<code>u_here</code> and <code>u_there</code>) which contain the dofs of each cell of the interface respectively.</p><p><code>here</code> determines which element to use for calculating function value. <code>true</code> uses the value on the first element's side of the interface, while <code>false</code> uses the value on the second element's side.</p><p>The gradient of a scalar function or a vector valued function with use of <code>VectorValues</code> is computed as <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i (\mathbf{x}) u_i$</span> or <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} \mathbf{N}_i (\mathbf{x}) u_i$</span> respectively, where <span>$u_i$</span> are the nodal values of the function. For a vector valued function with use of <code>ScalarValues</code> the gradient is computed as <span>$\mathbf{\nabla} \mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{u}_i \otimes \mathbf{\nabla} N_i (\mathbf{x})$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L182-L200">source</a></section><section><div><pre><code class="language-julia hljs">function_gradient(fe_v::AbstractValues{dim}, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the gradient of the function in a quadrature point. <code>u</code> is a vector with values for the degrees of freedom. For a scalar valued function, <code>u</code> contains scalars. For a vector valued function, <code>u</code> can be a vector of scalars (for use of <code>VectorValues</code>) or <code>u</code> can be a vector of <code>Vec</code>s (for use with ScalarValues).</p><p>The gradient of a scalar function or a vector valued function with use of <code>VectorValues</code> is computed as <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i (\mathbf{x}) u_i$</span> or <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} \mathbf{N}_i (\mathbf{x}) u_i$</span> respectively, where <span>$u_i$</span> are the nodal values of the function. For a vector valued function with use of <code>ScalarValues</code> the gradient is computed as <span>$\mathbf{\nabla} \mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{u}_i \otimes \mathbf{\nabla} N_i (\mathbf{x})$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L175-L190">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_symmetric_gradient" href="#Ferrite.function_symmetric_gradient"><code>Ferrite.function_symmetric_gradient</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_symmetric_gradient(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the symmetric gradient of the function, see <a href="#Ferrite.function_gradient"><code>function_gradient</code></a>. Return a <code>SymmetricTensor</code>.</p><p>The symmetric gradient of a scalar function is computed as <span>$\left[ \mathbf{\nabla} \mathbf{u}(\mathbf{x_q}) \right]^\text{sym} = \sum\limits_{i = 1}^n \frac{1}{2} \left[ \mathbf{\nabla} N_i (\mathbf{x}_q) \otimes \mathbf{u}_i + \mathbf{u}_i \otimes \mathbf{\nabla} N_i (\mathbf{x}_q) \right]$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of the function.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L264-L273">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_divergence" href="#Ferrite.function_divergence"><code>Ferrite.function_divergence</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_divergence(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the divergence of the vector valued function in a quadrature point.</p><p>The divergence of a vector valued functions in the quadrature point <span>$\mathbf{x}_q)$</span> is computed as <span>$\mathbf{\nabla} \cdot \mathbf{u}(\mathbf{x_q}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i (\mathbf{x_q}) \cdot \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of the function.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L283-L291">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_curl" href="#Ferrite.function_curl"><code>Ferrite.function_curl</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_curl(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the curl of the vector valued function in a quadrature point.</p><p>The curl of a vector valued functions in the quadrature point <span>$\mathbf{x}_q)$</span> is computed as <span>$\mathbf{\nabla} \times \mathbf{u}(\mathbf{x_q}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i \times (\mathbf{x_q}) \cdot \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of the function.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L308-L316">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.spatial_coordinate" href="#Ferrite.spatial_coordinate"><code>Ferrite.spatial_coordinate</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">spatial_coordinate(fe_v::AbstractValues, q_point::Int, x::AbstractVector)</code></pre><p>Compute the spatial coordinate in a quadrature point. <code>x</code> contains the nodal coordinates of the cell.</p><p>The coordinate is computed, using the geometric interpolation, as <span>$\mathbf{x} = \sum\limits_{i = 1}^n M_i (\mathbf{\xi}) \mathbf{\hat{x}}_i$</span>.</p><p>where <span>$\xi$</span>is the coordinate of the given quadrature point <code>q_point</code> of the associated quadrature rule.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L324-L335">source</a></section><section><div><pre><code class="language-julia hljs">spatial_coordinate(ip::ScalarInterpolation, ξ::Vec, x::AbstractVector{<:Vec{sdim, T}})</code></pre><p>Compute the spatial coordinate in a given quadrature point. <code>x</code> contains the nodal coordinates of the cell.</p><p>The coordinate is computed, using the geometric interpolation, as <span>$\mathbf{x} = \sum\limits_{i = 1}^n M_i (\mathbf{\xi}) \mathbf{\hat{x}}_i$</span></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/common_values.jl#L347-L354">source</a></section></article><p>In addition, there are some methods that are unique for <code>FacetValues</code>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcurrentfacet" href="#Ferrite.getcurrentfacet"><code>Ferrite.getcurrentfacet</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcurrentfacet(fv::FacetValues)</code></pre><p>Return the current active facet of the <code>FacetValues</code> object (from last <code>reinit!</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/FacetValues.jl#L98-L102">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnormal" href="#Ferrite.getnormal"><code>Ferrite.getnormal</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnormal(fv::FacetValues, qp::Int)</code></pre><p>Return the normal at the quadrature point <code>qp</code> for the active facet of the <code>FacetValues</code> object(from last <code>reinit!</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/FacetValues.jl#L105-L110">source</a></section><section><div><pre><code class="language-julia hljs">getnormal(iv::InterfaceValues, qp::Int; here::Bool=true)</code></pre><p>Return the normal vector in the quadrature point <code>qp</code> on the interface. If <code>here = true</code> (default) the outward normal to the "here" element is returned, otherwise the outward normal to the "there" element.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L147-L153">source</a></section></article><h2 id="reference-interfacevalues"><a class="docs-heading-anchor" href="#reference-interfacevalues">InterfaceValues</a><a id="reference-interfacevalues-1"></a><a class="docs-heading-anchor-permalink" href="#reference-interfacevalues" title="Permalink"></a></h2><p>All of the methods for <a href="#Ferrite.FacetValues"><code>FacetValues</code></a> apply for <code>InterfaceValues</code> as well. In addition, there are some methods that are unique for <code>InterfaceValues</code>:</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceValues" href="#Ferrite.InterfaceValues"><code>Ferrite.InterfaceValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceValues</code></pre><p>An <code>InterfaceValues</code> object facilitates the process of evaluating values, averages, jumps and gradients of shape functions and function on the interfaces between elements.</p><p>The first element of the interface is denoted "here" and the second element "there".</p><p><strong>Constructors</strong></p><ul><li><code>InterfaceValues(qr::FacetQuadratureRule, ip::Interpolation)</code>: same quadrature rule and interpolation on both sides, default linear Lagrange geometric interpolation.</li><li><code>InterfaceValues(qr::FacetQuadratureRule, ip::Interpolation, ip_geo::Interpolation)</code>: same as above but with given geometric interpolation.</li><li><code>InterfaceValues(qr_here::FacetQuadratureRule, ip_here::Interpolation, qr_there::FacetQuadratureRule, ip_there::Interpolation)</code>: different quadrature rule and interpolation on the two sides, default linear Lagrange geometric interpolation.</li><li><code>InterfaceValues(qr_here::FacetQuadratureRule, ip_here::Interpolation, ip_geo_here::Interpolation, qr_there::FacetQuadratureRule, ip_there::Interpolation, ip_geo_there::Interpolation)</code>: same as above but with given geometric interpolation.</li><li><code>InterfaceValues(fv::FacetValues)</code>: quadrature rule and interpolations from facet values (same on both sides).</li><li><code>InterfaceValues(fv_here::FacetValues, fv_there::FacetValues)</code>: quadrature rule and interpolations from the facet values.</li></ul><p><strong>Associated methods:</strong></p><ul><li><a href="#Ferrite.shape_value_average"><code>shape_value_average</code></a></li><li><a href="#Ferrite.shape_value_jump"><code>shape_value_jump</code></a></li><li><a href="#Ferrite.shape_gradient_average"><code>shape_gradient_average</code></a></li><li><a href="#Ferrite.shape_gradient_jump"><code>shape_gradient_jump</code></a></li></ul><p><strong>Common methods:</strong></p><ul><li><p><a href="#Ferrite.reinit!"><code>reinit!</code></a></p></li><li><p><a href="#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></p></li><li><p><a href="#Ferrite.getdetJdV"><code>getdetJdV</code></a></p></li><li><p><a href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></p></li><li><p><a href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_divergence"><code>shape_divergence</code></a></p></li><li><p><a href="#Ferrite.shape_curl"><code>shape_curl</code></a></p></li><li><p><a href="#Ferrite.function_value"><code>function_value</code></a></p></li><li><p><a href="#Ferrite.function_gradient"><code>function_gradient</code></a></p></li><li><p><a href="#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.function_divergence"><code>function_divergence</code></a></p></li><li><p><a href="#Ferrite.function_curl"><code>function_curl</code></a></p></li><li><p><a href="#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a></p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L2-L47">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_average" href="#Ferrite.shape_value_average"><code>Ferrite.shape_value_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_average(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the average of the value of shape function <code>i</code> at quadrature point <code>qp</code> across the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L203-L208">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_jump" href="#Ferrite.shape_value_jump"><code>Ferrite.shape_value_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_jump(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the jump of the value of shape function <code>i</code> at quadrature point <code>qp</code> across the interface in the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} \cdot \vec{n}^\text{there} + \vec{v}^\text{here} \cdot \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L211-L219">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient_average" href="#Ferrite.shape_gradient_average"><code>Ferrite.shape_gradient_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient_average(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the average of the gradient of shape function <code>i</code> at quadrature point <code>qp</code> across the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L222-L227">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient_jump" href="#Ferrite.shape_gradient_jump"><code>Ferrite.shape_gradient_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient_jump(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the jump of the gradient of shape function <code>i</code> at quadrature point <code>qp</code> across the interface in the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} ⋅ \vec{n}^\text{there} + \vec{v}^\text{here} ⋅ \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L230-L238">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_value_average" href="#Ferrite.function_value_average"><code>Ferrite.function_value_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_value_average(iv::InterfaceValues, q_point::Int, u)
-function_value_average(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the average of the function value at the quadrature point on the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L280-L285">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_value_jump" href="#Ferrite.function_value_jump"><code>Ferrite.function_value_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_value_jump(iv::InterfaceValues, q_point::Int, u)
-function_value_jump(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the jump of the function value at the quadrature point over the interface along the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} ⋅ \vec{n}^\text{there} + \vec{v}^\text{here} ⋅ \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L288-L297">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_gradient_average" href="#Ferrite.function_gradient_average"><code>Ferrite.function_gradient_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_gradient_average(iv::InterfaceValues, q_point::Int, u)
-function_gradient_average(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the average of the function gradient at the quadrature point on the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L300-L305">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_gradient_jump" href="#Ferrite.function_gradient_jump"><code>Ferrite.function_gradient_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_gradient_jump(iv::InterfaceValues, q_point::Int, u)
-function_gradient_jump(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the jump of the function gradient at the quadrature point over the interface along the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} ⋅ \vec{n}^\text{there} + \vec{v}^\text{here} ⋅ \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/FEValues/InterfaceValues.jl#L308-L317">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interpolations/">« Interpolation</a><a class="docs-footer-nextpage" href="../dofhandler/">Degrees of Freedom »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+reinit!(fv::FacetValues, x::AbstractVector, function_gradient::Int)</code></pre><p>Update the <code>CellValues</code>/<code>FacetValues</code> object for a cell or facet with cell coordinates <code>x</code>. The derivatives of the shape functions, and the new integration weights are computed. For interpolations with non-identity mappings, the current <code>cell</code> is also required.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L46-L55">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnquadpoints" href="#Ferrite.getnquadpoints"><code>Ferrite.getnquadpoints</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnquadpoints(fe_v::AbstractValues)</code></pre><p>Return the number of quadrature points. For <code>FacetValues</code>, this is the number for the current facet.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L58-L63">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getdetJdV" href="#Ferrite.getdetJdV"><code>Ferrite.getdetJdV</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getdetJdV(fe_v::AbstractValues, q_point::Int)</code></pre><p>Return the product between the determinant of the Jacobian and the quadrature point weight for the given quadrature point: <span>$\det(J(\mathbf{x})) w_q$</span>.</p><p>This value is typically used when one integrates a function on a finite element cell or facet as</p><p><span>$\int\limits_\Omega f(\mathbf{x}) d \Omega \approx \sum\limits_{q = 1}^{n_q} f(\mathbf{x}_q) \det(J(\mathbf{x})) w_q$</span> <span>$\int\limits_\Gamma f(\mathbf{x}) d \Gamma \approx \sum\limits_{q = 1}^{n_q} f(\mathbf{x}_q) \det(J(\mathbf{x})) w_q$</span></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L66-L78">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}" href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>Ferrite.shape_value</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the value of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L81-L86">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}" href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>Ferrite.shape_gradient</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the gradient of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L98-L103">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_symmetric_gradient" href="#Ferrite.shape_symmetric_gradient"><code>Ferrite.shape_symmetric_gradient</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_symmetric_gradient(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the symmetric gradient of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L106-L111">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_divergence" href="#Ferrite.shape_divergence"><code>Ferrite.shape_divergence</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_divergence(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the divergence of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L114-L119">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_curl" href="#Ferrite.shape_curl"><code>Ferrite.shape_curl</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_curl(fe_v::AbstractValues, q_point::Int, base_function::Int)</code></pre><p>Return the curl of shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L126-L131">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.geometric_value" href="#Ferrite.geometric_value"><code>Ferrite.geometric_value</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">geometric_value(fe_v::AbstractValues, q_point, base_function::Int)</code></pre><p>Return the value of the geometric shape function <code>base_function</code> evaluated in quadrature point <code>q_point</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L89-L94">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_value" href="#Ferrite.function_value"><code>Ferrite.function_value</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_value(iv::InterfaceValues, q_point::Int, u; here::Bool)
+function_value(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there; here::Bool)</code></pre><p>Compute the value of the function in quadrature point <code>q_point</code> on the "here" (<code>here=true</code>) or "there" (<code>here=false</code>) side of the interface. <code>u_here</code> and <code>u_there</code> are the values of the degrees of freedom for the respective element.</p><p><code>u</code> is a vector of scalar values for the degrees of freedom. This function can be used with a single <code>u</code> vector containing the dofs of both elements of the interface or two vectors (<code>u_here</code> and <code>u_there</code>) which contain the dofs of each cell of the interface respectively.</p><p><code>here</code> determines which element to use for calculating function value. <code>true</code> uses the value on the first element's side of the interface, while <code>false</code> uses the value on the second element's side.</p><p>The value of a scalar valued function is computed as <span>$u(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) u_i$</span> where <span>$u_i$</span> are the value of <span>$u$</span> in the nodes. For a vector valued function the value is calculated as <span>$\mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L159-L178">source</a></section><section><div><pre><code class="language-julia hljs">function_value(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the value of the function in a quadrature point. <code>u</code> is a vector with values for the degrees of freedom. For a scalar valued function, <code>u</code> contains scalars. For a vector valued function, <code>u</code> can be a vector of scalars (for use of <code>VectorValues</code>) or <code>u</code> can be a vector of <code>Vec</code>s (for use with ScalarValues).</p><p>The value of a scalar valued function is computed as <span>$u(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) u_i$</span> where <span>$u_i$</span> are the value of <span>$u$</span> in the nodes. For a vector valued function the value is calculated as <span>$\mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n N_i (\mathbf{x}) \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L138-L150">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_gradient" href="#Ferrite.function_gradient"><code>Ferrite.function_gradient</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_gradient(iv::InterfaceValues, q_point::Int, u; here::Bool)
+function_gradient(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there; here::Bool)</code></pre><p>Compute the gradient of the function in a quadrature point. <code>u</code> is a vector of scalar values for the degrees of freedom. This function can be used with a single <code>u</code> vector containing the dofs of both elements of the interface or two vectors (<code>u_here</code> and <code>u_there</code>) which contain the dofs of each cell of the interface respectively.</p><p><code>here</code> determines which element to use for calculating function value. <code>true</code> uses the value on the first element's side of the interface, while <code>false</code> uses the value on the second element's side.</p><p>The gradient of a scalar function or a vector valued function with use of <code>VectorValues</code> is computed as <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i (\mathbf{x}) u_i$</span> or <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} \mathbf{N}_i (\mathbf{x}) u_i$</span> respectively, where <span>$u_i$</span> are the nodal values of the function. For a vector valued function with use of <code>ScalarValues</code> the gradient is computed as <span>$\mathbf{\nabla} \mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{u}_i \otimes \mathbf{\nabla} N_i (\mathbf{x})$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L182-L200">source</a></section><section><div><pre><code class="language-julia hljs">function_gradient(fe_v::AbstractValues{dim}, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the gradient of the function in a quadrature point. <code>u</code> is a vector with values for the degrees of freedom. For a scalar valued function, <code>u</code> contains scalars. For a vector valued function, <code>u</code> can be a vector of scalars (for use of <code>VectorValues</code>) or <code>u</code> can be a vector of <code>Vec</code>s (for use with ScalarValues).</p><p>The gradient of a scalar function or a vector valued function with use of <code>VectorValues</code> is computed as <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i (\mathbf{x}) u_i$</span> or <span>$\mathbf{\nabla} u(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{\nabla} \mathbf{N}_i (\mathbf{x}) u_i$</span> respectively, where <span>$u_i$</span> are the nodal values of the function. For a vector valued function with use of <code>ScalarValues</code> the gradient is computed as <span>$\mathbf{\nabla} \mathbf{u}(\mathbf{x}) = \sum\limits_{i = 1}^n \mathbf{u}_i \otimes \mathbf{\nabla} N_i (\mathbf{x})$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of <span>$\mathbf{u}$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L175-L190">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_symmetric_gradient" href="#Ferrite.function_symmetric_gradient"><code>Ferrite.function_symmetric_gradient</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_symmetric_gradient(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the symmetric gradient of the function, see <a href="#Ferrite.function_gradient"><code>function_gradient</code></a>. Return a <code>SymmetricTensor</code>.</p><p>The symmetric gradient of a scalar function is computed as <span>$\left[ \mathbf{\nabla} \mathbf{u}(\mathbf{x_q}) \right]^\text{sym} = \sum\limits_{i = 1}^n \frac{1}{2} \left[ \mathbf{\nabla} N_i (\mathbf{x}_q) \otimes \mathbf{u}_i + \mathbf{u}_i \otimes \mathbf{\nabla} N_i (\mathbf{x}_q) \right]$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of the function.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L264-L273">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_divergence" href="#Ferrite.function_divergence"><code>Ferrite.function_divergence</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_divergence(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the divergence of the vector valued function in a quadrature point.</p><p>The divergence of a vector valued functions in the quadrature point <span>$\mathbf{x}_q)$</span> is computed as <span>$\mathbf{\nabla} \cdot \mathbf{u}(\mathbf{x_q}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i (\mathbf{x_q}) \cdot \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of the function.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L283-L291">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_curl" href="#Ferrite.function_curl"><code>Ferrite.function_curl</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_curl(fe_v::AbstractValues, q_point::Int, u::AbstractVector, [dof_range])</code></pre><p>Compute the curl of the vector valued function in a quadrature point.</p><p>The curl of a vector valued functions in the quadrature point <span>$\mathbf{x}_q)$</span> is computed as <span>$\mathbf{\nabla} \times \mathbf{u}(\mathbf{x_q}) = \sum\limits_{i = 1}^n \mathbf{\nabla} N_i \times (\mathbf{x_q}) \cdot \mathbf{u}_i$</span> where <span>$\mathbf{u}_i$</span> are the nodal values of the function.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L308-L316">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.spatial_coordinate" href="#Ferrite.spatial_coordinate"><code>Ferrite.spatial_coordinate</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">spatial_coordinate(fe_v::AbstractValues, q_point::Int, x::AbstractVector)</code></pre><p>Compute the spatial coordinate in a quadrature point. <code>x</code> contains the nodal coordinates of the cell.</p><p>The coordinate is computed, using the geometric interpolation, as <span>$\mathbf{x} = \sum\limits_{i = 1}^n M_i (\mathbf{\xi}) \mathbf{\hat{x}}_i$</span>.</p><p>where <span>$\xi$</span>is the coordinate of the given quadrature point <code>q_point</code> of the associated quadrature rule.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L324-L335">source</a></section><section><div><pre><code class="language-julia hljs">spatial_coordinate(ip::ScalarInterpolation, ξ::Vec, x::AbstractVector{<:Vec{sdim, T}})</code></pre><p>Compute the spatial coordinate in a given quadrature point. <code>x</code> contains the nodal coordinates of the cell.</p><p>The coordinate is computed, using the geometric interpolation, as <span>$\mathbf{x} = \sum\limits_{i = 1}^n M_i (\mathbf{\xi}) \mathbf{\hat{x}}_i$</span></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/common_values.jl#L347-L354">source</a></section></article><p>In addition, there are some methods that are unique for <code>FacetValues</code>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcurrentfacet" href="#Ferrite.getcurrentfacet"><code>Ferrite.getcurrentfacet</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcurrentfacet(fv::FacetValues)</code></pre><p>Return the current active facet of the <code>FacetValues</code> object (from last <code>reinit!</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/FacetValues.jl#L98-L102">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnormal" href="#Ferrite.getnormal"><code>Ferrite.getnormal</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnormal(fv::FacetValues, qp::Int)</code></pre><p>Return the normal at the quadrature point <code>qp</code> for the active facet of the <code>FacetValues</code> object(from last <code>reinit!</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/FacetValues.jl#L105-L110">source</a></section><section><div><pre><code class="language-julia hljs">getnormal(iv::InterfaceValues, qp::Int; here::Bool=true)</code></pre><p>Return the normal vector in the quadrature point <code>qp</code> on the interface. If <code>here = true</code> (default) the outward normal to the "here" element is returned, otherwise the outward normal to the "there" element.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L147-L153">source</a></section></article><h2 id="reference-interfacevalues"><a class="docs-heading-anchor" href="#reference-interfacevalues">InterfaceValues</a><a id="reference-interfacevalues-1"></a><a class="docs-heading-anchor-permalink" href="#reference-interfacevalues" title="Permalink"></a></h2><p>All of the methods for <a href="#Ferrite.FacetValues"><code>FacetValues</code></a> apply for <code>InterfaceValues</code> as well. In addition, there are some methods that are unique for <code>InterfaceValues</code>:</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.InterfaceValues" href="#Ferrite.InterfaceValues"><code>Ferrite.InterfaceValues</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">InterfaceValues</code></pre><p>An <code>InterfaceValues</code> object facilitates the process of evaluating values, averages, jumps and gradients of shape functions and function on the interfaces between elements.</p><p>The first element of the interface is denoted "here" and the second element "there".</p><p><strong>Constructors</strong></p><ul><li><code>InterfaceValues(qr::FacetQuadratureRule, ip::Interpolation)</code>: same quadrature rule and interpolation on both sides, default linear Lagrange geometric interpolation.</li><li><code>InterfaceValues(qr::FacetQuadratureRule, ip::Interpolation, ip_geo::Interpolation)</code>: same as above but with given geometric interpolation.</li><li><code>InterfaceValues(qr_here::FacetQuadratureRule, ip_here::Interpolation, qr_there::FacetQuadratureRule, ip_there::Interpolation)</code>: different quadrature rule and interpolation on the two sides, default linear Lagrange geometric interpolation.</li><li><code>InterfaceValues(qr_here::FacetQuadratureRule, ip_here::Interpolation, ip_geo_here::Interpolation, qr_there::FacetQuadratureRule, ip_there::Interpolation, ip_geo_there::Interpolation)</code>: same as above but with given geometric interpolation.</li><li><code>InterfaceValues(fv::FacetValues)</code>: quadrature rule and interpolations from facet values (same on both sides).</li><li><code>InterfaceValues(fv_here::FacetValues, fv_there::FacetValues)</code>: quadrature rule and interpolations from the facet values.</li></ul><p><strong>Associated methods:</strong></p><ul><li><a href="#Ferrite.shape_value_average"><code>shape_value_average</code></a></li><li><a href="#Ferrite.shape_value_jump"><code>shape_value_jump</code></a></li><li><a href="#Ferrite.shape_gradient_average"><code>shape_gradient_average</code></a></li><li><a href="#Ferrite.shape_gradient_jump"><code>shape_gradient_jump</code></a></li></ul><p><strong>Common methods:</strong></p><ul><li><p><a href="#Ferrite.reinit!"><code>reinit!</code></a></p></li><li><p><a href="#Ferrite.getnquadpoints"><code>getnquadpoints</code></a></p></li><li><p><a href="#Ferrite.getdetJdV"><code>getdetJdV</code></a></p></li><li><p><a href="#Ferrite.shape_value-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_value</code></a></p></li><li><p><a href="#Ferrite.shape_gradient-Tuple{Ferrite.AbstractValues, Int64, Int64}"><code>shape_gradient</code></a></p></li><li><p><a href="#Ferrite.shape_divergence"><code>shape_divergence</code></a></p></li><li><p><a href="#Ferrite.shape_curl"><code>shape_curl</code></a></p></li><li><p><a href="#Ferrite.function_value"><code>function_value</code></a></p></li><li><p><a href="#Ferrite.function_gradient"><code>function_gradient</code></a></p></li><li><p><a href="#Ferrite.function_symmetric_gradient"><code>function_symmetric_gradient</code></a></p></li><li><p><a href="#Ferrite.function_divergence"><code>function_divergence</code></a></p></li><li><p><a href="#Ferrite.function_curl"><code>function_curl</code></a></p></li><li><p><a href="#Ferrite.spatial_coordinate"><code>spatial_coordinate</code></a></p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L2-L47">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_average" href="#Ferrite.shape_value_average"><code>Ferrite.shape_value_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_average(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the average of the value of shape function <code>i</code> at quadrature point <code>qp</code> across the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L203-L208">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_value_jump" href="#Ferrite.shape_value_jump"><code>Ferrite.shape_value_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_value_jump(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the jump of the value of shape function <code>i</code> at quadrature point <code>qp</code> across the interface in the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} \cdot \vec{n}^\text{there} + \vec{v}^\text{here} \cdot \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L211-L219">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient_average" href="#Ferrite.shape_gradient_average"><code>Ferrite.shape_gradient_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient_average(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the average of the gradient of shape function <code>i</code> at quadrature point <code>qp</code> across the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L222-L227">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.shape_gradient_jump" href="#Ferrite.shape_gradient_jump"><code>Ferrite.shape_gradient_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">shape_gradient_jump(iv::InterfaceValues, qp::Int, i::Int)</code></pre><p>Compute the jump of the gradient of shape function <code>i</code> at quadrature point <code>qp</code> across the interface in the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} ⋅ \vec{n}^\text{there} + \vec{v}^\text{here} ⋅ \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L230-L238">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_value_average" href="#Ferrite.function_value_average"><code>Ferrite.function_value_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_value_average(iv::InterfaceValues, q_point::Int, u)
+function_value_average(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the average of the function value at the quadrature point on the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L280-L285">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_value_jump" href="#Ferrite.function_value_jump"><code>Ferrite.function_value_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_value_jump(iv::InterfaceValues, q_point::Int, u)
+function_value_jump(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the jump of the function value at the quadrature point over the interface along the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} ⋅ \vec{n}^\text{there} + \vec{v}^\text{here} ⋅ \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L288-L297">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_gradient_average" href="#Ferrite.function_gradient_average"><code>Ferrite.function_gradient_average</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_gradient_average(iv::InterfaceValues, q_point::Int, u)
+function_gradient_average(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the average of the function gradient at the quadrature point on the interface.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L300-L305">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.function_gradient_jump" href="#Ferrite.function_gradient_jump"><code>Ferrite.function_gradient_jump</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">function_gradient_jump(iv::InterfaceValues, q_point::Int, u)
+function_gradient_jump(iv::InterfaceValues, q_point::Int, u, dof_range_here, dof_range_there)</code></pre><p>Compute the jump of the function gradient at the quadrature point over the interface along the default normal direction.</p><p>This function uses the definition <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} -\vec{v}^\text{here}$</span>. To obtain the form, <span>$\llbracket \vec{v} \rrbracket=\vec{v}^\text{there} ⋅ \vec{n}^\text{there} + \vec{v}^\text{here} ⋅ \vec{n}^\text{here}$</span>, multiply by minus the outward facing normal to the first element's side of the interface (which is the default normal for <a href="#Ferrite.getnormal"><code>getnormal</code></a> with <a href="#Ferrite.InterfaceValues"><code>InterfaceValues</code></a>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/FEValues/InterfaceValues.jl#L308-L317">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interpolations/">« Interpolation</a><a class="docs-footer-nextpage" href="../dofhandler/">Degrees of Freedom »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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AbstractGrid</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/grid.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Grid-and-AbstractGrid"><a class="docs-heading-anchor" href="#Grid-and-AbstractGrid">Grid & AbstractGrid</a><a id="Grid-and-AbstractGrid-1"></a><a class="docs-heading-anchor-permalink" href="#Grid-and-AbstractGrid" title="Permalink"></a></h1><h2 id="Grid"><a class="docs-heading-anchor" href="#Grid">Grid</a><a id="Grid-1"></a><a class="docs-heading-anchor-permalink" href="#Grid" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.generate_grid" href="#Ferrite.generate_grid"><code>Ferrite.generate_grid</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">generate_grid(celltype::Cell, nel::NTuple, [left::Vec, right::Vec)</code></pre><p>Return a <code>Grid</code> for a rectangle in 1, 2 or 3 dimensions. <code>celltype</code> defined the type of cells, e.g. <code>Triangle</code> or <code>Hexahedron</code>. <code>nel</code> is a tuple of the number of elements in each direction. <code>left</code> and <code>right</code> are optional endpoints of the domain. Defaults to -1 and 1 in all directions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid_generators.jl#L1-L7">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Node" href="#Ferrite.Node"><code>Ferrite.Node</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Node{dim, T}</code></pre><p>A <code>Node</code> is a point in space.</p><p><strong>Fields</strong></p><ul><li><code>x::Vec{dim,T}</code>: stores the coordinates</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L4-L11">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellIndex" href="#Ferrite.CellIndex"><code>Ferrite.CellIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>CellIndex</code> wraps an Int and corresponds to a cell with that number in the mesh</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L75-L77">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.VertexIndex" href="#Ferrite.VertexIndex"><code>Ferrite.VertexIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>VertexIndex</code> wraps an (Int, Int) and defines a local vertex by pointing to a (cell, vert).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L96-L98">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.EdgeIndex" href="#Ferrite.EdgeIndex"><code>Ferrite.EdgeIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>EdgeIndex</code> wraps an (Int, Int) and defines a local edge by pointing to a (cell, edge).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L89-L91">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FaceIndex" href="#Ferrite.FaceIndex"><code>Ferrite.FaceIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>FaceIndex</code> wraps an (Int, Int) and defines a local face by pointing to a (cell, face).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L82-L84">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetIndex" href="#Ferrite.FacetIndex"><code>Ferrite.FacetIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>FacetIndex</code> wraps an (Int, Int) and defines a local facet by pointing to a (cell, facet).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Ferrite.jl#L103-L105">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Grid" href="#Ferrite.Grid"><code>Ferrite.Grid</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Grid{dim, C<:AbstractCell, T<:Real} <: AbstractGrid}</code></pre><p>A <code>Grid</code> is a collection of <code>Ferrite.AbstractCell</code>s and <code>Ferrite.Node</code>s which covers the computational domain. Helper structures for applying boundary conditions or define subdomains are gathered in <code>cellsets</code>, <code>nodesets</code>, <code>facetsets</code>, and <code>vertexsets</code>.</p><p><strong>Fields</strong></p><ul><li><code>cells::Vector{C}</code>: stores all cells of the grid</li><li><code>nodes::Vector{Node{dim,T}}</code>: stores the <code>dim</code> dimensional nodes of the grid</li><li><code>cellsets::Dict{String, OrderedSet{Int}}</code>: maps a <code>String</code> key to an <code>OrderedSet</code> of cell ids</li><li><code>nodesets::Dict{String, OrderedSet{Int}}</code>: maps a <code>String</code> key to an <code>OrderedSet</code> of global node ids</li><li><code>facetsets::Dict{String, OrderedSet{FacetIndex}}</code>: maps a <code>String</code> to an <code>OrderedSet</code> of <code>FacetIndex</code></li><li><code>vertexsets::Dict{String, OrderedSet{VertexIndex}}</code>: maps a <code>String</code> key to an <code>OrderedSet</code> of <code>VertexIndex</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L354-L368">source</a></section></article><h3 id="Utility-Functions"><a class="docs-heading-anchor" href="#Utility-Functions">Utility Functions</a><a id="Utility-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Utility-Functions" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcells" href="#Ferrite.getcells"><code>Ferrite.getcells</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcells(grid::AbstractGrid)
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assembly</a></li></ul></li><br><li><a class="tocitem" href="../../gallery/">Code gallery</a></li><li><a class="tocitem" href="../../devdocs/">Developer documentation</a></li><li><a class="tocitem" href="../../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">API reference</a></li><li class="is-active"><a href>Grid & AbstractGrid</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Grid & AbstractGrid</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/grid.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Grid-and-AbstractGrid"><a class="docs-heading-anchor" href="#Grid-and-AbstractGrid">Grid & AbstractGrid</a><a id="Grid-and-AbstractGrid-1"></a><a class="docs-heading-anchor-permalink" href="#Grid-and-AbstractGrid" title="Permalink"></a></h1><h2 id="Grid"><a class="docs-heading-anchor" href="#Grid">Grid</a><a id="Grid-1"></a><a class="docs-heading-anchor-permalink" href="#Grid" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.generate_grid" href="#Ferrite.generate_grid"><code>Ferrite.generate_grid</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">generate_grid(celltype::Cell, nel::NTuple, [left::Vec, right::Vec)</code></pre><p>Return a <code>Grid</code> for a rectangle in 1, 2 or 3 dimensions. <code>celltype</code> defined the type of cells, e.g. <code>Triangle</code> or <code>Hexahedron</code>. <code>nel</code> is a tuple of the number of elements in each direction. <code>left</code> and <code>right</code> are optional endpoints of the domain. Defaults to -1 and 1 in all directions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid_generators.jl#L1-L7">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Node" href="#Ferrite.Node"><code>Ferrite.Node</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Node{dim, T}</code></pre><p>A <code>Node</code> is a point in space.</p><p><strong>Fields</strong></p><ul><li><code>x::Vec{dim,T}</code>: stores the coordinates</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L4-L11">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CellIndex" href="#Ferrite.CellIndex"><code>Ferrite.CellIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>CellIndex</code> wraps an Int and corresponds to a cell with that number in the mesh</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L75-L77">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.VertexIndex" href="#Ferrite.VertexIndex"><code>Ferrite.VertexIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>VertexIndex</code> wraps an (Int, Int) and defines a local vertex by pointing to a (cell, vert).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L96-L98">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.EdgeIndex" href="#Ferrite.EdgeIndex"><code>Ferrite.EdgeIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>EdgeIndex</code> wraps an (Int, Int) and defines a local edge by pointing to a (cell, edge).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L89-L91">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FaceIndex" href="#Ferrite.FaceIndex"><code>Ferrite.FaceIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>FaceIndex</code> wraps an (Int, Int) and defines a local face by pointing to a (cell, face).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L82-L84">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetIndex" href="#Ferrite.FacetIndex"><code>Ferrite.FacetIndex</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>A <code>FacetIndex</code> wraps an (Int, Int) and defines a local facet by pointing to a (cell, facet).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Ferrite.jl#L103-L105">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Grid" href="#Ferrite.Grid"><code>Ferrite.Grid</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Grid{dim, C<:AbstractCell, T<:Real} <: AbstractGrid}</code></pre><p>A <code>Grid</code> is a collection of <code>Ferrite.AbstractCell</code>s and <code>Ferrite.Node</code>s which covers the computational domain. Helper structures for applying boundary conditions or define subdomains are gathered in <code>cellsets</code>, <code>nodesets</code>, <code>facetsets</code>, and <code>vertexsets</code>.</p><p><strong>Fields</strong></p><ul><li><code>cells::Vector{C}</code>: stores all cells of the grid</li><li><code>nodes::Vector{Node{dim,T}}</code>: stores the <code>dim</code> dimensional nodes of the grid</li><li><code>cellsets::Dict{String, OrderedSet{Int}}</code>: maps a <code>String</code> key to an <code>OrderedSet</code> of cell ids</li><li><code>nodesets::Dict{String, OrderedSet{Int}}</code>: maps a <code>String</code> key to an <code>OrderedSet</code> of global node ids</li><li><code>facetsets::Dict{String, OrderedSet{FacetIndex}}</code>: maps a <code>String</code> to an <code>OrderedSet</code> of <code>FacetIndex</code></li><li><code>vertexsets::Dict{String, OrderedSet{VertexIndex}}</code>: maps a <code>String</code> key to an <code>OrderedSet</code> of <code>VertexIndex</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L354-L368">source</a></section></article><h3 id="Utility-Functions"><a class="docs-heading-anchor" href="#Utility-Functions">Utility Functions</a><a id="Utility-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Utility-Functions" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcells" href="#Ferrite.getcells"><code>Ferrite.getcells</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcells(grid::AbstractGrid)
getcells(grid::AbstractGrid, v::Union{Int,Vector{Int}}
-getcells(grid::AbstractGrid, setname::String)</code></pre><p>Returns either all <code>cells::Collection{C<:AbstractCell}</code> of a <code><:AbstractGrid</code> or a subset based on an <code>Int</code>, <code>Vector{Int}</code> or <code>String</code>. Whereas the last option tries to call a <code>cellset</code> of the <code>grid</code>. <code>Collection</code> can be any indexable type, for <code>Grid</code> it is <code>Vector{C<:AbstractCell}</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L459-L466">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getncells" href="#Ferrite.getncells"><code>Ferrite.getncells</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Returns the number of cells in the <code><:AbstractGrid</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L470">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnodes" href="#Ferrite.getnodes"><code>Ferrite.getnodes</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnodes(grid::AbstractGrid)
+getcells(grid::AbstractGrid, setname::String)</code></pre><p>Returns either all <code>cells::Collection{C<:AbstractCell}</code> of a <code><:AbstractGrid</code> or a subset based on an <code>Int</code>, <code>Vector{Int}</code> or <code>String</code>. Whereas the last option tries to call a <code>cellset</code> of the <code>grid</code>. <code>Collection</code> can be any indexable type, for <code>Grid</code> it is <code>Vector{C<:AbstractCell}</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L459-L466">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getncells" href="#Ferrite.getncells"><code>Ferrite.getncells</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Returns the number of cells in the <code><:AbstractGrid</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L470">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnodes" href="#Ferrite.getnodes"><code>Ferrite.getnodes</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnodes(grid::AbstractGrid)
getnodes(grid::AbstractGrid, v::Union{Int,Vector{Int}}
-getnodes(grid::AbstractGrid, setname::String)</code></pre><p>Returns either all <code>nodes::Collection{N}</code> of a <code><:AbstractGrid</code> or a subset based on an <code>Int</code>, <code>Vector{Int}</code> or <code>String</code>. The last option tries to call a <code>nodeset</code> of the <code><:AbstractGrid</code>. <code>Collection{N}</code> refers to some indexable collection where each element corresponds to a Node.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L476-L484">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnnodes" href="#Ferrite.getnnodes"><code>Ferrite.getnnodes</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Returns the number of nodes in the grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L488">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.nnodes_per_cell" href="#Ferrite.nnodes_per_cell"><code>Ferrite.nnodes_per_cell</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Returns the number of nodes of the <code>i</code>-th cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L490">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcellset" href="#Ferrite.getcellset"><code>Ferrite.getcellset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcellset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all cells as cellid in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L502-L506">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnodeset" href="#Ferrite.getnodeset"><code>Ferrite.getnodeset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnodeset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all nodes as nodeid in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L515-L519">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getfacetset" href="#Ferrite.getfacetset"><code>Ferrite.getfacetset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getfacetset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all facets as <code>FacetIndex</code> in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L528-L532">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getvertexset" href="#Ferrite.getvertexset"><code>Ferrite.getvertexset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getvertexset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all vertices as <code>VertexIndex</code> in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L542-L546">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.transform_coordinates!" href="#Ferrite.transform_coordinates!"><code>Ferrite.transform_coordinates!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">transform_coordinates!(grid::Abstractgrid, f::Function)</code></pre><p>Transform the coordinates of all nodes of the <code>grid</code> based on some transformation function <code>f(x)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L556-L560">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcoordinates" href="#Ferrite.getcoordinates"><code>Ferrite.getcoordinates</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcoordinates(grid::AbstractGrid, idx::Union{Int,CellIndex})
-getcoordinates(cache::CellCache)</code></pre><p>Get a vector with the coordinates of the cell corresponding to <code>idx</code> or <code>cache</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L566-L571">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcoordinates!" href="#Ferrite.getcoordinates!"><code>Ferrite.getcoordinates!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcoordinates!(x::Vector{<:Vec}, grid::AbstractGrid, idx::Union{Int,CellIndex})
-getcoordinates!(x::Vector{<:Vec}, grid::AbstractGrid, cell::AbstractCell)</code></pre><p>Mutate <code>x</code> to the coordinates of the cell corresponding to <code>idx</code> or <code>cell</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L581-L586">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.geometric_interpolation-Tuple{Ferrite.AbstractCell}" href="#Ferrite.geometric_interpolation-Tuple{Ferrite.AbstractCell}"><code>Ferrite.geometric_interpolation</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">geometric_interpolation(::AbstractCell)::ScalarInterpolation
-geometric_interpolation(::Type{<:AbstractCell})::ScalarInterpolation</code></pre><p>Each <code>AbstractCell</code> type has a unique geometric interpolation describing its geometry. This function returns that interpolation, which is always a scalar interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L156-L162">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_node_coordinate" href="#Ferrite.get_node_coordinate"><code>Ferrite.get_node_coordinate</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_node_coordinate(::Node)</code></pre><p>Get the value of the node coordinate.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L17-L21">source</a></section><section><div><pre><code class="language-julia hljs">get_node_coordinate(grid::AbstractGrid, n::Int)</code></pre><p>Return the coordinate of the <code>n</code>th node in <code>grid</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L600-L604">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getspatialdim-Tuple{Ferrite.AbstractGrid}" href="#Ferrite.getspatialdim-Tuple{Ferrite.AbstractGrid}"><code>Ferrite.getspatialdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getspatialdim(grid::AbstractGrid)</code></pre><p>Get the spatial dimension of the grid, corresponding to the vector dimension of the grid's coordinates.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L430-L434">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefdim-Tuple{Ferrite.AbstractCell}" href="#Ferrite.getrefdim-Tuple{Ferrite.AbstractCell}"><code>Ferrite.getrefdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefdim(cell::AbstractCell)
-Ferrite.getrefdim(::Type{<:AbstractCell})</code></pre><p>Get the reference dimension of the cell, i.e. the dimension of the cell's reference shape.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/grid.jl#L338-L344">source</a></section></article><h3 id="Topology"><a class="docs-heading-anchor" href="#Topology">Topology</a><a id="Topology-1"></a><a class="docs-heading-anchor-permalink" href="#Topology" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ExclusiveTopology" href="#Ferrite.ExclusiveTopology"><code>Ferrite.ExclusiveTopology</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ExclusiveTopology(grid::AbstractGrid)</code></pre><p>The <strong>experimental feature</strong> <code>ExclusiveTopology</code> saves topological (connectivity/neighborhood) data of the grid. Only the highest dimensional neighborhood is saved. I.e., if something is connected by a face and an edge, only the face neighborhood is saved. The lower dimensional neighborhood is recomputed when calling getneighborhood if needed.</p><p><strong>Fields</strong></p><ul><li><code>vertex_to_cell::AbstractArray{AbstractVector{Int}, 1}</code>: global vertex id to all cells containing the vertex</li><li><code>cell_neighbor::AbstractArray{AbstractVector{Int}, 1}</code>: cellid to all connected cells</li><li><code>face_neighbor::AbstractArray{AbstractVector{FaceIndex}, 2}</code>: <code>face_neighbor[cellid, local_face_id]</code> -> neighboring faces</li><li><code>edge_neighbor::AbstractArray{AbstractVector{EdgeIndex}, 2}</code>: <code>edge_neighbor[cellid, local_edge_id]</code> -> neighboring edges</li><li><code>vertex_neighbor::AbstractArray{AbstractVector{VertexIndex}, 2}</code>: <code>vertex_neighbor[cellid, local_vertex_id]</code> -> neighboring vertices</li><li><code>face_skeleton::Union{Vector{FaceIndex}, Nothing}</code>: List of unique faces in the grid given as <code>FaceIndex</code></li><li><code>edge_skeleton::Union{Vector{EdgeIndex}, Nothing}</code>: List of unique edges in the grid given as <code>EdgeIndex</code></li><li><code>vertex_skeleton::Union{Vector{VertexIndex}, Nothing}</code>: List of unique vertices in the grid given as <code>VertexIndex</code></li></ul><div class="admonition is-warning"><header class="admonition-header">Limitations</header><div class="admonition-body"><p>The implementation only works with conforming grids, i.e. grids without "hanging nodes". Non-conforming grids will give unexpected results. Grids with embedded cells (different reference dimension compared to the spatial dimension) are not supported, and will error on construction.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/topology.jl#L19-L41">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getneighborhood" href="#Ferrite.getneighborhood"><code>Ferrite.getneighborhood</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getneighborhood(topology, grid::AbstractGrid, cellidx::CellIndex, include_self=false)
+getnodes(grid::AbstractGrid, setname::String)</code></pre><p>Returns either all <code>nodes::Collection{N}</code> of a <code><:AbstractGrid</code> or a subset based on an <code>Int</code>, <code>Vector{Int}</code> or <code>String</code>. The last option tries to call a <code>nodeset</code> of the <code><:AbstractGrid</code>. <code>Collection{N}</code> refers to some indexable collection where each element corresponds to a Node.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L476-L484">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnnodes" href="#Ferrite.getnnodes"><code>Ferrite.getnnodes</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Returns the number of nodes in the grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L488">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.nnodes_per_cell" href="#Ferrite.nnodes_per_cell"><code>Ferrite.nnodes_per_cell</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Returns the number of nodes of the <code>i</code>-th cell.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L490">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcellset" href="#Ferrite.getcellset"><code>Ferrite.getcellset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcellset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all cells as cellid in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L502-L506">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnodeset" href="#Ferrite.getnodeset"><code>Ferrite.getnodeset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnodeset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all nodes as nodeid in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L515-L519">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getfacetset" href="#Ferrite.getfacetset"><code>Ferrite.getfacetset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getfacetset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all facets as <code>FacetIndex</code> in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L528-L532">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getvertexset" href="#Ferrite.getvertexset"><code>Ferrite.getvertexset</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getvertexset(grid::AbstractGrid, setname::String)</code></pre><p>Returns all vertices as <code>VertexIndex</code> in the set with name <code>setname</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L542-L546">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.transform_coordinates!" href="#Ferrite.transform_coordinates!"><code>Ferrite.transform_coordinates!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">transform_coordinates!(grid::Abstractgrid, f::Function)</code></pre><p>Transform the coordinates of all nodes of the <code>grid</code> based on some transformation function <code>f(x)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L556-L560">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcoordinates" href="#Ferrite.getcoordinates"><code>Ferrite.getcoordinates</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcoordinates(grid::AbstractGrid, idx::Union{Int,CellIndex})
+getcoordinates(cache::CellCache)</code></pre><p>Get a vector with the coordinates of the cell corresponding to <code>idx</code> or <code>cache</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L566-L571">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getcoordinates!" href="#Ferrite.getcoordinates!"><code>Ferrite.getcoordinates!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getcoordinates!(x::Vector{<:Vec}, grid::AbstractGrid, idx::Union{Int,CellIndex})
+getcoordinates!(x::Vector{<:Vec}, grid::AbstractGrid, cell::AbstractCell)</code></pre><p>Mutate <code>x</code> to the coordinates of the cell corresponding to <code>idx</code> or <code>cell</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L581-L586">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.geometric_interpolation-Tuple{Ferrite.AbstractCell}" href="#Ferrite.geometric_interpolation-Tuple{Ferrite.AbstractCell}"><code>Ferrite.geometric_interpolation</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">geometric_interpolation(::AbstractCell)::ScalarInterpolation
+geometric_interpolation(::Type{<:AbstractCell})::ScalarInterpolation</code></pre><p>Each <code>AbstractCell</code> type has a unique geometric interpolation describing its geometry. This function returns that interpolation, which is always a scalar interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L156-L162">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.get_node_coordinate" href="#Ferrite.get_node_coordinate"><code>Ferrite.get_node_coordinate</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_node_coordinate(::Node)</code></pre><p>Get the value of the node coordinate.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L17-L21">source</a></section><section><div><pre><code class="language-julia hljs">get_node_coordinate(grid::AbstractGrid, n::Int)</code></pre><p>Return the coordinate of the <code>n</code>th node in <code>grid</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L600-L604">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getspatialdim-Tuple{Ferrite.AbstractGrid}" href="#Ferrite.getspatialdim-Tuple{Ferrite.AbstractGrid}"><code>Ferrite.getspatialdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getspatialdim(grid::AbstractGrid)</code></pre><p>Get the spatial dimension of the grid, corresponding to the vector dimension of the grid's coordinates.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L430-L434">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefdim-Tuple{Ferrite.AbstractCell}" href="#Ferrite.getrefdim-Tuple{Ferrite.AbstractCell}"><code>Ferrite.getrefdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefdim(cell::AbstractCell)
+Ferrite.getrefdim(::Type{<:AbstractCell})</code></pre><p>Get the reference dimension of the cell, i.e. the dimension of the cell's reference shape.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/grid.jl#L338-L344">source</a></section></article><h3 id="Topology"><a class="docs-heading-anchor" href="#Topology">Topology</a><a id="Topology-1"></a><a class="docs-heading-anchor-permalink" href="#Topology" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.ExclusiveTopology" href="#Ferrite.ExclusiveTopology"><code>Ferrite.ExclusiveTopology</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ExclusiveTopology(grid::AbstractGrid)</code></pre><p>The <strong>experimental feature</strong> <code>ExclusiveTopology</code> saves topological (connectivity/neighborhood) data of the grid. Only the highest dimensional neighborhood is saved. I.e., if something is connected by a face and an edge, only the face neighborhood is saved. The lower dimensional neighborhood is recomputed when calling getneighborhood if needed.</p><p><strong>Fields</strong></p><ul><li><code>vertex_to_cell::AbstractArray{AbstractVector{Int}, 1}</code>: global vertex id to all cells containing the vertex</li><li><code>cell_neighbor::AbstractArray{AbstractVector{Int}, 1}</code>: cellid to all connected cells</li><li><code>face_neighbor::AbstractArray{AbstractVector{FaceIndex}, 2}</code>: <code>face_neighbor[cellid, local_face_id]</code> -> neighboring faces</li><li><code>edge_neighbor::AbstractArray{AbstractVector{EdgeIndex}, 2}</code>: <code>edge_neighbor[cellid, local_edge_id]</code> -> neighboring edges</li><li><code>vertex_neighbor::AbstractArray{AbstractVector{VertexIndex}, 2}</code>: <code>vertex_neighbor[cellid, local_vertex_id]</code> -> neighboring vertices</li><li><code>face_skeleton::Union{Vector{FaceIndex}, Nothing}</code>: List of unique faces in the grid given as <code>FaceIndex</code></li><li><code>edge_skeleton::Union{Vector{EdgeIndex}, Nothing}</code>: List of unique edges in the grid given as <code>EdgeIndex</code></li><li><code>vertex_skeleton::Union{Vector{VertexIndex}, Nothing}</code>: List of unique vertices in the grid given as <code>VertexIndex</code></li></ul><div class="admonition is-warning"><header class="admonition-header">Limitations</header><div class="admonition-body"><p>The implementation only works with conforming grids, i.e. grids without "hanging nodes". Non-conforming grids will give unexpected results. Grids with embedded cells (different reference dimension compared to the spatial dimension) are not supported, and will error on construction.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/topology.jl#L19-L41">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getneighborhood" href="#Ferrite.getneighborhood"><code>Ferrite.getneighborhood</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getneighborhood(topology, grid::AbstractGrid, cellidx::CellIndex, include_self=false)
getneighborhood(topology, grid::AbstractGrid, faceidx::FaceIndex, include_self=false)
getneighborhood(topology, grid::AbstractGrid, vertexidx::VertexIndex, include_self=false)
-getneighborhood(topology, grid::AbstractGrid, edgeidx::EdgeIndex, include_self=false)</code></pre><p>Returns all connected entities of the same type as defined by the respective topology. If <code>include_self</code> is true, the given entity is included in the returned list as well.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/topology.jl#L5-L13">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facetskeleton" href="#Ferrite.facetskeleton"><code>Ferrite.facetskeleton</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facetskeleton(top::ExclusiveTopology, grid::AbstractGrid)</code></pre><p>Materializes the skeleton from the <code>neighborhood</code> information by returning an iterable over the unique facets in the grid, described by <code>FacetIndex</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/topology.jl#L375-L380">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vertex_star_stencils" href="#Ferrite.vertex_star_stencils"><code>Ferrite.vertex_star_stencils</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">vertex_star_stencils(top::ExclusiveTopology, grid::Grid) -> AbstractVector{AbstractVector{VertexIndex}}</code></pre><p>Computes the stencils induced by the edge connectivity of the vertices.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/topology.jl#L320-L323">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getstencil" href="#Ferrite.getstencil"><code>Ferrite.getstencil</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getstencil(top::ArrayOfVectorViews{VertexIndex, 1}, grid::AbstractGrid, vertex_idx::VertexIndex) -> AbstractVector{VertexIndex}</code></pre><p>Get an iterateable over the stencil members for a given local entity.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/topology.jl#L347-L350">source</a></section></article><h3 id="Grid-Sets-Utility"><a class="docs-heading-anchor" href="#Grid-Sets-Utility">Grid Sets Utility</a><a id="Grid-Sets-Utility-1"></a><a class="docs-heading-anchor-permalink" href="#Grid-Sets-Utility" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addcellset!" href="#Ferrite.addcellset!"><code>Ferrite.addcellset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addcellset!(grid::AbstractGrid, name::String, cellid::AbstractVecOrSet{Int})
+getneighborhood(topology, grid::AbstractGrid, edgeidx::EdgeIndex, include_self=false)</code></pre><p>Returns all connected entities of the same type as defined by the respective topology. If <code>include_self</code> is true, the given entity is included in the returned list as well.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/topology.jl#L5-L13">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.facetskeleton" href="#Ferrite.facetskeleton"><code>Ferrite.facetskeleton</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">facetskeleton(top::ExclusiveTopology, grid::AbstractGrid)</code></pre><p>Materializes the skeleton from the <code>neighborhood</code> information by returning an iterable over the unique facets in the grid, described by <code>FacetIndex</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/topology.jl#L375-L380">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.vertex_star_stencils" href="#Ferrite.vertex_star_stencils"><code>Ferrite.vertex_star_stencils</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">vertex_star_stencils(top::ExclusiveTopology, grid::Grid) -> AbstractVector{AbstractVector{VertexIndex}}</code></pre><p>Computes the stencils induced by the edge connectivity of the vertices.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/topology.jl#L320-L323">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getstencil" href="#Ferrite.getstencil"><code>Ferrite.getstencil</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getstencil(top::ArrayOfVectorViews{VertexIndex, 1}, grid::AbstractGrid, vertex_idx::VertexIndex) -> AbstractVector{VertexIndex}</code></pre><p>Get an iterateable over the stencil members for a given local entity.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/topology.jl#L347-L350">source</a></section></article><h3 id="Grid-Sets-Utility"><a class="docs-heading-anchor" href="#Grid-Sets-Utility">Grid Sets Utility</a><a id="Grid-Sets-Utility-1"></a><a class="docs-heading-anchor-permalink" href="#Grid-Sets-Utility" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addcellset!" href="#Ferrite.addcellset!"><code>Ferrite.addcellset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addcellset!(grid::AbstractGrid, name::String, cellid::AbstractVecOrSet{Int})
addcellset!(grid::AbstractGrid, name::String, f::function; all::Bool=true)</code></pre><p>Adds a cellset to the grid with key <code>name</code>. Cellsets are typically used to define subdomains of the problem, e.g. two materials in the computational domain. The <code>DofHandler</code> can construct different fields which live not on the whole domain, but rather on a cellset. <code>all=true</code> implies that <code>f(x)</code> must return <code>true</code> for all nodal coordinates <code>x</code> in the cell if the cell should be added to the set, otherwise it suffices that <code>f(x)</code> returns <code>true</code> for one node.</p><pre><code class="language-julia hljs">addcellset!(grid, "left", Set((1,3))) #add cells with id 1 and 3 to cellset left
-addcellset!(grid, "right", x -> norm(x[1]) < 2.0 ) #add cell to cellset right, if x[1] of each cell's node is smaller than 2.0</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/utils.jl#L6-L20">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addfacetset!" href="#Ferrite.addfacetset!"><code>Ferrite.addfacetset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addfacetset!(grid::AbstractGrid, name::String, faceid::AbstractVecOrSet{FacetIndex})
+addcellset!(grid, "right", x -> norm(x[1]) < 2.0 ) #add cell to cellset right, if x[1] of each cell's node is smaller than 2.0</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/utils.jl#L6-L20">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addfacetset!" href="#Ferrite.addfacetset!"><code>Ferrite.addfacetset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addfacetset!(grid::AbstractGrid, name::String, faceid::AbstractVecOrSet{FacetIndex})
addfacetset!(grid::AbstractGrid, name::String, f::Function; all::Bool=true)</code></pre><p>Adds a facetset to the grid with key <code>name</code>. A facetset maps a <code>String</code> key to a <code>OrderedSet</code> of tuples corresponding to <code>(global_cell_id, local_facet_id)</code>. Facetsets can be used to initialize <code>Dirichlet</code> boundary conditions for the <code>ConstraintHandler</code>. <code>all=true</code> implies that <code>f(x)</code> must return <code>true</code> for all nodal coordinates <code>x</code> on the facet if the facet should be added to the set, otherwise it suffices that <code>f(x)</code> returns <code>true</code> for one node.</p><pre><code class="language-julia hljs">addfacetset!(grid, "right", Set((FacetIndex(2,2), FacetIndex(4,2)))) #see grid manual example for reference
-addfacetset!(grid, "clamped", x -> norm(x[1]) ≈ 0.0) #see incompressible elasticity example for reference</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/utils.jl#L42-L56">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addboundaryfacetset!" href="#Ferrite.addboundaryfacetset!"><code>Ferrite.addboundaryfacetset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>addboundaryfacetset!(grid::AbstractGrid, topology::ExclusiveTopology, name::String, f::Function; all::Bool=true)</p><p>Adds a boundary facetset to the grid with key <code>name</code>. A facetset maps a <code>String</code> key to a <code>OrderedSet</code> of tuples corresponding to <code>(global_cell_id, local_facet_id)</code>. Facetsets are used to initialize <code>Dirichlet</code> structs, that are needed to specify the boundary for the <code>ConstraintHandler</code>. <code>all=true</code> implies that <code>f(x)</code> must return <code>true</code> for all nodal coordinates <code>x</code> on the facet if the facet should be added to the set, otherwise it suffices that <code>f(x)</code> returns <code>true</code> for one node.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/utils.jl#L104-L113">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addvertexset!" href="#Ferrite.addvertexset!"><code>Ferrite.addvertexset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addvertexset!(grid::AbstractGrid, name::String, faceid::AbstractVecOrSet{FaceIndex})
+addfacetset!(grid, "clamped", x -> norm(x[1]) ≈ 0.0) #see incompressible elasticity example for reference</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/utils.jl#L42-L56">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addboundaryfacetset!" href="#Ferrite.addboundaryfacetset!"><code>Ferrite.addboundaryfacetset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>addboundaryfacetset!(grid::AbstractGrid, topology::ExclusiveTopology, name::String, f::Function; all::Bool=true)</p><p>Adds a boundary facetset to the grid with key <code>name</code>. A facetset maps a <code>String</code> key to a <code>OrderedSet</code> of tuples corresponding to <code>(global_cell_id, local_facet_id)</code>. Facetsets are used to initialize <code>Dirichlet</code> structs, that are needed to specify the boundary for the <code>ConstraintHandler</code>. <code>all=true</code> implies that <code>f(x)</code> must return <code>true</code> for all nodal coordinates <code>x</code> on the facet if the facet should be added to the set, otherwise it suffices that <code>f(x)</code> returns <code>true</code> for one node.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/utils.jl#L104-L113">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addvertexset!" href="#Ferrite.addvertexset!"><code>Ferrite.addvertexset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addvertexset!(grid::AbstractGrid, name::String, faceid::AbstractVecOrSet{FaceIndex})
addvertexset!(grid::AbstractGrid, name::String, f::Function)</code></pre><p>Adds a vertexset to the grid with key <code>name</code>. A vertexset maps a <code>String</code> key to a <code>OrderedSet</code> of tuples corresponding to <code>(global_cell_id, local_vertex_id)</code>. Vertexsets can be used to initialize <code>Dirichlet</code> boundary conditions for the <code>ConstraintHandler</code>.</p><pre><code class="language-julia hljs">addvertexset!(grid, "right", Set((VertexIndex(2,2), VertexIndex(4,2))))
-addvertexset!(grid, "clamped", x -> norm(x[1]) ≈ 0.0)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/utils.jl#L63-L75">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addboundaryvertexset!" href="#Ferrite.addboundaryvertexset!"><code>Ferrite.addboundaryvertexset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>addboundaryvertexset!(grid::AbstractGrid, topology::ExclusiveTopology, name::String, f::Function; all::Bool=true)</p><p>Adds a boundary vertexset to the grid with key <code>name</code>. A vertexset maps a <code>String</code> key to an <code>OrderedSet</code> of tuples corresponding to <code>(global_cell_id, local_vertex_id)</code>. <code>all=true</code> implies that <code>f(x)</code> must return <code>true</code> for all nodal coordinates <code>x</code> on the facet if the facet should be added to the set, otherwise it suffices that <code>f(x)</code> returns <code>true</code> for one node.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/utils.jl#L90-L98">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addnodeset!" href="#Ferrite.addnodeset!"><code>Ferrite.addnodeset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addnodeset!(grid::AbstractGrid, name::String, nodeid::AbstractVecOrSet{Int})
-addnodeset!(grid::AbstractGrid, name::String, f::Function)</code></pre><p>Adds a <code>nodeset::OrderedSet{Int}</code> to the <code>grid</code>'s <code>nodesets</code> with key <code>name</code>. Has the same interface as <code>addcellset</code>. However, instead of mapping a cell id to the <code>String</code> key, a set of node ids is returned.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/utils.jl#L29-L35">source</a></section></article><h3 id="Multithreaded-Assembly"><a class="docs-heading-anchor" href="#Multithreaded-Assembly">Multithreaded Assembly</a><a id="Multithreaded-Assembly-1"></a><a class="docs-heading-anchor-permalink" href="#Multithreaded-Assembly" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.create_coloring" href="#Ferrite.create_coloring"><code>Ferrite.create_coloring</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">create_coloring(g::Grid, cellset=1:getncells(g); alg::ColoringAlgorithm)</code></pre><p>Create a coloring of the cells in grid <code>g</code> such that no neighboring cells have the same color. If only a subset of cells should be colored, the cells to color can be specified by <code>cellset</code>.</p><p>Returns a vector of vectors with cell indexes, e.g.:</p><pre><code class="language-julia hljs">ret = [
+addvertexset!(grid, "clamped", x -> norm(x[1]) ≈ 0.0)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/utils.jl#L63-L75">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addboundaryvertexset!" href="#Ferrite.addboundaryvertexset!"><code>Ferrite.addboundaryvertexset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>addboundaryvertexset!(grid::AbstractGrid, topology::ExclusiveTopology, name::String, f::Function; all::Bool=true)</p><p>Adds a boundary vertexset to the grid with key <code>name</code>. A vertexset maps a <code>String</code> key to an <code>OrderedSet</code> of tuples corresponding to <code>(global_cell_id, local_vertex_id)</code>. <code>all=true</code> implies that <code>f(x)</code> must return <code>true</code> for all nodal coordinates <code>x</code> on the facet if the facet should be added to the set, otherwise it suffices that <code>f(x)</code> returns <code>true</code> for one node.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/utils.jl#L90-L98">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.addnodeset!" href="#Ferrite.addnodeset!"><code>Ferrite.addnodeset!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">addnodeset!(grid::AbstractGrid, name::String, nodeid::AbstractVecOrSet{Int})
+addnodeset!(grid::AbstractGrid, name::String, f::Function)</code></pre><p>Adds a <code>nodeset::OrderedSet{Int}</code> to the <code>grid</code>'s <code>nodesets</code> with key <code>name</code>. Has the same interface as <code>addcellset</code>. However, instead of mapping a cell id to the <code>String</code> key, a set of node ids is returned.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/utils.jl#L29-L35">source</a></section></article><h3 id="Multithreaded-Assembly"><a class="docs-heading-anchor" href="#Multithreaded-Assembly">Multithreaded Assembly</a><a id="Multithreaded-Assembly-1"></a><a class="docs-heading-anchor-permalink" href="#Multithreaded-Assembly" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.create_coloring" href="#Ferrite.create_coloring"><code>Ferrite.create_coloring</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">create_coloring(g::Grid, cellset=1:getncells(g); alg::ColoringAlgorithm)</code></pre><p>Create a coloring of the cells in grid <code>g</code> such that no neighboring cells have the same color. If only a subset of cells should be colored, the cells to color can be specified by <code>cellset</code>.</p><p>Returns a vector of vectors with cell indexes, e.g.:</p><pre><code class="language-julia hljs">ret = [
[1, 3, 5, 10, ...], # cells for color 1
[2, 4, 6, 12, ...], # cells for color 2
]</code></pre><p>Two different algorithms are available, specified with the <code>alg</code> keyword argument:</p><ul><li><code>alg = ColoringAlgorithm.WorkStream</code> (default): Three step algorithm from Turcksin et al. [<a href="../../cited-literature/#Turcksin2016">11</a>], albeit with a greedy coloring in the second step. Generally results in more colors than <code>ColoringAlgorithm.Greedy</code>, however the cells are more equally distributed among the colors.</li><li><code>alg = ColoringAlgorithm.Greedy</code>: greedy algorithm that works well for structured quadrilateral grids such as e.g. quadrilateral grids from <code>generate_grid</code>.</li></ul><p>The resulting colors can be visualized using <a href="../export/#Ferrite.write_cell_colors"><code>Ferrite.write_cell_colors</code></a>.</p><div class="admonition is-info"><header class="admonition-header">Cell to color mapping</header><div class="admonition-body"><p>In a previous version of Ferrite this function returned a dictionary mapping cell ID to color numbers as the first argument. If you need this mapping you can create it using the following construct:</p><pre><code class="language-julia hljs">colors = create_coloring(...)
cell_colormap = Dict{Int,Int}(
cellid => color for (color, cellids) in enumerate(final_colors) for cellid in cellids
-)</code></pre></div></div><p><strong>References</strong></p><ul><li>[<a href="../../cited-literature/#Turcksin2016">11</a>] Turcksin et al. ACM Trans. Math. Softw. 43 (2016).</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Grid/coloring.jl#L160-L197">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../boundary_conditions/">« Boundary conditions</a><a class="docs-footer-nextpage" href="../export/">Postprocessing »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+)</code></pre></div></div><p><strong>References</strong></p><ul><li>[<a href="../../cited-literature/#Turcksin2016">11</a>] Turcksin et al. ACM Trans. Math. Softw. 43 (2016).</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Grid/coloring.jl#L160-L197">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../boundary_conditions/">« Boundary conditions</a><a class="docs-footer-nextpage" href="../export/">Postprocessing »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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diff --git a/dev/reference/interpolations/index.html b/dev/reference/interpolations/index.html
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Lagrange{RefTriangle, 2}()
julia> getnbasefunctions(ip)
-6</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L1-L46">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnbasefunctions" href="#Ferrite.getnbasefunctions"><code>Ferrite.getnbasefunctions</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getnbasefunctions(ip::Interpolation)</code></pre><p>Return the number of base functions for the interpolation <code>ip</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L148-L152">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefdim-Tuple{Interpolation}" href="#Ferrite.getrefdim-Tuple{Interpolation}"><code>Ferrite.getrefdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefdim(::Interpolation)</code></pre><p>Return the dimension of the reference element for a given interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L121-L125">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefshape" href="#Ferrite.getrefshape"><code>Ferrite.getrefshape</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefshape(::Interpolation)::AbstractRefShape</code></pre><p>Return the reference element shape of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L129-L133">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getorder" href="#Ferrite.getorder"><code>Ferrite.getorder</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getorder(::Interpolation)</code></pre><p>Return order of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L136-L140">source</a></section></article><p>Implemented interpolations:</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Lagrange" href="#Ferrite.Lagrange"><code>Ferrite.Lagrange</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Lagrange{refshape, order} <: ScalarInterpolation</code></pre><p>Standard continuous Lagrange polynomials with equidistant node placement.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L500-L504">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Serendipity" href="#Ferrite.Serendipity"><code>Ferrite.Serendipity</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Serendipity{refshape, order} <: ScalarInterpolation</code></pre><p>Serendipity element on hypercubes. Currently only second order variants are implemented.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L1357-L1361">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.DiscontinuousLagrange" href="#Ferrite.DiscontinuousLagrange"><code>Ferrite.DiscontinuousLagrange</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Piecewise discontinuous Lagrange basis via Gauss-Lobatto points.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L445-L447">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BubbleEnrichedLagrange" href="#Ferrite.BubbleEnrichedLagrange"><code>Ferrite.BubbleEnrichedLagrange</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Lagrange element with bubble stabilization.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L1314-L1316">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CrouzeixRaviart" href="#Ferrite.CrouzeixRaviart"><code>Ferrite.CrouzeixRaviart</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CrouzeixRaviart{refshape, order} <: ScalarInterpolation</code></pre><p>Classical non-conforming Crouzeix–Raviart element.</p><p>For details we refer to the original paper [<a href="../../cited-literature/#CroRav:1973:cnf">9</a>].</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L1506-L1512">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RannacherTurek" href="#Ferrite.RannacherTurek"><code>Ferrite.RannacherTurek</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RannacherTurek{refshape, order} <: ScalarInterpolation</code></pre><p>Classical non-conforming Rannacher-Turek element.</p><p>This element is basically the idea from Crouzeix and Raviart applied to hypercubes. For details see the original paper [<a href="../../cited-literature/#RanTur:1992:snq">10</a>].</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/interpolations.jl#L1576-L1583">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../quadrature/">« Quadrature</a><a class="docs-footer-nextpage" href="../fevalues/">FEValues »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+6</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L1-L46">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnbasefunctions" href="#Ferrite.getnbasefunctions"><code>Ferrite.getnbasefunctions</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getnbasefunctions(ip::Interpolation)</code></pre><p>Return the number of base functions for the interpolation <code>ip</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L148-L152">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefdim-Tuple{Interpolation}" href="#Ferrite.getrefdim-Tuple{Interpolation}"><code>Ferrite.getrefdim</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefdim(::Interpolation)</code></pre><p>Return the dimension of the reference element for a given interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L121-L125">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getrefshape" href="#Ferrite.getrefshape"><code>Ferrite.getrefshape</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getrefshape(::Interpolation)::AbstractRefShape</code></pre><p>Return the reference element shape of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L129-L133">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getorder" href="#Ferrite.getorder"><code>Ferrite.getorder</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.getorder(::Interpolation)</code></pre><p>Return order of the interpolation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L136-L140">source</a></section></article><p>Implemented interpolations:</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Lagrange" href="#Ferrite.Lagrange"><code>Ferrite.Lagrange</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Lagrange{refshape, order} <: ScalarInterpolation</code></pre><p>Standard continuous Lagrange polynomials with equidistant node placement.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L500-L504">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.Serendipity" href="#Ferrite.Serendipity"><code>Ferrite.Serendipity</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Serendipity{refshape, order} <: ScalarInterpolation</code></pre><p>Serendipity element on hypercubes. Currently only second order variants are implemented.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L1357-L1361">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.DiscontinuousLagrange" href="#Ferrite.DiscontinuousLagrange"><code>Ferrite.DiscontinuousLagrange</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Piecewise discontinuous Lagrange basis via Gauss-Lobatto points.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L445-L447">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BubbleEnrichedLagrange" href="#Ferrite.BubbleEnrichedLagrange"><code>Ferrite.BubbleEnrichedLagrange</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Lagrange element with bubble stabilization.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L1314-L1316">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.CrouzeixRaviart" href="#Ferrite.CrouzeixRaviart"><code>Ferrite.CrouzeixRaviart</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">CrouzeixRaviart{refshape, order} <: ScalarInterpolation</code></pre><p>Classical non-conforming Crouzeix–Raviart element.</p><p>For details we refer to the original paper [<a href="../../cited-literature/#CroRav:1973:cnf">9</a>].</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L1506-L1512">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.RannacherTurek" href="#Ferrite.RannacherTurek"><code>Ferrite.RannacherTurek</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RannacherTurek{refshape, order} <: ScalarInterpolation</code></pre><p>Classical non-conforming Rannacher-Turek element.</p><p>This element is basically the idea from Crouzeix and Raviart applied to hypercubes. For details see the original paper [<a href="../../cited-literature/#RanTur:1992:snq">10</a>].</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/interpolations.jl#L1576-L1583">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../quadrature/">« Quadrature</a><a class="docs-footer-nextpage" href="../fevalues/">FEValues »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/reference/quadrature/index.html b/dev/reference/quadrature/index.html
index 48279d8338..1885c4250d 100644
--- a/dev/reference/quadrature/index.html
+++ b/dev/reference/quadrature/index.html
@@ -5,20 +5,20 @@
julia> getpoints(qr)
1-element Vector{Vec{2, Float64}}:
- [0.33333333333333, 0.33333333333333]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Quadrature/quadrature.jl#L13-L51">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetQuadratureRule" href="#Ferrite.FacetQuadratureRule"><code>Ferrite.FacetQuadratureRule</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetQuadratureRule{shape}([::Type{T},] [quad_rule_type::Symbol,] order::Int)
+ [0.33333333333333, 0.33333333333333]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Quadrature/quadrature.jl#L13-L51">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.FacetQuadratureRule" href="#Ferrite.FacetQuadratureRule"><code>Ferrite.FacetQuadratureRule</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">FacetQuadratureRule{shape}([::Type{T},] [quad_rule_type::Symbol,] order::Int)
FacetQuadratureRule{shape}(facet_rules::NTuple{<:Any, <:QuadratureRule{shape}})
-FacetQuadratureRule{shape}(facet_rules::AbstractVector{<:QuadratureRule{shape}})</code></pre><p>Create a <code>FacetQuadratureRule</code> used for integration of the facets of the refshape <code>shape</code> (of type <a href="../../devdocs/reference_cells/#Ferrite.AbstractRefShape"><code>AbstractRefShape</code></a>). <code>order</code> is the order of the quadrature rule. If no symbol is provided, the default <code>quad_rule_type</code> for each facet's reference shape is used (see <a href="#Ferrite.QuadratureRule">QuadratureRule</a>). For non-default <code>quad_rule_type</code>s on cells with mixed facet types (e.g. <code>RefPrism</code> and <code>RefPyramid</code>), the <code>facet_rules</code> must be provided explicitly.</p><p><code>FacetQuadratureRule</code> is used as one of the components to create <a href="../fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Quadrature/quadrature.jl#L174-L186">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnquadpoints-Tuple{QuadratureRule}" href="#Ferrite.getnquadpoints-Tuple{QuadratureRule}"><code>Ferrite.getnquadpoints</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnquadpoints(qr::QuadratureRule)</code></pre><p>Return the number of quadrature points in <code>qr</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Quadrature/quadrature.jl#L263-L267">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnquadpoints-Tuple{FacetQuadratureRule, Int64}" href="#Ferrite.getnquadpoints-Tuple{FacetQuadratureRule, Int64}"><code>Ferrite.getnquadpoints</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnquadpoints(qr::FacetQuadratureRule, facet::Int)</code></pre><p>Return the number of quadrature points in <code>qr</code> for local facet index <code>facet</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Quadrature/quadrature.jl#L270-L274">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getpoints" href="#Ferrite.getpoints"><code>Ferrite.getpoints</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getpoints(qr::QuadratureRule)
+FacetQuadratureRule{shape}(facet_rules::AbstractVector{<:QuadratureRule{shape}})</code></pre><p>Create a <code>FacetQuadratureRule</code> used for integration of the facets of the refshape <code>shape</code> (of type <a href="../../devdocs/reference_cells/#Ferrite.AbstractRefShape"><code>AbstractRefShape</code></a>). <code>order</code> is the order of the quadrature rule. If no symbol is provided, the default <code>quad_rule_type</code> for each facet's reference shape is used (see <a href="#Ferrite.QuadratureRule">QuadratureRule</a>). For non-default <code>quad_rule_type</code>s on cells with mixed facet types (e.g. <code>RefPrism</code> and <code>RefPyramid</code>), the <code>facet_rules</code> must be provided explicitly.</p><p><code>FacetQuadratureRule</code> is used as one of the components to create <a href="../fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Quadrature/quadrature.jl#L174-L186">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnquadpoints-Tuple{QuadratureRule}" href="#Ferrite.getnquadpoints-Tuple{QuadratureRule}"><code>Ferrite.getnquadpoints</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnquadpoints(qr::QuadratureRule)</code></pre><p>Return the number of quadrature points in <code>qr</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Quadrature/quadrature.jl#L263-L267">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getnquadpoints-Tuple{FacetQuadratureRule, Int64}" href="#Ferrite.getnquadpoints-Tuple{FacetQuadratureRule, Int64}"><code>Ferrite.getnquadpoints</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getnquadpoints(qr::FacetQuadratureRule, facet::Int)</code></pre><p>Return the number of quadrature points in <code>qr</code> for local facet index <code>facet</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Quadrature/quadrature.jl#L270-L274">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getpoints" href="#Ferrite.getpoints"><code>Ferrite.getpoints</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getpoints(qr::QuadratureRule)
getpoints(qr::FacetQuadratureRule, facet::Int)</code></pre><p>Return the points of the quadrature rule.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia> qr = QuadratureRule{RefTriangle}(:legendre, 2);
julia> getpoints(qr)
3-element Vector{Vec{2, Float64}}:
[0.16666666666667, 0.16666666666667]
[0.16666666666667, 0.66666666666667]
- [0.66666666666667, 0.16666666666667]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Quadrature/quadrature.jl#L298-L314">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getweights" href="#Ferrite.getweights"><code>Ferrite.getweights</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getweights(qr::QuadratureRule)
+ [0.66666666666667, 0.16666666666667]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Quadrature/quadrature.jl#L298-L314">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.getweights" href="#Ferrite.getweights"><code>Ferrite.getweights</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">getweights(qr::QuadratureRule)
getweights(qr::FacetQuadratureRule, facet::Int)</code></pre><p>Return the weights of the quadrature rule.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia> qr = QuadratureRule{RefTriangle}(:legendre, 2);
julia> getweights(qr)
3-element Array{Float64,1}:
0.166667
0.166667
- 0.166667</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Quadrature/quadrature.jl#L277-L293">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Reference overview</a><a class="docs-footer-nextpage" href="../interpolations/">Interpolation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ 0.166667</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Quadrature/quadrature.jl#L277-L293">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Reference overview</a><a class="docs-footer-nextpage" href="../interpolations/">Interpolation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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reference</a></li><li class="is-active"><a href>Sparsity pattern and sparse matrices</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Sparsity pattern and sparse matrices</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/sparsity_pattern.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Sparsity-pattern-and-sparse-matrices"><a class="docs-heading-anchor" href="#Sparsity-pattern-and-sparse-matrices">Sparsity pattern and sparse matrices</a><a id="Sparsity-pattern-and-sparse-matrices-1"></a><a class="docs-heading-anchor-permalink" href="#Sparsity-pattern-and-sparse-matrices" title="Permalink"></a></h1><p>This is the reference documentation for sparsity patterns and sparse matrix instantiation. See the topic section on <a href="../../topics/sparse_matrix/#topic-sparse-matrix">Sparsity pattern and sparse matrices</a>.</p><h2 id="Sparsity-patterns"><a class="docs-heading-anchor" href="#Sparsity-patterns">Sparsity patterns</a><a id="Sparsity-patterns-1"></a><a class="docs-heading-anchor-permalink" href="#Sparsity-patterns" title="Permalink"></a></h2><h3 id="AbstractSparsityPattern"><a class="docs-heading-anchor" href="#AbstractSparsityPattern"><code>AbstractSparsityPattern</code></a><a id="AbstractSparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#AbstractSparsityPattern" title="Permalink"></a></h3><p>The following applies to all subtypes of <code>AbstractSparsityPattern</code>:</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.AbstractSparsityPattern" href="#Ferrite.AbstractSparsityPattern"><code>Ferrite.AbstractSparsityPattern</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.AbstractSparsityPattern</code></pre><p>Supertype for sparsity pattern implementations, e.g. <a href="#SparsityPattern"><code>SparsityPattern</code></a> and <a href="#BlockSparsityPattern"><code>BlockSparsityPattern</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L5-L10">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.init_sparsity_pattern" href="#Ferrite.init_sparsity_pattern"><code>Ferrite.init_sparsity_pattern</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">init_sparsity_pattern(dh::DofHandler; nnz_per_row::Int)</code></pre><p>Initialize an empty <a href="#SparsityPattern"><code>SparsityPattern</code></a> with <code>ndofs(dh)</code> rows and <code>ndofs(dh)</code> columns.</p><p><strong>Keyword arguments</strong></p><ul><li><code>nnz_per_row</code>: memory optimization hint for the number of non-zero entries per row that will be added to the pattern.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L184-L192">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_sparsity_entries!" href="#Ferrite.add_sparsity_entries!"><code>Ferrite.add_sparsity_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_sparsity_entries!(
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reference</a></li><li class="is-active"><a href>Sparsity pattern and sparse matrices</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Sparsity pattern and sparse matrices</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/sparsity_pattern.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Sparsity-pattern-and-sparse-matrices"><a class="docs-heading-anchor" href="#Sparsity-pattern-and-sparse-matrices">Sparsity pattern and sparse matrices</a><a id="Sparsity-pattern-and-sparse-matrices-1"></a><a class="docs-heading-anchor-permalink" href="#Sparsity-pattern-and-sparse-matrices" title="Permalink"></a></h1><p>This is the reference documentation for sparsity patterns and sparse matrix instantiation. See the topic section on <a href="../../topics/sparse_matrix/#topic-sparse-matrix">Sparsity pattern and sparse matrices</a>.</p><h2 id="Sparsity-patterns"><a class="docs-heading-anchor" href="#Sparsity-patterns">Sparsity patterns</a><a id="Sparsity-patterns-1"></a><a class="docs-heading-anchor-permalink" href="#Sparsity-patterns" title="Permalink"></a></h2><h3 id="AbstractSparsityPattern"><a class="docs-heading-anchor" href="#AbstractSparsityPattern"><code>AbstractSparsityPattern</code></a><a id="AbstractSparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#AbstractSparsityPattern" title="Permalink"></a></h3><p>The following applies to all subtypes of <code>AbstractSparsityPattern</code>:</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.AbstractSparsityPattern" href="#Ferrite.AbstractSparsityPattern"><code>Ferrite.AbstractSparsityPattern</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.AbstractSparsityPattern</code></pre><p>Supertype for sparsity pattern implementations, e.g. <a href="#SparsityPattern"><code>SparsityPattern</code></a> and <a href="#BlockSparsityPattern"><code>BlockSparsityPattern</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L5-L10">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.init_sparsity_pattern" href="#Ferrite.init_sparsity_pattern"><code>Ferrite.init_sparsity_pattern</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">init_sparsity_pattern(dh::DofHandler; nnz_per_row::Int)</code></pre><p>Initialize an empty <a href="#SparsityPattern"><code>SparsityPattern</code></a> with <code>ndofs(dh)</code> rows and <code>ndofs(dh)</code> columns.</p><p><strong>Keyword arguments</strong></p><ul><li><code>nnz_per_row</code>: memory optimization hint for the number of non-zero entries per row that will be added to the pattern.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L184-L192">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_sparsity_entries!" href="#Ferrite.add_sparsity_entries!"><code>Ferrite.add_sparsity_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_sparsity_entries!(
sp::AbstractSparsityPattern,
dh::DofHandler,
ch::Union{ConstraintHandler, Nothing} = nothing;
@@ -7,37 +7,37 @@
keep_constrained::Bool = true,
coupling = nothing,
interface_coupling = nothing,
-)</code></pre><p>Convenience method for doing the common task of calling <a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>, <a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>, and <a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>, depending on what arguments are passed:</p><ul><li><code>add_cell_entries!</code> is always called</li><li><code>add_interface_entries!</code> is called if <code>topology</code> is provided (i.e. not <code>nothing</code>)</li><li><code>add_constraint_entries!</code> is called if the ConstraintHandler is provided</li></ul><p>For more details about arguments and keyword arguments, see the respective functions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L202-L221">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_cell_entries!" href="#Ferrite.add_cell_entries!"><code>Ferrite.add_cell_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_cell_entries!(
+)</code></pre><p>Convenience method for doing the common task of calling <a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>, <a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>, and <a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>, depending on what arguments are passed:</p><ul><li><code>add_cell_entries!</code> is always called</li><li><code>add_interface_entries!</code> is called if <code>topology</code> is provided (i.e. not <code>nothing</code>)</li><li><code>add_constraint_entries!</code> is called if the ConstraintHandler is provided</li></ul><p>For more details about arguments and keyword arguments, see the respective functions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L202-L221">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_cell_entries!" href="#Ferrite.add_cell_entries!"><code>Ferrite.add_cell_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_cell_entries!(
sp::AbstractSparsityPattern,
dh::DofHandler,
ch::Union{ConstraintHandler, Nothing} = nothing;
keep_constrained::Bool = true,
coupling::Union{AbstractMatrix{Bool}, Nothing}, = nothing
-)</code></pre><p>Add entries to the sparsity pattern <code>sp</code> corresponding to DoF couplings within the cells as described by the DofHandler <code>dh</code>.</p><p><strong>Keyword arguments</strong></p><ul><li><code>keep_constrained</code>: whether or not entries for constrained DoFs should be kept (<code>keep_constrained = true</code>) or eliminated (<code>keep_constrained = false</code>) from the sparsity pattern. <code>keep_constrained = false</code> requires passing the ConstraintHandler <code>ch</code>.</li><li><code>coupling</code>: the coupling between fields/components within each cell. By default (<code>coupling = nothing</code>) it is assumed that all DoFs in each cell couple with each other.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L247-L265">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_interface_entries!" href="#Ferrite.add_interface_entries!"><code>Ferrite.add_interface_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_interface_entries!(
+)</code></pre><p>Add entries to the sparsity pattern <code>sp</code> corresponding to DoF couplings within the cells as described by the DofHandler <code>dh</code>.</p><p><strong>Keyword arguments</strong></p><ul><li><code>keep_constrained</code>: whether or not entries for constrained DoFs should be kept (<code>keep_constrained = true</code>) or eliminated (<code>keep_constrained = false</code>) from the sparsity pattern. <code>keep_constrained = false</code> requires passing the ConstraintHandler <code>ch</code>.</li><li><code>coupling</code>: the coupling between fields/components within each cell. By default (<code>coupling = nothing</code>) it is assumed that all DoFs in each cell couple with each other.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L247-L265">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_interface_entries!" href="#Ferrite.add_interface_entries!"><code>Ferrite.add_interface_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_interface_entries!(
sp::SparsityPattern, dh::DofHandler, ch::Union{ConstraintHandler, Nothing};
topology::ExclusiveTopology, keep_constrained::Bool = true,
interface_coupling::AbstractMatrix{Bool},
-)</code></pre><p>Add entries to the sparsity pattern <code>sp</code> corresponding to DoF couplings on the interface between cells as described by the DofHandler <code>dh</code>.</p><p><strong>Keyword arguments</strong></p><ul><li><code>topology</code>: the topology corresponding to the grid.</li><li><code>keep_constrained</code>: whether or not entries for constrained DoFs should be kept (<code>keep_constrained = true</code>) or eliminated (<code>keep_constrained = false</code>) from the sparsity pattern. <code>keep_constrained = false</code> requires passing the ConstraintHandler <code>ch</code>.</li><li><code>interface_coupling</code>: the coupling between fields/components across the interface.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L284-L300">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_constraint_entries!" href="#Ferrite.add_constraint_entries!"><code>Ferrite.add_constraint_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_constraint_entries!(
+)</code></pre><p>Add entries to the sparsity pattern <code>sp</code> corresponding to DoF couplings on the interface between cells as described by the DofHandler <code>dh</code>.</p><p><strong>Keyword arguments</strong></p><ul><li><code>topology</code>: the topology corresponding to the grid.</li><li><code>keep_constrained</code>: whether or not entries for constrained DoFs should be kept (<code>keep_constrained = true</code>) or eliminated (<code>keep_constrained = false</code>) from the sparsity pattern. <code>keep_constrained = false</code> requires passing the ConstraintHandler <code>ch</code>.</li><li><code>interface_coupling</code>: the coupling between fields/components across the interface.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L284-L300">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_constraint_entries!" href="#Ferrite.add_constraint_entries!"><code>Ferrite.add_constraint_entries!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_constraint_entries!(
sp::AbstractSparsityPattern, ch::ConstraintHandler;
keep_constrained::Bool = true,
-)</code></pre><p>Add all entries resulting from constraints in the ConstraintHandler <code>ch</code> to the sparsity pattern. Note that, since this operation depends on existing entries in the pattern, this function must be called as the <em>last</em> step when creating the sparsity pattern.</p><p><strong>Keyword arguments</strong></p><ul><li><code>keep_constrained</code>: whether or not entries for constrained DoFs should be kept (<code>keep_constrained = true</code>) or eliminated (<code>keep_constrained = false</code>) from the sparsity pattern.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L314-L328">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_entry!" href="#Ferrite.add_entry!"><code>Ferrite.add_entry!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_entry!(sp::AbstractSparsityPattern, row::Int, col::Int)</code></pre><p>Add an entry to the sparsity pattern <code>sp</code> at row <code>row</code> and column <code>col</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L27-L31">source</a></section></article><h3 id="SparsityPattern"><a class="docs-heading-anchor" href="#SparsityPattern"><code>SparsityPattern</code></a><a id="SparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#SparsityPattern" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SparsityPattern-Tuple{Int64, Int64}" href="#Ferrite.SparsityPattern-Tuple{Int64, Int64}"><code>Ferrite.SparsityPattern</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SparsityPattern(nrows::Int, ncols::Int; nnz_per_row::Int = 8)</code></pre><p>Create an empty <a href="#SparsityPattern"><code>SparsityPattern</code></a> with <code>nrows</code> rows and <code>ncols</code> columns. <code>nnz_per_row</code> is used as a memory hint for the number of non zero entries per row.</p><p><code>SparsityPattern</code> is the default sparsity pattern type for the standard DofHandler and is therefore commonly constructed using <a href="#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern</code></a> instead of with this constructor.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs"># Create a sparsity pattern for an 100 x 100 matrix, hinting at 10 entries per row
-sparsity_pattern = SparsityPattern(100, 100; nnz_per_row = 10)</code></pre><p><strong>Methods</strong></p><p>The following methods apply to <code>SparsityPattern</code> (see their respective documentation for more details):</p><ul><li><a href="#Ferrite.add_sparsity_entries!"><code>add_sparsity_entries!</code></a>: convenience method for calling <a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>, <a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>, and <a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>.</li><li><a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>: add entries corresponding to DoF couplings within the cells.</li><li><a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>: add entries corresponding to DoF couplings on the interface between cells.</li><li><a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>: add entries resulting from constraints.</li><li><a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a>: instantiate a matrix from the pattern. The default matrix type is <code>SparseMatrixCSC{Float64, Int}</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L87-L116">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Tuple{SparsityPattern}" href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(sp::SparsityPattern)</code></pre><p>Allocate a sparse matrix of type <code>SparseMatrixCSC{Float64, Int}</code> from the sparsity pattern <code>sp</code>.</p><p>This method is a shorthand for the equivalent <a href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{S}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}"><code>allocate_matrix(SparseMatrixCSC{Float64, Int}, sp)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L368-L377">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SparsityPattern" href="#Ferrite.SparsityPattern"><code>Ferrite.SparsityPattern</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">struct SparsityPattern <: AbstractSparsityPattern</code></pre><p>Data structure representing non-zero entries in the eventual sparse matrix.</p><p>See the constructor <a href="#Ferrite.SparsityPattern-Tuple{Int64, Int64}"><code>SparsityPattern(::Int, ::Int)</code></a> for the user-facing documentation.</p><p><strong>Struct fields</strong></p><ul><li><code>nrows::Int</code>: number of rows</li><li><code>ncols::Int</code>: number of column</li><li><code>rows::Vector{Vector{Int}}</code>: vector of length <code>nrows</code>, where <code>rows[i]</code> is a <em>sorted</em> vector of column indices for non zero entries in row <code>i</code>.</li></ul><div class="admonition is-warning"><header class="admonition-header">Internal struct</header><div class="admonition-body"><p>The specific implementation of this struct, such as struct fields, type layout and type parameters, are internal and should not be relied upon.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L62-L79">source</a></section></article><h3 id="BlockSparsityPattern"><a class="docs-heading-anchor" href="#BlockSparsityPattern"><code>BlockSparsityPattern</code></a><a id="BlockSparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#BlockSparsityPattern" title="Permalink"></a></h3><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BlockSparsityPattern-Tuple{Vector{Int64}}" href="#Ferrite.BlockSparsityPattern-Tuple{Vector{Int64}}"><code>Ferrite.BlockSparsityPattern</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">BlockSparsityPattern(block_sizes::Vector{Int})</code></pre><p>Create an empty <code>BlockSparsityPattern</code> with row and column block sizes given by <code>block_sizes</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs"># Create a block sparsity pattern with block size 10 x 5
-sparsity_pattern = BlockSparsityPattern([10, 5])</code></pre><p><strong>Methods</strong></p><p>The following methods apply to <code>BlockSparsityPattern</code> (see their respective documentation for more details):</p><ul><li><a href="#Ferrite.add_sparsity_entries!"><code>add_sparsity_entries!</code></a>: convenience method for calling <a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>, <a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>, and <a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>.</li><li><a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>: add entries corresponding to DoF couplings within the cells.</li><li><a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>: add entries corresponding to DoF couplings on the interface between cells.</li><li><a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>: add entries resulting from constraints.</li><li><a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a>: instantiate a (block) matrix from the pattern. The default matrix type is <code>BlockMatrix{Float64, Matrix{SparseMatrixCSC{Float64, Int}}}</code>, i.e. a <code>BlockMatrix</code>, where the individual blocks are of type <code>SparseMatrixCSC{Float64, Int}</code>.</li></ul><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/block_sparsity_pattern.jl#L32-L64">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BlockSparsityPattern" href="#Ferrite.BlockSparsityPattern"><code>Ferrite.BlockSparsityPattern</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">struct BlockSparsityPattern <: AbstractSparsityPattern</code></pre><p>Data structure representing non-zero entries for an eventual <em>blocked</em> sparse matrix.</p><p>See the constructor <a href="#Ferrite.BlockSparsityPattern-Tuple{Vector{Int64}}"><code>BlockSparsityPattern(::Vector{Int})</code></a> for the user-facing documentation.</p><p><strong>Struct fields</strong></p><ul><li><code>nrows::Int</code>: number of rows</li><li><code>ncols::Int</code>: number of column</li><li><code>block_sizes::Vector{Int}</code>: row and column block sizes</li><li><code>blocks::Matrix{SparsityPattern}</code>: matrix of size <code>length(block_sizes) × length(block_sizes)</code> where <code>blocks[i, j]</code> is a <a href="#SparsityPattern"><code>SparsityPattern</code></a> corresponding to block <code>(i, j)</code>.</li></ul><div class="admonition is-warning"><header class="admonition-header">Internal struct</header><div class="admonition-body"><p>The specific implementation of this struct, such as struct fields, type layout and type parameters, are internal and should not be relied upon.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/block_sparsity_pattern.jl#L5-L24">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Tuple{BlockSparsityPattern}" href="#Ferrite.allocate_matrix-Tuple{BlockSparsityPattern}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{SparseMatrixCSC{Tv, Ti}}, sp::SparsityPattern)</code></pre><p>Allocate a sparse matrix of type <code>SparseMatrixCSC{Tv, Ti}</code> from the sparsity pattern <code>sp</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L348-L352">source</a></section><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}}, sp::SparsityPattern)</code></pre><p>Instantiate a sparse matrix of type <code>Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}</code>, i.e. a <code>LinearAlgebra.Symmetric</code>-wrapped <code>SparseMatrixCSC</code>, from the sparsity pattern <code>sp</code>. The resulting matrix will only store entries above, and including, the diagonal.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L357-L363">source</a></section><section><div><pre><code class="language-julia hljs">allocate_matrix(MatrixType, dh::DofHandler, args...; kwargs...)</code></pre><p>Allocate a matrix of type <code>MatrixType</code> from the DofHandler <code>dh</code>.</p><p>This is a convenience method and is equivalent to:</p><p><code>julia sp = init_sparsity_pattern(dh) add_sparsity_entries!(sp, dh, args...; kwargs...) allocate_matrix(MatrixType, sp)</code>`</p><p>Refer to <a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> for supported matrix types, and to <a href="#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern</code></a> for details about supported arguments <code>args</code> and keyword arguments <code>kwargs</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>If more than one sparse matrix is needed (e.g. a stiffness and a mass matrix) it is more efficient to explicitly create the sparsity pattern instead of using this method, i.e. use</p><pre><code class="language-julia hljs">sp = init_sparsity_pattern(dh)
+)</code></pre><p>Add all entries resulting from constraints in the ConstraintHandler <code>ch</code> to the sparsity pattern. Note that, since this operation depends on existing entries in the pattern, this function must be called as the <em>last</em> step when creating the sparsity pattern.</p><p><strong>Keyword arguments</strong></p><ul><li><code>keep_constrained</code>: whether or not entries for constrained DoFs should be kept (<code>keep_constrained = true</code>) or eliminated (<code>keep_constrained = false</code>) from the sparsity pattern.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L314-L328">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.add_entry!" href="#Ferrite.add_entry!"><code>Ferrite.add_entry!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_entry!(sp::AbstractSparsityPattern, row::Int, col::Int)</code></pre><p>Add an entry to the sparsity pattern <code>sp</code> at row <code>row</code> and column <code>col</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L27-L31">source</a></section></article><h3 id="SparsityPattern"><a class="docs-heading-anchor" href="#SparsityPattern"><code>SparsityPattern</code></a><a id="SparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#SparsityPattern" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SparsityPattern-Tuple{Int64, Int64}" href="#Ferrite.SparsityPattern-Tuple{Int64, Int64}"><code>Ferrite.SparsityPattern</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SparsityPattern(nrows::Int, ncols::Int; nnz_per_row::Int = 8)</code></pre><p>Create an empty <a href="#SparsityPattern"><code>SparsityPattern</code></a> with <code>nrows</code> rows and <code>ncols</code> columns. <code>nnz_per_row</code> is used as a memory hint for the number of non zero entries per row.</p><p><code>SparsityPattern</code> is the default sparsity pattern type for the standard DofHandler and is therefore commonly constructed using <a href="#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern</code></a> instead of with this constructor.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs"># Create a sparsity pattern for an 100 x 100 matrix, hinting at 10 entries per row
+sparsity_pattern = SparsityPattern(100, 100; nnz_per_row = 10)</code></pre><p><strong>Methods</strong></p><p>The following methods apply to <code>SparsityPattern</code> (see their respective documentation for more details):</p><ul><li><a href="#Ferrite.add_sparsity_entries!"><code>add_sparsity_entries!</code></a>: convenience method for calling <a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>, <a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>, and <a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>.</li><li><a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>: add entries corresponding to DoF couplings within the cells.</li><li><a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>: add entries corresponding to DoF couplings on the interface between cells.</li><li><a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>: add entries resulting from constraints.</li><li><a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a>: instantiate a matrix from the pattern. The default matrix type is <code>SparseMatrixCSC{Float64, Int}</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L87-L116">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Tuple{SparsityPattern}" href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(sp::SparsityPattern)</code></pre><p>Allocate a sparse matrix of type <code>SparseMatrixCSC{Float64, Int}</code> from the sparsity pattern <code>sp</code>.</p><p>This method is a shorthand for the equivalent <a href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{S}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}"><code>allocate_matrix(SparseMatrixCSC{Float64, Int}, sp)</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L368-L377">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.SparsityPattern" href="#Ferrite.SparsityPattern"><code>Ferrite.SparsityPattern</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">struct SparsityPattern <: AbstractSparsityPattern</code></pre><p>Data structure representing non-zero entries in the eventual sparse matrix.</p><p>See the constructor <a href="#Ferrite.SparsityPattern-Tuple{Int64, Int64}"><code>SparsityPattern(::Int, ::Int)</code></a> for the user-facing documentation.</p><p><strong>Struct fields</strong></p><ul><li><code>nrows::Int</code>: number of rows</li><li><code>ncols::Int</code>: number of column</li><li><code>rows::Vector{Vector{Int}}</code>: vector of length <code>nrows</code>, where <code>rows[i]</code> is a <em>sorted</em> vector of column indices for non zero entries in row <code>i</code>.</li></ul><div class="admonition is-warning"><header class="admonition-header">Internal struct</header><div class="admonition-body"><p>The specific implementation of this struct, such as struct fields, type layout and type parameters, are internal and should not be relied upon.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L62-L79">source</a></section></article><h3 id="BlockSparsityPattern"><a class="docs-heading-anchor" href="#BlockSparsityPattern"><code>BlockSparsityPattern</code></a><a id="BlockSparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#BlockSparsityPattern" title="Permalink"></a></h3><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BlockSparsityPattern-Tuple{Vector{Int64}}" href="#Ferrite.BlockSparsityPattern-Tuple{Vector{Int64}}"><code>Ferrite.BlockSparsityPattern</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">BlockSparsityPattern(block_sizes::Vector{Int})</code></pre><p>Create an empty <code>BlockSparsityPattern</code> with row and column block sizes given by <code>block_sizes</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs"># Create a block sparsity pattern with block size 10 x 5
+sparsity_pattern = BlockSparsityPattern([10, 5])</code></pre><p><strong>Methods</strong></p><p>The following methods apply to <code>BlockSparsityPattern</code> (see their respective documentation for more details):</p><ul><li><a href="#Ferrite.add_sparsity_entries!"><code>add_sparsity_entries!</code></a>: convenience method for calling <a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>, <a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>, and <a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>.</li><li><a href="#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a>: add entries corresponding to DoF couplings within the cells.</li><li><a href="#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a>: add entries corresponding to DoF couplings on the interface between cells.</li><li><a href="#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a>: add entries resulting from constraints.</li><li><a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a>: instantiate a (block) matrix from the pattern. The default matrix type is <code>BlockMatrix{Float64, Matrix{SparseMatrixCSC{Float64, Int}}}</code>, i.e. a <code>BlockMatrix</code>, where the individual blocks are of type <code>SparseMatrixCSC{Float64, Int}</code>.</li></ul><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/block_sparsity_pattern.jl#L32-L64">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.BlockSparsityPattern" href="#Ferrite.BlockSparsityPattern"><code>Ferrite.BlockSparsityPattern</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">struct BlockSparsityPattern <: AbstractSparsityPattern</code></pre><p>Data structure representing non-zero entries for an eventual <em>blocked</em> sparse matrix.</p><p>See the constructor <a href="#Ferrite.BlockSparsityPattern-Tuple{Vector{Int64}}"><code>BlockSparsityPattern(::Vector{Int})</code></a> for the user-facing documentation.</p><p><strong>Struct fields</strong></p><ul><li><code>nrows::Int</code>: number of rows</li><li><code>ncols::Int</code>: number of column</li><li><code>block_sizes::Vector{Int}</code>: row and column block sizes</li><li><code>blocks::Matrix{SparsityPattern}</code>: matrix of size <code>length(block_sizes) × length(block_sizes)</code> where <code>blocks[i, j]</code> is a <a href="#SparsityPattern"><code>SparsityPattern</code></a> corresponding to block <code>(i, j)</code>.</li></ul><div class="admonition is-warning"><header class="admonition-header">Internal struct</header><div class="admonition-body"><p>The specific implementation of this struct, such as struct fields, type layout and type parameters, are internal and should not be relied upon.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/block_sparsity_pattern.jl#L5-L24">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Tuple{BlockSparsityPattern}" href="#Ferrite.allocate_matrix-Tuple{BlockSparsityPattern}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{SparseMatrixCSC{Tv, Ti}}, sp::SparsityPattern)</code></pre><p>Allocate a sparse matrix of type <code>SparseMatrixCSC{Tv, Ti}</code> from the sparsity pattern <code>sp</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L348-L352">source</a></section><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}}, sp::SparsityPattern)</code></pre><p>Instantiate a sparse matrix of type <code>Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}</code>, i.e. a <code>LinearAlgebra.Symmetric</code>-wrapped <code>SparseMatrixCSC</code>, from the sparsity pattern <code>sp</code>. The resulting matrix will only store entries above, and including, the diagonal.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L357-L363">source</a></section><section><div><pre><code class="language-julia hljs">allocate_matrix(MatrixType, dh::DofHandler, args...; kwargs...)</code></pre><p>Allocate a matrix of type <code>MatrixType</code> from the DofHandler <code>dh</code>.</p><p>This is a convenience method and is equivalent to:</p><p><code>julia sp = init_sparsity_pattern(dh) add_sparsity_entries!(sp, dh, args...; kwargs...) allocate_matrix(MatrixType, sp)</code>`</p><p>Refer to <a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> for supported matrix types, and to <a href="#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern</code></a> for details about supported arguments <code>args</code> and keyword arguments <code>kwargs</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>If more than one sparse matrix is needed (e.g. a stiffness and a mass matrix) it is more efficient to explicitly create the sparsity pattern instead of using this method, i.e. use</p><pre><code class="language-julia hljs">sp = init_sparsity_pattern(dh)
add_sparsity_entries!(sp, dh)
K = allocate_matrix(sp)
M = allocate_matrix(sp)</code></pre><p>instead of</p><pre><code class="language-julia hljs">K = allocate_matrix(dh)
-M = allocate_matrix(dh)</code></pre><p>Note that for some matrix types it is possible to <code>copy</code> the instantiated matrix (<code>M = copy(K)</code>) instead.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L380-L414">source</a></section><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{BlockMatrix}, sp::BlockSparsityPattern)
+M = allocate_matrix(dh)</code></pre><p>Note that for some matrix types it is possible to <code>copy</code> the instantiated matrix (<code>M = copy(K)</code>) instead.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L380-L414">source</a></section><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{BlockMatrix}, sp::BlockSparsityPattern)
allocate_matrix(::Type{BlockMatrix{T, Matrix{S}}}, sp::BlockSparsityPattern)</code></pre><p>Instantiate a blocked sparse matrix from the blocked sparsity pattern <code>sp</code>.</p><p>The type of the returned matrix is a <code>BlockMatrix</code> with blocks of type <code>S</code> (defaults to <code>SparseMatrixCSC{T, Int}</code>).</p><p><strong>Examples</strong></p><pre><code class="nohighlight hljs"># Create a sparse matrix with default block type
allocate_matrix(BlockMatrix, sparsity_pattern)
# Create a sparse matrix with blocks of type SparseMatrixCSC{Float32, Int}
-allocate_matrix(BlockMatrix{Float32, Matrix{SparseMatrixCSC{Float32, Int}}}, sparsity_pattern)</code></pre><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/ext/FerriteBlockArrays.jl#L26-L48">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{T}, Tuple{Type{<:BlockArray{T, 2, Matrix{S}, BS} where BS<:Tuple{AbstractUnitRange{<:Integer}, AbstractUnitRange{<:Integer}}}, BlockSparsityPattern}} where {T, S<:AbstractMatrix{T}}" href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{T}, Tuple{Type{<:BlockArray{T, 2, Matrix{S}, BS} where BS<:Tuple{AbstractUnitRange{<:Integer}, AbstractUnitRange{<:Integer}}}, BlockSparsityPattern}} where {T, S<:AbstractMatrix{T}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{BlockMatrix}, sp::BlockSparsityPattern)
+allocate_matrix(BlockMatrix{Float32, Matrix{SparseMatrixCSC{Float32, Int}}}, sparsity_pattern)</code></pre><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/ext/FerriteBlockArrays.jl#L26-L48">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{T}, Tuple{Type{<:BlockArray{T, 2, Matrix{S}, BS} where BS<:Tuple{AbstractUnitRange{<:Integer}, AbstractUnitRange{<:Integer}}}, BlockSparsityPattern}} where {T, S<:AbstractMatrix{T}}" href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{T}, Tuple{Type{<:BlockArray{T, 2, Matrix{S}, BS} where BS<:Tuple{AbstractUnitRange{<:Integer}, AbstractUnitRange{<:Integer}}}, BlockSparsityPattern}} where {T, S<:AbstractMatrix{T}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{BlockMatrix}, sp::BlockSparsityPattern)
allocate_matrix(::Type{BlockMatrix{T, Matrix{S}}}, sp::BlockSparsityPattern)</code></pre><p>Instantiate a blocked sparse matrix from the blocked sparsity pattern <code>sp</code>.</p><p>The type of the returned matrix is a <code>BlockMatrix</code> with blocks of type <code>S</code> (defaults to <code>SparseMatrixCSC{T, Int}</code>).</p><p><strong>Examples</strong></p><pre><code class="nohighlight hljs"># Create a sparse matrix with default block type
allocate_matrix(BlockMatrix, sparsity_pattern)
# Create a sparse matrix with blocks of type SparseMatrixCSC{Float32, Int}
-allocate_matrix(BlockMatrix{Float32, Matrix{SparseMatrixCSC{Float32, Int}}}, sparsity_pattern)</code></pre><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/ext/FerriteBlockArrays.jl#L26-L48">source</a></section></article><h2 id="Sparse-matrices"><a class="docs-heading-anchor" href="#Sparse-matrices">Sparse matrices</a><a id="Sparse-matrices-1"></a><a class="docs-heading-anchor-permalink" href="#Sparse-matrices" title="Permalink"></a></h2><h3 id="Creating-matrix-from-SparsityPattern"><a class="docs-heading-anchor" href="#Creating-matrix-from-SparsityPattern">Creating matrix from <code>SparsityPattern</code></a><a id="Creating-matrix-from-SparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-matrix-from-SparsityPattern" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{S}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}" href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{S}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{SparseMatrixCSC{Tv, Ti}}, sp::SparsityPattern)</code></pre><p>Allocate a sparse matrix of type <code>SparseMatrixCSC{Tv, Ti}</code> from the sparsity pattern <code>sp</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L348-L352">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{Symmetric{Tv, S}}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}" href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{Symmetric{Tv, S}}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}}, sp::SparsityPattern)</code></pre><p>Instantiate a sparse matrix of type <code>Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}</code>, i.e. a <code>LinearAlgebra.Symmetric</code>-wrapped <code>SparseMatrixCSC</code>, from the sparsity pattern <code>sp</code>. The resulting matrix will only store entries above, and including, the diagonal.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L357-L363">source</a></section></article><h3 id="Creating-matrix-from-DofHandler"><a class="docs-heading-anchor" href="#Creating-matrix-from-DofHandler">Creating matrix from <code>DofHandler</code></a><a id="Creating-matrix-from-DofHandler-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-matrix-from-DofHandler" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{MatrixType}, Tuple{Type{MatrixType}, DofHandler, Vararg{Any}}} where MatrixType" href="#Ferrite.allocate_matrix-Union{Tuple{MatrixType}, Tuple{Type{MatrixType}, DofHandler, Vararg{Any}}} where MatrixType"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(MatrixType, dh::DofHandler, args...; kwargs...)</code></pre><p>Allocate a matrix of type <code>MatrixType</code> from the DofHandler <code>dh</code>.</p><p>This is a convenience method and is equivalent to:</p><p><code>julia sp = init_sparsity_pattern(dh) add_sparsity_entries!(sp, dh, args...; kwargs...) allocate_matrix(MatrixType, sp)</code>`</p><p>Refer to <a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> for supported matrix types, and to <a href="#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern</code></a> for details about supported arguments <code>args</code> and keyword arguments <code>kwargs</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>If more than one sparse matrix is needed (e.g. a stiffness and a mass matrix) it is more efficient to explicitly create the sparsity pattern instead of using this method, i.e. use</p><pre><code class="language-julia hljs">sp = init_sparsity_pattern(dh)
+allocate_matrix(BlockMatrix{Float32, Matrix{SparseMatrixCSC{Float32, Int}}}, sparsity_pattern)</code></pre><div class="admonition is-info"><header class="admonition-header">Package extension</header><div class="admonition-body"><p>This functionality is only enabled when the package <a href="https://github.com/JuliaArrays/BlockArrays.jl">BlockArrays.jl</a> is installed (<code>pkg> add BlockArrays</code>) and loaded (<code>using BlockArrays</code>) in the session.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/ext/FerriteBlockArrays.jl#L26-L48">source</a></section></article><h2 id="Sparse-matrices"><a class="docs-heading-anchor" href="#Sparse-matrices">Sparse matrices</a><a id="Sparse-matrices-1"></a><a class="docs-heading-anchor-permalink" href="#Sparse-matrices" title="Permalink"></a></h2><h3 id="Creating-matrix-from-SparsityPattern"><a class="docs-heading-anchor" href="#Creating-matrix-from-SparsityPattern">Creating matrix from <code>SparsityPattern</code></a><a id="Creating-matrix-from-SparsityPattern-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-matrix-from-SparsityPattern" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{S}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}" href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{S}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{SparseMatrixCSC{Tv, Ti}}, sp::SparsityPattern)</code></pre><p>Allocate a sparse matrix of type <code>SparseMatrixCSC{Tv, Ti}</code> from the sparsity pattern <code>sp</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L348-L352">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{Symmetric{Tv, S}}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}" href="#Ferrite.allocate_matrix-Union{Tuple{S}, Tuple{Ti}, Tuple{Tv}, Tuple{Type{Symmetric{Tv, S}}, Ferrite.AbstractSparsityPattern}} where {Tv, Ti, S<:SparseMatrixCSC{Tv, Ti}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(::Type{Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}}, sp::SparsityPattern)</code></pre><p>Instantiate a sparse matrix of type <code>Symmetric{Tv, SparseMatrixCSC{Tv, Ti}}</code>, i.e. a <code>LinearAlgebra.Symmetric</code>-wrapped <code>SparseMatrixCSC</code>, from the sparsity pattern <code>sp</code>. The resulting matrix will only store entries above, and including, the diagonal.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L357-L363">source</a></section></article><h3 id="Creating-matrix-from-DofHandler"><a class="docs-heading-anchor" href="#Creating-matrix-from-DofHandler">Creating matrix from <code>DofHandler</code></a><a id="Creating-matrix-from-DofHandler-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-matrix-from-DofHandler" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Union{Tuple{MatrixType}, Tuple{Type{MatrixType}, DofHandler, Vararg{Any}}} where MatrixType" href="#Ferrite.allocate_matrix-Union{Tuple{MatrixType}, Tuple{Type{MatrixType}, DofHandler, Vararg{Any}}} where MatrixType"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(MatrixType, dh::DofHandler, args...; kwargs...)</code></pre><p>Allocate a matrix of type <code>MatrixType</code> from the DofHandler <code>dh</code>.</p><p>This is a convenience method and is equivalent to:</p><p><code>julia sp = init_sparsity_pattern(dh) add_sparsity_entries!(sp, dh, args...; kwargs...) allocate_matrix(MatrixType, sp)</code>`</p><p>Refer to <a href="#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> for supported matrix types, and to <a href="#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern</code></a> for details about supported arguments <code>args</code> and keyword arguments <code>kwargs</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>If more than one sparse matrix is needed (e.g. a stiffness and a mass matrix) it is more efficient to explicitly create the sparsity pattern instead of using this method, i.e. use</p><pre><code class="language-julia hljs">sp = init_sparsity_pattern(dh)
add_sparsity_entries!(sp, dh)
K = allocate_matrix(sp)
M = allocate_matrix(sp)</code></pre><p>instead of</p><pre><code class="language-julia hljs">K = allocate_matrix(dh)
-M = allocate_matrix(dh)</code></pre><p>Note that for some matrix types it is possible to <code>copy</code> the instantiated matrix (<code>M = copy(K)</code>) instead.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L380-L414">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Tuple{DofHandler, Vararg{Any}}" href="#Ferrite.allocate_matrix-Tuple{DofHandler, Vararg{Any}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(dh::DofHandler, args...; kwargs...)</code></pre><p>Allocate a matrix of type <code>SparseMatrixCSC{Float64, Int}</code> from the DofHandler <code>dh</code>.</p><p>This method is a shorthand for the equivalent <a href="#Ferrite.allocate_matrix-Union{Tuple{MatrixType}, Tuple{Type{MatrixType}, DofHandler, Vararg{Any}}} where MatrixType"><code>allocate_matrix(SparseMatrixCSC{Float64, Int}, dh, args...; kwargs...)</code></a> – refer to that method for details.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/Dofs/sparsity_pattern.jl#L421-L429">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../dofhandler/">« Degrees of Freedom</a><a class="docs-footer-nextpage" href="../assembly/">Assembly »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+M = allocate_matrix(dh)</code></pre><p>Note that for some matrix types it is possible to <code>copy</code> the instantiated matrix (<code>M = copy(K)</code>) instead.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L380-L414">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.allocate_matrix-Tuple{DofHandler, Vararg{Any}}" href="#Ferrite.allocate_matrix-Tuple{DofHandler, Vararg{Any}}"><code>Ferrite.allocate_matrix</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">allocate_matrix(dh::DofHandler, args...; kwargs...)</code></pre><p>Allocate a matrix of type <code>SparseMatrixCSC{Float64, Int}</code> from the DofHandler <code>dh</code>.</p><p>This method is a shorthand for the equivalent <a href="#Ferrite.allocate_matrix-Union{Tuple{MatrixType}, Tuple{Type{MatrixType}, DofHandler, Vararg{Any}}} where MatrixType"><code>allocate_matrix(SparseMatrixCSC{Float64, Int}, dh, args...; kwargs...)</code></a> – refer to that method for details.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/Dofs/sparsity_pattern.jl#L421-L429">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../dofhandler/">« Degrees of Freedom</a><a class="docs-footer-nextpage" href="../assembly/">Assembly »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/reference/utils/index.html b/dev/reference/utils/index.html
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href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/utils.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Development-utility-functions"><a class="docs-heading-anchor" href="#Development-utility-functions">Development utility functions</a><a id="Development-utility-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Development-utility-functions" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.debug_mode" href="#Ferrite.debug_mode"><code>Ferrite.debug_mode</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.debug_mode(; enable=true)</code></pre><p>Helper to turn on (<code>enable=true</code>) or off (<code>enable=false</code>) debug expressions in Ferrite.</p><p>Debug mode influences <code>Ferrite.@debug expr</code>: when debug mode is enabled, <code>expr</code> is evaluated, and when debug mode is disabled <code>expr</code> is ignored.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/907c8c9ebd08c77c745ec2bc63b0993b5c761cab/src/utils.jl#L5-L12">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../export/">« Postprocessing</a><a class="docs-footer-nextpage" href="../../howto/">How-to guide overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/reference/utils.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Development-utility-functions"><a class="docs-heading-anchor" href="#Development-utility-functions">Development utility functions</a><a id="Development-utility-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Development-utility-functions" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Ferrite.debug_mode" href="#Ferrite.debug_mode"><code>Ferrite.debug_mode</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Ferrite.debug_mode(; enable=true)</code></pre><p>Helper to turn on (<code>enable=true</code>) or off (<code>enable=false</code>) debug expressions in Ferrite.</p><p>Debug mode influences <code>Ferrite.@debug expr</code>: when debug mode is enabled, <code>expr</code> is evaluated, and when debug mode is disabled <code>expr</code> is ignored.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/db375ff4af88a8f5eb73a21438d8a58325ae10a9/src/utils.jl#L5-L12">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../export/">« Postprocessing</a><a class="docs-footer-nextpage" href="../../howto/">How-to guide overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/FEValues/index.html b/dev/topics/FEValues/index.html
index a995a3b52f..290986db72 100644
--- a/dev/topics/FEValues/index.html
+++ b/dev/topics/FEValues/index.html
@@ -125,4 +125,4 @@
reinit!(cv, x);</code></pre><p>If we now pretend we are inside an element routine and have a vector of element degree of freedom values, <code>ue</code>. Then, we can check that our function values and gradients match Ferrite's builtin <code>CellValues</code>:</p><pre><code class="language-julia hljs">ue = rand(getnbasefunctions(simple_cv))
q_point = 2
@test function_value(cv, q_point, ue) ≈ function_value(simple_cv, q_point, ue)
-@test function_gradient(cv, q_point, ue) ≈ function_gradient(simple_cv, q_point, ue)</code></pre><pre><code class="nohighlight hljs">Test Passed</code></pre><h2 id="Further-reading"><a class="docs-heading-anchor" href="#Further-reading">Further reading</a><a id="Further-reading-1"></a><a class="docs-heading-anchor-permalink" href="#Further-reading" title="Permalink"></a></h2><ul><li><a href="https://defelement.com/ciarlet.html#Mapping+finite+elements">defelement.com</a></li><li>Kirby (2017) [<a href="../../cited-literature/#Kirby2017">5</a>]</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reference_shapes/">« Reference shapes</a><a class="docs-footer-nextpage" href="../degrees_of_freedom/">Degrees of Freedom »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+@test function_gradient(cv, q_point, ue) ≈ function_gradient(simple_cv, q_point, ue)</code></pre><pre><code class="nohighlight hljs">Test Passed</code></pre><h2 id="Further-reading"><a class="docs-heading-anchor" href="#Further-reading">Further reading</a><a id="Further-reading-1"></a><a class="docs-heading-anchor-permalink" href="#Further-reading" title="Permalink"></a></h2><ul><li><a href="https://defelement.com/ciarlet.html#Mapping+finite+elements">defelement.com</a></li><li>Kirby (2017) [<a href="../../cited-literature/#Kirby2017">5</a>]</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reference_shapes/">« Reference shapes</a><a class="docs-footer-nextpage" href="../degrees_of_freedom/">Degrees of Freedom »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/assembly/index.html b/dev/topics/assembly/index.html
index 2e61359fbd..c21e97e431 100644
--- a/dev/topics/assembly/index.html
+++ b/dev/topics/assembly/index.html
@@ -90,4 +90,4 @@
@time assemble_system!(assemble_v4, K, dh, cellvalues)</code></pre><p>We then obtain the following results (running on the same machine as above):</p><pre><code class="nohighlight hljs">12.175625 seconds (719.99 k allocations: 149.809 GiB, 11.59% gc time)
0.009313 seconds (8 allocations: 928 bytes)
0.006055 seconds (8 allocations: 928 bytes)
- 0.004530 seconds (10 allocations: 1.062 KiB)</code></pre><p>This follows the same trend as for the benchmarks for individual cell assembly and shows that the efficiency of the assembly strategy is crucial for the overall performance of the program. In particular this benchmark shows that allocations in such a tight loop from the first strategy is very costly and puts a strain on the garbage collector: 11% of the time is spent in GC instead of crunching numbers.</p><p>It should of course be noted that the more expensive the element routine is, the less the performance of the assembly strategy matters for the total runtime. However, there are no reason not to use the fastest method given that it is readily available in Ferrite.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sparse_matrix/">« Sparsity pattern and sparse matrices</a><a class="docs-footer-nextpage" href="../boundary_conditions/">Boundary and initial conditions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ 0.004530 seconds (10 allocations: 1.062 KiB)</code></pre><p>This follows the same trend as for the benchmarks for individual cell assembly and shows that the efficiency of the assembly strategy is crucial for the overall performance of the program. In particular this benchmark shows that allocations in such a tight loop from the first strategy is very costly and puts a strain on the garbage collector: 11% of the time is spent in GC instead of crunching numbers.</p><p>It should of course be noted that the more expensive the element routine is, the less the performance of the assembly strategy matters for the total runtime. However, there are no reason not to use the fastest method given that it is readily available in Ferrite.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sparse_matrix/">« Sparsity pattern and sparse matrices</a><a class="docs-footer-nextpage" href="../boundary_conditions/">Boundary and initial conditions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/boundary_conditions/index.html b/dev/topics/boundary_conditions/index.html
index 922a7b0b20..ce1556f4fc 100644
--- a/dev/topics/boundary_conditions/index.html
+++ b/dev/topics/boundary_conditions/index.html
@@ -78,4 +78,4 @@
grid = generate_grid(Quadrilateral, (10,10))
dh = DofHandler(grid); add!(dh, :u, 2); add!(dh, :p, 1); close!(dh)
u = zeros(ndofs(dh))
-apply_analytical!(u, dh, :p, x -> ρ * g * x[2])</code></pre><p>See also <a href="../../tutorials/transient_heat_equation/#tutorial-transient-heat-equation">Transient heat equation</a> for one example.</p><div class="admonition is-info"><header class="admonition-header">Consistency</header><div class="admonition-body"><p><code>apply_analytical!</code> does not enforce consistency of the applied solution with the system of equations. Some problems, like for example differential-algebraic systems of equations (DAEs) need extra care during initialization. We refer to the paper <a href="https://dx.doi.org/10.1137/S1064827595289996">"Consistent Initial Condition Calculation for Differential-Algebraic Systems" by Brown et al.</a> for more details on this matter.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../assembly/">« Assembly</a><a class="docs-footer-nextpage" href="../constraints/">Constraints »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+apply_analytical!(u, dh, :p, x -> ρ * g * x[2])</code></pre><p>See also <a href="../../tutorials/transient_heat_equation/#tutorial-transient-heat-equation">Transient heat equation</a> for one example.</p><div class="admonition is-info"><header class="admonition-header">Consistency</header><div class="admonition-body"><p><code>apply_analytical!</code> does not enforce consistency of the applied solution with the system of equations. Some problems, like for example differential-algebraic systems of equations (DAEs) need extra care during initialization. We refer to the paper <a href="https://dx.doi.org/10.1137/S1064827595289996">"Consistent Initial Condition Calculation for Differential-Algebraic Systems" by Brown et al.</a> for more details on this matter.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../assembly/">« Assembly</a><a class="docs-footer-nextpage" href="../constraints/">Constraints »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/constraints/index.html b/dev/topics/constraints/index.html
index 0eb883d1c7..a94c1dcb6a 100644
--- a/dev/topics/constraints/index.html
+++ b/dev/topics/constraints/index.html
@@ -21,4 +21,4 @@
apply_zero!(Δa, ch) # Change the constrained values in `Δa` such that `a-Δa`
# fulfills constraints if `a` did.
a .-= Δa
-end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../boundary_conditions/">« Boundary and initial conditions</a><a class="docs-footer-nextpage" href="../grid/">Grid »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../boundary_conditions/">« Boundary and initial conditions</a><a class="docs-footer-nextpage" href="../grid/">Grid »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/degrees_of_freedom/index.html b/dev/topics/degrees_of_freedom/index.html
index 26cf76da88..8dba399b5b 100644
--- a/dev/topics/degrees_of_freedom/index.html
+++ b/dev/topics/degrees_of_freedom/index.html
@@ -12,4 +12,4 @@
:p, Lagrange{RefTriangle, 1}()
:u, Lagrange{RefTriangle, 1}()^2
Dofs per cell: 9
- Total dofs: 1323</code></pre><h2 id="Ordering-of-Dofs"><a class="docs-heading-anchor" href="#Ordering-of-Dofs">Ordering of Dofs</a><a id="Ordering-of-Dofs-1"></a><a class="docs-heading-anchor-permalink" href="#Ordering-of-Dofs" title="Permalink"></a></h2><div class="admonition is-todo"><header class="admonition-header">Todo</header><div class="admonition-body"><p>Describe dof ordering within elements (vertices -> edges -> faces -> volumes) and <code>dof_range</code>. Describe (global) dof renumbering</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../FEValues/">« FEValues</a><a class="docs-footer-nextpage" href="../sparse_matrix/">Sparsity pattern and sparse matrices »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ Total dofs: 1323</code></pre><h2 id="Ordering-of-Dofs"><a class="docs-heading-anchor" href="#Ordering-of-Dofs">Ordering of Dofs</a><a id="Ordering-of-Dofs-1"></a><a class="docs-heading-anchor-permalink" href="#Ordering-of-Dofs" title="Permalink"></a></h2><div class="admonition is-todo"><header class="admonition-header">Todo</header><div class="admonition-body"><p>Describe dof ordering within elements (vertices -> edges -> faces -> volumes) and <code>dof_range</code>. Describe (global) dof renumbering</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../FEValues/">« FEValues</a><a class="docs-footer-nextpage" href="../sparse_matrix/">Sparsity pattern and sparse matrices »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/export/index.html b/dev/topics/export/index.html
index eb96c2ac2b..4db3bf058e 100644
--- a/dev/topics/export/index.html
+++ b/dev/topics/export/index.html
@@ -19,4 +19,4 @@
"my_results_2.vtu"
"my_results_3.vtu"
"my_results_4.vtu"
- "my_results_5.vtu"</code></pre><p>See <a href="../../tutorials/transient_heat_equation/#tutorial-transient-heat-equation">Transient heat equation</a> for an example</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../grid/">« Grid</a><a class="docs-footer-nextpage" href="../../reference/">Reference overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ "my_results_5.vtu"</code></pre><p>See <a href="../../tutorials/transient_heat_equation/#tutorial-transient-heat-equation">Transient heat equation</a> for an example</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../grid/">« Grid</a><a class="docs-footer-nextpage" href="../../reference/">Reference overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/fe_intro/index.html b/dev/topics/fe_intro/index.html
index d28e51bdb6..57392242ea 100644
--- a/dev/topics/fe_intro/index.html
+++ b/dev/topics/fe_intro/index.html
@@ -12,4 +12,4 @@
\int_{\Gamma_\mathrm{N}} \phi_i \, q^\mathrm{p} \, \mathrm{d}\Gamma + \int_{\Omega_\mathrm{h}} \phi_i \, f \, \mathrm{d}\Omega \, .\]</p><p>Finally we also need to take care of the Dirichlet boundary conditions. These are enforced by setting the corresponding <span>$\hat{u}_i$</span> to the prescribed values and eliminating the associated equations from the system. Now, solving this equation system yields the nodal values and thus an approximation to the true solution.</p><h2 id="Notes-on-the-implementation"><a class="docs-heading-anchor" href="#Notes-on-the-implementation">Notes on the implementation</a><a id="Notes-on-the-implementation-1"></a><a class="docs-heading-anchor-permalink" href="#Notes-on-the-implementation" title="Permalink"></a></h2><p>In practice, the shape functions <span>$\phi_i$</span> are only non-zero on parts of the domain <span>$\Omega_\mathrm{h}$</span>. Thus, the integrals are evaluated on sub-domains, called <em>elements</em> or <em>cells</em>.</p><p>Each cell gives a contribution to the global stiffness matrix and force vector. The process of constructing the system of equations is also called <em>assembly</em>. For clarification, let us rewrite the formula for the stiffness matrix entries as follows:</p><p class="math-container">\[(\underline{\underline{K}})_{ij}
= \int_{\Omega_\mathrm{h}} \nabla \phi_i \cdot (k \nabla \phi_j) \mathrm{d}\Omega
= \sum_{E \in \Omega_\mathrm{h}} \int_E \nabla \phi_i \cdot (k \nabla \phi_j) \mathrm{d}\Omega \, .\]</p><p>This formulation underlines the element-centric perspective of finite element methods and reflects how it is usually implemented in software.</p><p>Computing the element integrals by hand can become a tedious task. To avoid this issue we approximate the element integrals with a technique called <em>numerical integration</em>. Skipping any of the mathematical details, the basic idea is to evaluate the function under the integral at specific points and weighting the evaluations accordingly, such that their sum approximates the volume properly. A very nice feature of these techniques is, that under quite general circumstances the formula is not just an approximation, but the exact evaluation of the integral. To avoid the recomputation of the just mentioned evaluation positions of the integral for each individual element, we perform a coordinate transformation onto a so-called <em>reference element</em>. Formally we write</p><p class="math-container">\[ \int_E \nabla \phi_i \cdot (k \nabla \phi_j) \mathrm{d}\Omega
- \approx \sum_q \nabla \phi_i(\textbf{x}_q) \cdot (k(\textbf{x}_q) \nabla \phi_j(\textbf{x}_q)) \, w_q \, \textrm{det}(J(\textbf{x}_q)) \, ,\]</p><p>where <span>$J$</span> is the Jacobian of the coordinate transformation function. The computation of the transformation, weights, positions and of the Jacobi determinant is handled by Ferrite. On an intuitive level, and to explain the notation used in the implementation, we think of</p><p class="math-container">\[ \mathrm{d}\Omega \approx \, w \, \textrm{det}(J)\]</p><p>being the chosen approximation when changing from the integral to the finite summation.</p><p>For an example of the implementation to solve a heat problem with Ferrite check out <a href="../../tutorials/heat_equation/#tutorial-heat-equation">this thoroughly commented example</a>.</p><h2 id="More-details"><a class="docs-heading-anchor" href="#More-details">More details</a><a id="More-details-1"></a><a class="docs-heading-anchor-permalink" href="#More-details" title="Permalink"></a></h2><p>We finally want to note that this quick introduction barely scratches the surface of the finite element method. Also, we presented some things in a simplified way for the sake of keeping this article short and concise. There is a large corpus of literature and online tutorials containing more details about the finite element method. To give a few recommendations there is:</p><ul><li><a href="https://hplgit.github.io/INF5620/doc/pub/sphinx-fem/index.html">Hans Petter Langtangen's Script</a></li><li><a href="https://www.math.colostate.edu/~bangerth/videos.html">Wolfgang Bangerth's Lecture Series</a></li><li><em>Introduction to the Finite Element Method</em> by Niels Ottosen and Hans Petersson</li><li><em>The Finite Element Method for Elliptic Problems</em> by Philippe Ciarlet</li><li><em>Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory</em> by Dietrich Braess</li><li><em>An Analysis of the Finite Element Method</em> by Gilbert Strang and George Fix</li><li><em>Finite Element Procedures</em> by Klaus-Jürgen Bathe</li><li><em>The Finite Element Method: Its Basis and Fundamentals</em> by Olgierd Cecil Zienkiewicz, Robert Taylor and J.Z. Zhu</li><li><em>Higher-Order Finite Element Methods</em> by Pavel Šolín, Karel Segeth and Ivo Doležel</li></ul><p>This list is neither meant to be exhaustive, nor does the absence of a work mean that it is in any way bad or not recommendable. The ordering of the articles also has no particular meaning.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Topic guide overview</a><a class="docs-footer-nextpage" href="../reference_shapes/">Reference shapes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ \approx \sum_q \nabla \phi_i(\textbf{x}_q) \cdot (k(\textbf{x}_q) \nabla \phi_j(\textbf{x}_q)) \, w_q \, \textrm{det}(J(\textbf{x}_q)) \, ,\]</p><p>where <span>$J$</span> is the Jacobian of the coordinate transformation function. The computation of the transformation, weights, positions and of the Jacobi determinant is handled by Ferrite. On an intuitive level, and to explain the notation used in the implementation, we think of</p><p class="math-container">\[ \mathrm{d}\Omega \approx \, w \, \textrm{det}(J)\]</p><p>being the chosen approximation when changing from the integral to the finite summation.</p><p>For an example of the implementation to solve a heat problem with Ferrite check out <a href="../../tutorials/heat_equation/#tutorial-heat-equation">this thoroughly commented example</a>.</p><h2 id="More-details"><a class="docs-heading-anchor" href="#More-details">More details</a><a id="More-details-1"></a><a class="docs-heading-anchor-permalink" href="#More-details" title="Permalink"></a></h2><p>We finally want to note that this quick introduction barely scratches the surface of the finite element method. Also, we presented some things in a simplified way for the sake of keeping this article short and concise. There is a large corpus of literature and online tutorials containing more details about the finite element method. To give a few recommendations there is:</p><ul><li><a href="https://hplgit.github.io/INF5620/doc/pub/sphinx-fem/index.html">Hans Petter Langtangen's Script</a></li><li><a href="https://www.math.colostate.edu/~bangerth/videos.html">Wolfgang Bangerth's Lecture Series</a></li><li><em>Introduction to the Finite Element Method</em> by Niels Ottosen and Hans Petersson</li><li><em>The Finite Element Method for Elliptic Problems</em> by Philippe Ciarlet</li><li><em>Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory</em> by Dietrich Braess</li><li><em>An Analysis of the Finite Element Method</em> by Gilbert Strang and George Fix</li><li><em>Finite Element Procedures</em> by Klaus-Jürgen Bathe</li><li><em>The Finite Element Method: Its Basis and Fundamentals</em> by Olgierd Cecil Zienkiewicz, Robert Taylor and J.Z. Zhu</li><li><em>Higher-Order Finite Element Methods</em> by Pavel Šolín, Karel Segeth and Ivo Doležel</li></ul><p>This list is neither meant to be exhaustive, nor does the absence of a work mean that it is in any way bad or not recommendable. The ordering of the articles also has no particular meaning.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Topic guide overview</a><a class="docs-footer-nextpage" href="../reference_shapes/">Reference shapes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/grid/index.html b/dev/topics/grid/index.html
index 925465297b..ee09ae0133 100644
--- a/dev/topics/grid/index.html
+++ b/dev/topics/grid/index.html
@@ -19,4 +19,4 @@
Ferrite.getnnodes(grid::SmallGrid) = length(grid.nodes_test)
Ferrite.get_coordinate_eltype(::SmallGrid) = Float64
Ferrite.get_coordinate_type(::SmallGrid{dim}) where dim = Vec{dim,Float64}
-Ferrite.nnodes_per_cell(grid::SmallGrid, i::Int=1) = Ferrite.nnodes(grid.cells_test[i])</code></pre><p>These definitions make many of Ferrite functions work out of the box, e.g. you can now call <code>getcoordinates(grid, cellid)</code> on the <code>SmallGrid</code>.</p><p>Now, you would be able to assemble the heat equation example over the new custom <code>SmallGrid</code> type. Note that this particular subtype isn't able to handle boundary entity sets and so, you can't describe boundaries with it. In order to use boundaries, e.g. for Dirichlet constraints in the ConstraintHandler, you would need to dispatch the <code>AbstractGrid</code> sets utility functions on <code>SmallGrid</code>.</p><h2 id="Topology"><a class="docs-heading-anchor" href="#Topology">Topology</a><a id="Topology-1"></a><a class="docs-heading-anchor-permalink" href="#Topology" title="Permalink"></a></h2><p>Ferrite.jl's <code>Grid</code> type offers experimental features w.r.t. topology information. The functions <a href="../../reference/grid/#Ferrite.getneighborhood"><code>getneighborhood</code></a> and <a href="../../reference/grid/#Ferrite.facetskeleton"><code>facetskeleton</code></a> are the interface to obtain topological information. The <a href="../../reference/grid/#Ferrite.getneighborhood"><code>getneighborhood</code></a> can construct lists of directly connected entities based on a given entity (<code>CellIndex</code>, <code>FacetIndex</code>, <code>FaceIndex</code>, <code>EdgeIndex</code>, or <code>VertexIndex</code>). The <a href="../../reference/grid/#Ferrite.facetskeleton"><code>facetskeleton</code></a> function can be used to evaluate integrals over material interfaces or computing element interface values such as jumps.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../constraints/">« Constraints</a><a class="docs-footer-nextpage" href="../export/">Export »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+Ferrite.nnodes_per_cell(grid::SmallGrid, i::Int=1) = Ferrite.nnodes(grid.cells_test[i])</code></pre><p>These definitions make many of Ferrite functions work out of the box, e.g. you can now call <code>getcoordinates(grid, cellid)</code> on the <code>SmallGrid</code>.</p><p>Now, you would be able to assemble the heat equation example over the new custom <code>SmallGrid</code> type. Note that this particular subtype isn't able to handle boundary entity sets and so, you can't describe boundaries with it. In order to use boundaries, e.g. for Dirichlet constraints in the ConstraintHandler, you would need to dispatch the <code>AbstractGrid</code> sets utility functions on <code>SmallGrid</code>.</p><h2 id="Topology"><a class="docs-heading-anchor" href="#Topology">Topology</a><a id="Topology-1"></a><a class="docs-heading-anchor-permalink" href="#Topology" title="Permalink"></a></h2><p>Ferrite.jl's <code>Grid</code> type offers experimental features w.r.t. topology information. The functions <a href="../../reference/grid/#Ferrite.getneighborhood"><code>getneighborhood</code></a> and <a href="../../reference/grid/#Ferrite.facetskeleton"><code>facetskeleton</code></a> are the interface to obtain topological information. The <a href="../../reference/grid/#Ferrite.getneighborhood"><code>getneighborhood</code></a> can construct lists of directly connected entities based on a given entity (<code>CellIndex</code>, <code>FacetIndex</code>, <code>FaceIndex</code>, <code>EdgeIndex</code>, or <code>VertexIndex</code>). The <a href="../../reference/grid/#Ferrite.facetskeleton"><code>facetskeleton</code></a> function can be used to evaluate integrals over material interfaces or computing element interface values such as jumps.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../constraints/">« Constraints</a><a class="docs-footer-nextpage" href="../export/">Export »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/topics/index.html b/dev/topics/index.html
index 86c9d77116..f44f080e05 100644
--- a/dev/topics/index.html
+++ b/dev/topics/index.html
@@ -1,2 +1,2 @@
<!DOCTYPE html>
-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Topic guide overview · Ferrite.jl</title><meta name="title" content="Topic guide overview · Ferrite.jl"/><meta property="og:title" content="Topic guide overview · Ferrite.jl"/><meta property="twitter:title" content="Topic guide overview · Ferrite.jl"/><meta name="description" content="Documentation for Ferrite.jl."/><meta property="og:description" content="Documentation for Ferrite.jl."/><meta property="twitter:description" content="Documentation for Ferrite.jl."/><meta property="og:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/topics/"/><meta property="twitter:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/topics/"/><link rel="canonical" href="https://ferrite-fem.github.io/Ferrite.jl/stable/topics/"/><script data-outdated-warner src="../assets/warner.js"></script><link 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literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Topic guides</a></li><li class="is-active"><a href>Topic guide overview</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Topic guide overview</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/topics/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Topic-guides"><a class="docs-heading-anchor" href="#Topic-guides">Topic guides</a><a id="Topic-guides-1"></a><a class="docs-heading-anchor-permalink" href="#Topic-guides" title="Permalink"></a></h1><p>This is an overview of the <em>topic guides</em>.</p><ul><li><a href="fe_intro/#Introduction-to-FEM">Introduction to FEM</a></li><li class="no-marker"><ul><li><a href="fe_intro/#Strong-form">Strong form</a></li><li><a href="fe_intro/#Weak-form">Weak form</a></li><li><a href="fe_intro/#Finite-Element-approximation">Finite Element approximation</a></li><li><a href="fe_intro/#Notes-on-the-implementation">Notes on the implementation</a></li><li><a href="fe_intro/#More-details">More details</a></li></ul></li><li><a href="reference_shapes/#Reference-shapes">Reference shapes</a></li><li class="no-marker"><ul><li><a href="reference_shapes/#Entity-naming">Entity naming</a></li><li><a href="reference_shapes/#Entity-numbering">Entity numbering</a></li></ul></li><li><a href="FEValues/#fevalues_topicguide">FEValues</a></li><li class="no-marker"><ul><li><a href="FEValues/#mapping_theory">Mapping of finite elements</a></li><li><a href="FEValues/#SimpleCellValues">Walkthrough: Creating <code>SimpleCellValues</code></a></li><li><a href="FEValues/#Further-reading">Further reading</a></li></ul></li><li><a href="degrees_of_freedom/#Degrees-of-Freedom">Degrees of Freedom</a></li><li class="no-marker"><ul><li><a href="degrees_of_freedom/#Fields">Fields</a></li><li><a href="degrees_of_freedom/#Ordering-of-Dofs">Ordering of Dofs</a></li></ul></li><li><a href="assembly/#man-assembly">Assembly</a></li><li class="no-marker"><ul><li><a href="assembly/#Assembler"><code>Assembler</code></a></li><li><a href="assembly/#Pseudo-code-for-efficient-assembly">Pseudo-code for efficient assembly</a></li><li><a href="assembly/#Comparison-of-assembly-strategies">Comparison of assembly strategies</a></li></ul></li><li><a href="boundary_conditions/#Boundary-and-initial-conditions">Boundary and initial conditions</a></li><li class="no-marker"><ul><li><a href="boundary_conditions/#Dirichlet-boundary-conditions">Dirichlet boundary conditions</a></li><li><a href="boundary_conditions/#Neumann-boundary-conditions">Neumann boundary conditions</a></li><li><a href="boundary_conditions/#Periodic-boundary-conditions">Periodic boundary conditions</a></li><li><a href="boundary_conditions/#Initial-conditions">Initial conditions</a></li></ul></li><li><a href="constraints/#Constraints">Constraints</a></li><li class="no-marker"><ul><li><a href="constraints/#Affine-constraints">Affine constraints</a></li></ul></li><li><a href="grid/#Grid">Grid</a></li><li class="no-marker"><ul><li><a href="grid/#Mesh-reading">Mesh reading</a></li><li><a href="grid/#Grid-datastructure"><code>Grid</code> datastructure</a></li><li><a href="grid/#AbstractGrid">AbstractGrid</a></li><li><a href="grid/#Topology">Topology</a></li></ul></li><li><a href="export/#Export">Export</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorials/dg_heat_equation/">« Discontinuous Galerkin heat equation</a><a class="docs-footer-nextpage" href="fe_intro/">Introduction to FEM »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 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Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Topic guide overview · Ferrite.jl</title><meta name="title" content="Topic guide overview · Ferrite.jl"/><meta property="og:title" content="Topic guide overview · Ferrite.jl"/><meta property="twitter:title" content="Topic guide overview · Ferrite.jl"/><meta name="description" content="Documentation for Ferrite.jl."/><meta property="og:description" content="Documentation for Ferrite.jl."/><meta property="twitter:description" content="Documentation for Ferrite.jl."/><meta property="og:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/topics/"/><meta property="twitter:url" content="https://ferrite-fem.github.io/Ferrite.jl/stable/topics/"/><link rel="canonical" href="https://ferrite-fem.github.io/Ferrite.jl/stable/topics/"/><script data-outdated-warner src="../assets/warner.js"></script><link 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href="../assets/custom.css" rel="stylesheet" type="text/css"/><link href="../assets/citations.css" rel="stylesheet" type="text/css"/><link href="../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.svg" alt="Ferrite.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">Ferrite.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><input class="collapse-toggle" id="menuitem-3" type="checkbox"/><label class="tocitem" for="menuitem-3"><span class="docs-label">Tutorials</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../tutorials/">Tutorials overview</a></li><li><a class="tocitem" 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surface</a></li><li><a class="tocitem" href="../tutorials/linear_shell/">Linear shell</a></li><li><a class="tocitem" href="../tutorials/dg_heat_equation/">Discontinuous Galerkin heat equation</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-4" type="checkbox" checked/><label class="tocitem" for="menuitem-4"><span class="docs-label">Topic guides</span><i class="docs-chevron"></i></label><ul class="collapsed"><li class="is-active"><a class="tocitem" href>Topic guide overview</a></li><li><a class="tocitem" href="fe_intro/">Introduction to FEM</a></li><li><a class="tocitem" href="reference_shapes/">Reference shapes</a></li><li><a class="tocitem" href="FEValues/">FEValues</a></li><li><a class="tocitem" href="degrees_of_freedom/">Degrees of Freedom</a></li><li><a class="tocitem" href="sparse_matrix/">Sparsity pattern and sparse matrices</a></li><li><a class="tocitem" href="assembly/">Assembly</a></li><li><a class="tocitem" href="boundary_conditions/">Boundary and initial conditions</a></li><li><a class="tocitem" href="constraints/">Constraints</a></li><li><a class="tocitem" href="grid/">Grid</a></li><li><a class="tocitem" href="export/">Export</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-5" type="checkbox"/><label class="tocitem" for="menuitem-5"><span class="docs-label">API reference</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../reference/">Reference overview</a></li><li><a class="tocitem" href="../reference/quadrature/">Quadrature</a></li><li><a class="tocitem" href="../reference/interpolations/">Interpolation</a></li><li><a class="tocitem" href="../reference/fevalues/">FEValues</a></li><li><a class="tocitem" href="../reference/dofhandler/">Degrees of Freedom</a></li><li><a class="tocitem" href="../reference/sparsity_pattern/">Sparsity pattern and sparse matrices</a></li><li><a class="tocitem" href="../reference/assembly/">Assembly</a></li><li><a class="tocitem" href="../reference/boundary_conditions/">Boundary conditions</a></li><li><a class="tocitem" href="../reference/grid/">Grid & AbstractGrid</a></li><li><a class="tocitem" href="../reference/export/">Postprocessing</a></li><li><a class="tocitem" href="../reference/utils/">Development utility functions</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-6" type="checkbox"/><label class="tocitem" for="menuitem-6"><span class="docs-label">How-to guides</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../howto/">How-to guide overview</a></li><li><a class="tocitem" href="../howto/postprocessing/">Post processing and visualization</a></li><li><a class="tocitem" href="../howto/threaded_assembly/">Multi-threaded assembly</a></li></ul></li><br><li><a class="tocitem" href="../gallery/">Code gallery</a></li><li><a class="tocitem" href="../devdocs/">Developer documentation</a></li><li><a class="tocitem" href="../cited-literature/">Cited literature</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Topic guides</a></li><li class="is-active"><a href>Topic guide overview</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Topic guide overview</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/topics/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Topic-guides"><a class="docs-heading-anchor" href="#Topic-guides">Topic guides</a><a id="Topic-guides-1"></a><a class="docs-heading-anchor-permalink" href="#Topic-guides" title="Permalink"></a></h1><p>This is an overview of the <em>topic guides</em>.</p><ul><li><a href="fe_intro/#Introduction-to-FEM">Introduction to FEM</a></li><li class="no-marker"><ul><li><a href="fe_intro/#Strong-form">Strong form</a></li><li><a href="fe_intro/#Weak-form">Weak form</a></li><li><a href="fe_intro/#Finite-Element-approximation">Finite Element approximation</a></li><li><a href="fe_intro/#Notes-on-the-implementation">Notes on the implementation</a></li><li><a href="fe_intro/#More-details">More details</a></li></ul></li><li><a href="reference_shapes/#Reference-shapes">Reference shapes</a></li><li class="no-marker"><ul><li><a href="reference_shapes/#Entity-naming">Entity naming</a></li><li><a href="reference_shapes/#Entity-numbering">Entity numbering</a></li></ul></li><li><a href="FEValues/#fevalues_topicguide">FEValues</a></li><li class="no-marker"><ul><li><a href="FEValues/#mapping_theory">Mapping of finite elements</a></li><li><a href="FEValues/#SimpleCellValues">Walkthrough: Creating <code>SimpleCellValues</code></a></li><li><a href="FEValues/#Further-reading">Further reading</a></li></ul></li><li><a href="degrees_of_freedom/#Degrees-of-Freedom">Degrees of Freedom</a></li><li class="no-marker"><ul><li><a href="degrees_of_freedom/#Fields">Fields</a></li><li><a href="degrees_of_freedom/#Ordering-of-Dofs">Ordering of Dofs</a></li></ul></li><li><a href="assembly/#man-assembly">Assembly</a></li><li class="no-marker"><ul><li><a href="assembly/#Assembler"><code>Assembler</code></a></li><li><a href="assembly/#Pseudo-code-for-efficient-assembly">Pseudo-code for efficient assembly</a></li><li><a href="assembly/#Comparison-of-assembly-strategies">Comparison of assembly strategies</a></li></ul></li><li><a href="boundary_conditions/#Boundary-and-initial-conditions">Boundary and initial conditions</a></li><li class="no-marker"><ul><li><a href="boundary_conditions/#Dirichlet-boundary-conditions">Dirichlet boundary conditions</a></li><li><a href="boundary_conditions/#Neumann-boundary-conditions">Neumann boundary conditions</a></li><li><a href="boundary_conditions/#Periodic-boundary-conditions">Periodic boundary conditions</a></li><li><a href="boundary_conditions/#Initial-conditions">Initial conditions</a></li></ul></li><li><a href="constraints/#Constraints">Constraints</a></li><li class="no-marker"><ul><li><a href="constraints/#Affine-constraints">Affine constraints</a></li></ul></li><li><a href="grid/#Grid">Grid</a></li><li class="no-marker"><ul><li><a href="grid/#Mesh-reading">Mesh reading</a></li><li><a href="grid/#Grid-datastructure"><code>Grid</code> datastructure</a></li><li><a href="grid/#AbstractGrid">AbstractGrid</a></li><li><a href="grid/#Topology">Topology</a></li></ul></li><li><a href="export/#Export">Export</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorials/dg_heat_equation/">« Discontinuous Galerkin heat equation</a><a class="docs-footer-nextpage" href="fe_intro/">Introduction to FEM »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming 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Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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guides</a></li><li class="is-active"><a href>Reference shapes</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Reference shapes</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/topics/reference_shapes.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Reference-shapes"><a class="docs-heading-anchor" href="#Reference-shapes">Reference shapes</a><a id="Reference-shapes-1"></a><a class="docs-heading-anchor-permalink" href="#Reference-shapes" title="Permalink"></a></h1><p>The reference shapes in Ferrite are used to define grid cells, function interpolations (i.e. shape functions), and quadrature rules. Currently, the following reference shapes are defined</p><ul><li><code>RefLine</code></li><li><code>RefTriangle</code></li><li><code>RefQuadrilateral</code></li><li><code>RefTetrahedron</code></li><li><code>RefHexahedron</code></li><li><code>RefPrism</code></li><li><code>RefPyramid</code></li></ul><h2 id="Entity-naming"><a class="docs-heading-anchor" href="#Entity-naming">Entity naming</a><a id="Entity-naming-1"></a><a class="docs-heading-anchor-permalink" href="#Entity-naming" title="Permalink"></a></h2><p>Ferrite denotes the entities of a reference shape as follows</p><table><tr><th style="text-align: left">Entity</th><th style="text-align: left">Description</th></tr><tr><td style="text-align: left">Vertex</td><td style="text-align: left">0-dimensional entity in the reference shape.</td></tr><tr><td style="text-align: left">Edge</td><td style="text-align: left">1-dimensional entity connecting two vertices.</td></tr><tr><td style="text-align: left">Face</td><td style="text-align: left">2-dimensional entity enclosed by edges.</td></tr><tr><td style="text-align: left">Volume</td><td style="text-align: left">3-dimensional entity enclosed by faces.</td></tr></table><p>Note that a node in Ferrite is not the same as a vertex. Vertices denote endpoints of edges, while nodes may also be located in the middle of edges (e.g. for a <code>QuadraticLine</code> cell).</p><p>To write dimensionally independent code, Ferrite also denotes entities by their <a href="https://en.wikipedia.org/wiki/Codimension"><em>codimension</em></a>, defined relative the reference shape dimension. Specifically, Ferrite has the entities</p><table><tr><th style="text-align: left">Entity</th><th style="text-align: left">Description</th></tr><tr><td style="text-align: left"><code>Cell</code></td><td style="text-align: left"><em>0-codimensional</em> entity, i.e. the same as the reference shape.</td></tr><tr><td style="text-align: left"><code>Facet</code></td><td style="text-align: left"><em>1-codimensional</em> entity defining the boundary of cells.</td></tr></table><p>Standard use cases mostly deal with these codimensional entities, such as <a href="../../reference/fevalues/#Ferrite.CellValues"><code>CellValues</code></a> and <a href="../../reference/fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a>.</p><div class="admonition is-info"><header class="admonition-header">Definition of codimension</header><div class="admonition-body"><p>In Ferrite, <em>codimension</em> is defined relative to the reference dimension of the specific entity. Note that other finite element codes may define it differently (e.g. relative the highest reference dimension in the grid).</p></div></div><h2 id="Entity-numbering"><a class="docs-heading-anchor" href="#Entity-numbering">Entity numbering</a><a id="Entity-numbering-1"></a><a class="docs-heading-anchor-permalink" href="#Entity-numbering" title="Permalink"></a></h2><p>Each reference shape defines the numbering of its vertices, edges, and faces entities, where the edge and face entities are defined from their vertex numbers.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The numbering and identification of entities is (mostly) for internal use and typically not something users of Ferrite need to interact with.</p></div></div><h3 id="Example"><a class="docs-heading-anchor" href="#Example">Example</a><a id="Example-1"></a><a class="docs-heading-anchor-permalink" href="#Example" title="Permalink"></a></h3><p>The <code>RefQuadrilateral</code> is defined on the domain <span>$[-1, 1] \times [-1, 1]$</span> in the local <span>$\xi_1-\xi_2$</span> coordinate system.</p><p><img src="../assets/local_element.svg" alt="local element"/></p><p>The vertices of a <code>RefQuadrilateral</code> are then</p><pre><code class="language-julia hljs">Ferrite.reference_vertices(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(1, 2, 3, 4)</code></pre><p>and its edges are then defined as</p><pre><code class="language-julia hljs">Ferrite.reference_edges(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">((1, 2), (2, 3), (3, 4), (4, 1))</code></pre><p>where the numbers refer to the vertex number. Finally, this reference shape is 2-dimensional, so it only has a single face, corresponding to the cell itself,</p><pre><code class="language-julia hljs">Ferrite.reference_faces(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">((1, 2, 3, 4),)</code></pre><p>also defined in terms of its vertices.</p><p>As this is a 2-dimensional reference shape, the facets are the edges, i.e.</p><pre><code class="language-julia hljs">Ferrite.reference_facets(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">((1, 2), (2, 3), (3, 4), (4, 1))</code></pre><div class="admonition is-info"><header class="admonition-header">Not public API</header><div class="admonition-body"><p>The functions <code>reference_vertices</code>, <code>reference_edges</code>, <code>reference_faces</code>, and <code>reference_facets</code> are not public and only shown here to explain the numbering concept. The specific ordering may also change, and is therefore only documented in the <a href="../../devdocs/#Developer-documentation">Developer documentation</a>.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fe_intro/">« Introduction to FEM</a><a class="docs-footer-nextpage" href="../FEValues/">FEValues »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. 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guides</a></li><li class="is-active"><a href>Reference shapes</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Reference shapes</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/topics/reference_shapes.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Reference-shapes"><a class="docs-heading-anchor" href="#Reference-shapes">Reference shapes</a><a id="Reference-shapes-1"></a><a class="docs-heading-anchor-permalink" href="#Reference-shapes" title="Permalink"></a></h1><p>The reference shapes in Ferrite are used to define grid cells, function interpolations (i.e. shape functions), and quadrature rules. Currently, the following reference shapes are defined</p><ul><li><code>RefLine</code></li><li><code>RefTriangle</code></li><li><code>RefQuadrilateral</code></li><li><code>RefTetrahedron</code></li><li><code>RefHexahedron</code></li><li><code>RefPrism</code></li><li><code>RefPyramid</code></li></ul><h2 id="Entity-naming"><a class="docs-heading-anchor" href="#Entity-naming">Entity naming</a><a id="Entity-naming-1"></a><a class="docs-heading-anchor-permalink" href="#Entity-naming" title="Permalink"></a></h2><p>Ferrite denotes the entities of a reference shape as follows</p><table><tr><th style="text-align: left">Entity</th><th style="text-align: left">Description</th></tr><tr><td style="text-align: left">Vertex</td><td style="text-align: left">0-dimensional entity in the reference shape.</td></tr><tr><td style="text-align: left">Edge</td><td style="text-align: left">1-dimensional entity connecting two vertices.</td></tr><tr><td style="text-align: left">Face</td><td style="text-align: left">2-dimensional entity enclosed by edges.</td></tr><tr><td style="text-align: left">Volume</td><td style="text-align: left">3-dimensional entity enclosed by faces.</td></tr></table><p>Note that a node in Ferrite is not the same as a vertex. Vertices denote endpoints of edges, while nodes may also be located in the middle of edges (e.g. for a <code>QuadraticLine</code> cell).</p><p>To write dimensionally independent code, Ferrite also denotes entities by their <a href="https://en.wikipedia.org/wiki/Codimension"><em>codimension</em></a>, defined relative the reference shape dimension. Specifically, Ferrite has the entities</p><table><tr><th style="text-align: left">Entity</th><th style="text-align: left">Description</th></tr><tr><td style="text-align: left"><code>Cell</code></td><td style="text-align: left"><em>0-codimensional</em> entity, i.e. the same as the reference shape.</td></tr><tr><td style="text-align: left"><code>Facet</code></td><td style="text-align: left"><em>1-codimensional</em> entity defining the boundary of cells.</td></tr></table><p>Standard use cases mostly deal with these codimensional entities, such as <a href="../../reference/fevalues/#Ferrite.CellValues"><code>CellValues</code></a> and <a href="../../reference/fevalues/#Ferrite.FacetValues"><code>FacetValues</code></a>.</p><div class="admonition is-info"><header class="admonition-header">Definition of codimension</header><div class="admonition-body"><p>In Ferrite, <em>codimension</em> is defined relative to the reference dimension of the specific entity. Note that other finite element codes may define it differently (e.g. relative the highest reference dimension in the grid).</p></div></div><h2 id="Entity-numbering"><a class="docs-heading-anchor" href="#Entity-numbering">Entity numbering</a><a id="Entity-numbering-1"></a><a class="docs-heading-anchor-permalink" href="#Entity-numbering" title="Permalink"></a></h2><p>Each reference shape defines the numbering of its vertices, edges, and faces entities, where the edge and face entities are defined from their vertex numbers.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The numbering and identification of entities is (mostly) for internal use and typically not something users of Ferrite need to interact with.</p></div></div><h3 id="Example"><a class="docs-heading-anchor" href="#Example">Example</a><a id="Example-1"></a><a class="docs-heading-anchor-permalink" href="#Example" title="Permalink"></a></h3><p>The <code>RefQuadrilateral</code> is defined on the domain <span>$[-1, 1] \times [-1, 1]$</span> in the local <span>$\xi_1-\xi_2$</span> coordinate system.</p><p><img src="../assets/local_element.svg" alt="local element"/></p><p>The vertices of a <code>RefQuadrilateral</code> are then</p><pre><code class="language-julia hljs">Ferrite.reference_vertices(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(1, 2, 3, 4)</code></pre><p>and its edges are then defined as</p><pre><code class="language-julia hljs">Ferrite.reference_edges(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">((1, 2), (2, 3), (3, 4), (4, 1))</code></pre><p>where the numbers refer to the vertex number. Finally, this reference shape is 2-dimensional, so it only has a single face, corresponding to the cell itself,</p><pre><code class="language-julia hljs">Ferrite.reference_faces(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">((1, 2, 3, 4),)</code></pre><p>also defined in terms of its vertices.</p><p>As this is a 2-dimensional reference shape, the facets are the edges, i.e.</p><pre><code class="language-julia hljs">Ferrite.reference_facets(RefQuadrilateral)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">((1, 2), (2, 3), (3, 4), (4, 1))</code></pre><div class="admonition is-info"><header class="admonition-header">Not public API</header><div class="admonition-body"><p>The functions <code>reference_vertices</code>, <code>reference_edges</code>, <code>reference_faces</code>, and <code>reference_facets</code> are not public and only shown here to explain the numbering concept. The specific ordering may also change, and is therefore only documented in the <a href="../../devdocs/#Developer-documentation">Developer documentation</a>.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fe_intro/">« Introduction to FEM</a><a class="docs-footer-nextpage" href="../FEValues/">FEValues »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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0.0 0.0 ⋅ ⋅
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- ⋅ ⋅ 0.0 0.0</code></pre><p>Moreover, if the problem is solved with periodic boundary conditions, for example by constraining the value on the right side to the value on the left side, there will be additional couplings. In the example above, this means that DoF 4 should be equal to DoF</p><ol><li>Since DoF 4 is constrained it has to be eliminated from the system. Existing entries</li></ol><p>that include DoF 4 are <code>(3, 4)</code>, <code>(4, 3)</code>, and <code>(4, 4)</code>. Given the simple constraint in this case we can simply replace DoF 4 with DoF 1 in these entries and we end up with entries <code>(3, 1)</code>, <code>(1, 3)</code>, and <code>(1, 1)</code>. This results in two new entries: <code>(3, 1)</code> and <code>(1, 3)</code> (entry <code>(1, 1)</code> is already included).</p></div></details><h2 id="Creating-sparsity-patterns"><a class="docs-heading-anchor" href="#Creating-sparsity-patterns">Creating sparsity patterns</a><a id="Creating-sparsity-patterns-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-sparsity-patterns" title="Permalink"></a></h2><p>Creating a sparsity pattern can be quite expensive if not done properly and therefore Ferrite provides efficient methods and data structures for this. In general the sparsity pattern is not known in advance and has to be created incrementally. To make this incremental construction efficient it is necessary to use a dynamic data structure which allow for fast insertions.</p><p>The sparsity pattern also serves as a "matrix builder". When all entries are inserted into the sparsity pattern the dynamic data structure is typically converted, or "compressed", into a sparse matrix format such as e.g. the <a href="https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_row_(CSR,_CRS_or_Yale_format)"><em>compressed sparse row (CSR)</em></a> format or the <a href="https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_column_(CSC_or_CCS)"><em>compressed sparse column (CSC)</em></a> format, where the latter is the default sparse matrix type implemented in the <a href="https://github.com/JuliaSparse/SparseArrays.jl">SparseArrays standard library</a>. These matrix formats allow for fast linear algebra operations, such as factorizations and matrix-vector multiplications, that are needed when the linear system is solved. See <a href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a> for more details.</p><p>In summary, a dynamic structure is more efficient when incrementally building the pattern by inserting new entries, and a static or compressed structure is more efficient for linear algebra operations.</p><h3 id="Basic-sparsity-patterns-construction"><a class="docs-heading-anchor" href="#Basic-sparsity-patterns-construction">Basic sparsity patterns construction</a><a id="Basic-sparsity-patterns-construction-1"></a><a class="docs-heading-anchor-permalink" href="#Basic-sparsity-patterns-construction" title="Permalink"></a></h3><p>Working with the sparsity pattern explicitly is in many cases not necessary. For basic usage (e.g. when only one matrix needed, when no customization of the pattern is required, etc) there exist convenience methods of <a href="../../reference/sparsity_pattern/#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> that return the matrix directly. Most examples in this documentation don't deal with the sparsity pattern explicitly because the basic method suffice. See also <a href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a> for more details.</p><h3 id="Custom-sparsity-pattern-construction"><a class="docs-heading-anchor" href="#Custom-sparsity-pattern-construction">Custom sparsity pattern construction</a><a id="Custom-sparsity-pattern-construction-1"></a><a class="docs-heading-anchor-permalink" href="#Custom-sparsity-pattern-construction" title="Permalink"></a></h3><p>In more advanced cases there might be a need for more fine grained control of the sparsity pattern. The following steps are typically taken when constructing a sparsity pattern in Ferrite:</p><ol><li><p><strong>Initialize an empty pattern:</strong> This can be done by either using the <a href="../../reference/sparsity_pattern/#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern(dh)</code></a> function or by using a constructor directly. <code>init_sparsity_pattern</code> will return a default pattern type that is compatible with the DofHandler. In some cases you might require another type of pattern (for example a blocked pattern, see <a href="#Blocked-sparsity-pattern">Blocked sparsity pattern</a>) and in that case you can use the constructor directly.</p></li><li><p><strong>Add entries to the pattern:</strong> There are a number of functions that add entries to the pattern:</p><ul><li><a href="../../reference/sparsity_pattern/#Ferrite.add_sparsity_entries!"><code>add_sparsity_entries!</code></a> is a convenience method for performing the common task of calling <code>add_cell_entries!</code>, <code>add_interface_entries!</code>, and <code>add_constraint_entries!</code> after each other (see below).</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a> adds entries for all couplings between the DoFs within each element. These entries correspond to assembling the standard element matrix and is thus almost always required.</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a> adds entries for couplings between the DoFs in neighboring elements. These entries are required when integrating along internal interfaces between elements (e.g. for discontinuous Galerkin methods).</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a> adds entries required from constraints and boundary conditions in the ConstraintHandler. Note that this operation depends on existing entries in the pattern and <em>must</em> be called as the last operation on the pattern.</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_entry!"><code>Ferrite.add_entry!</code></a> adds a single entry to the pattern. This can be used if you need to add custom entries that are not covered by the other functions.</li></ul></li><li><p><strong>Instantiate the matrix:</strong> A sparse matrix can be created from the sparsity pattern using <a href="../../reference/sparsity_pattern/#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a>, see <a href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a> below for more details.</p></li></ol><h3 id="Increasing-the-sparsity"><a class="docs-heading-anchor" href="#Increasing-the-sparsity">Increasing the sparsity</a><a id="Increasing-the-sparsity-1"></a><a class="docs-heading-anchor-permalink" href="#Increasing-the-sparsity" title="Permalink"></a></h3><p>By default, when creating a sparsity pattern, it is assumed that each DoF within an element couple with with <em>all</em> other DoFs in the element.</p><div class="admonition is-todo"><header class="admonition-header">Todo</header><div class="admonition-body"><ul><li>Discuss the <code>coupling</code> keyword argument.</li><li>Discuss the <code>keep_constrained</code> keyword argument.</li></ul></div></div><h3 id="Blocked-sparsity-pattern"><a class="docs-heading-anchor" href="#Blocked-sparsity-pattern">Blocked sparsity pattern</a><a id="Blocked-sparsity-pattern-1"></a><a class="docs-heading-anchor-permalink" href="#Blocked-sparsity-pattern" title="Permalink"></a></h3><div class="admonition is-todo"><header class="admonition-header">Todo</header><div class="admonition-body"><p>Discuss <code>BlockSparsityPattern</code> and <code>BlockArrays</code> extension.</p></div></div><h2 id="Instantiating-the-sparse-matrix"><a class="docs-heading-anchor" href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a><a id="Instantiating-the-sparse-matrix-1"></a><a class="docs-heading-anchor-permalink" href="#Instantiating-the-sparse-matrix" title="Permalink"></a></h2><p>As mentioned above, for many simple cases there is no need to work with the sparsity pattern directly and using methods of <a href="../../reference/sparsity_pattern/#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> that take the DofHandler as input is enough, for example:</p><pre><code class="language-julia hljs">K = allocate_matrix(dh, ch)</code></pre><p><code>allocate_matrix</code> is also used to instantiate a matrix from a sparsity pattern, for example:</p><pre><code class="language-julia hljs">K = allocate_matrix(sp)</code></pre><div class="admonition is-info"><header class="admonition-header">Multiple matrices with the same pattern</header><div class="admonition-body"><p>For some problems there is a need for multiple matrices with the same sparsity pattern, for example a mass matrix and a stiffness matrix. In this case it is more efficient to create the sparsity pattern once and then instantiate both matrices from it.</p></div></div><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Structurally nonzero means that there is a possibility of a nonzero value even though the computed value might become zero in the end for various reasons.</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>At least for most practical problems using low order interpolations.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../degrees_of_freedom/">« Degrees of Freedom</a><a class="docs-footer-nextpage" href="../assembly/">Assembly »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ ⋅ ⋅ 0.0 0.0</code></pre><p>Moreover, if the problem is solved with periodic boundary conditions, for example by constraining the value on the right side to the value on the left side, there will be additional couplings. In the example above, this means that DoF 4 should be equal to DoF</p><ol><li>Since DoF 4 is constrained it has to be eliminated from the system. Existing entries</li></ol><p>that include DoF 4 are <code>(3, 4)</code>, <code>(4, 3)</code>, and <code>(4, 4)</code>. Given the simple constraint in this case we can simply replace DoF 4 with DoF 1 in these entries and we end up with entries <code>(3, 1)</code>, <code>(1, 3)</code>, and <code>(1, 1)</code>. This results in two new entries: <code>(3, 1)</code> and <code>(1, 3)</code> (entry <code>(1, 1)</code> is already included).</p></div></details><h2 id="Creating-sparsity-patterns"><a class="docs-heading-anchor" href="#Creating-sparsity-patterns">Creating sparsity patterns</a><a id="Creating-sparsity-patterns-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-sparsity-patterns" title="Permalink"></a></h2><p>Creating a sparsity pattern can be quite expensive if not done properly and therefore Ferrite provides efficient methods and data structures for this. In general the sparsity pattern is not known in advance and has to be created incrementally. To make this incremental construction efficient it is necessary to use a dynamic data structure which allow for fast insertions.</p><p>The sparsity pattern also serves as a "matrix builder". When all entries are inserted into the sparsity pattern the dynamic data structure is typically converted, or "compressed", into a sparse matrix format such as e.g. the <a href="https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_row_(CSR,_CRS_or_Yale_format)"><em>compressed sparse row (CSR)</em></a> format or the <a href="https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_column_(CSC_or_CCS)"><em>compressed sparse column (CSC)</em></a> format, where the latter is the default sparse matrix type implemented in the <a href="https://github.com/JuliaSparse/SparseArrays.jl">SparseArrays standard library</a>. These matrix formats allow for fast linear algebra operations, such as factorizations and matrix-vector multiplications, that are needed when the linear system is solved. See <a href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a> for more details.</p><p>In summary, a dynamic structure is more efficient when incrementally building the pattern by inserting new entries, and a static or compressed structure is more efficient for linear algebra operations.</p><h3 id="Basic-sparsity-patterns-construction"><a class="docs-heading-anchor" href="#Basic-sparsity-patterns-construction">Basic sparsity patterns construction</a><a id="Basic-sparsity-patterns-construction-1"></a><a class="docs-heading-anchor-permalink" href="#Basic-sparsity-patterns-construction" title="Permalink"></a></h3><p>Working with the sparsity pattern explicitly is in many cases not necessary. For basic usage (e.g. when only one matrix needed, when no customization of the pattern is required, etc) there exist convenience methods of <a href="../../reference/sparsity_pattern/#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> that return the matrix directly. Most examples in this documentation don't deal with the sparsity pattern explicitly because the basic method suffice. See also <a href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a> for more details.</p><h3 id="Custom-sparsity-pattern-construction"><a class="docs-heading-anchor" href="#Custom-sparsity-pattern-construction">Custom sparsity pattern construction</a><a id="Custom-sparsity-pattern-construction-1"></a><a class="docs-heading-anchor-permalink" href="#Custom-sparsity-pattern-construction" title="Permalink"></a></h3><p>In more advanced cases there might be a need for more fine grained control of the sparsity pattern. The following steps are typically taken when constructing a sparsity pattern in Ferrite:</p><ol><li><p><strong>Initialize an empty pattern:</strong> This can be done by either using the <a href="../../reference/sparsity_pattern/#Ferrite.init_sparsity_pattern"><code>init_sparsity_pattern(dh)</code></a> function or by using a constructor directly. <code>init_sparsity_pattern</code> will return a default pattern type that is compatible with the DofHandler. In some cases you might require another type of pattern (for example a blocked pattern, see <a href="#Blocked-sparsity-pattern">Blocked sparsity pattern</a>) and in that case you can use the constructor directly.</p></li><li><p><strong>Add entries to the pattern:</strong> There are a number of functions that add entries to the pattern:</p><ul><li><a href="../../reference/sparsity_pattern/#Ferrite.add_sparsity_entries!"><code>add_sparsity_entries!</code></a> is a convenience method for performing the common task of calling <code>add_cell_entries!</code>, <code>add_interface_entries!</code>, and <code>add_constraint_entries!</code> after each other (see below).</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_cell_entries!"><code>add_cell_entries!</code></a> adds entries for all couplings between the DoFs within each element. These entries correspond to assembling the standard element matrix and is thus almost always required.</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_interface_entries!"><code>add_interface_entries!</code></a> adds entries for couplings between the DoFs in neighboring elements. These entries are required when integrating along internal interfaces between elements (e.g. for discontinuous Galerkin methods).</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_constraint_entries!"><code>add_constraint_entries!</code></a> adds entries required from constraints and boundary conditions in the ConstraintHandler. Note that this operation depends on existing entries in the pattern and <em>must</em> be called as the last operation on the pattern.</li><li><a href="../../reference/sparsity_pattern/#Ferrite.add_entry!"><code>Ferrite.add_entry!</code></a> adds a single entry to the pattern. This can be used if you need to add custom entries that are not covered by the other functions.</li></ul></li><li><p><strong>Instantiate the matrix:</strong> A sparse matrix can be created from the sparsity pattern using <a href="../../reference/sparsity_pattern/#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a>, see <a href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a> below for more details.</p></li></ol><h3 id="Increasing-the-sparsity"><a class="docs-heading-anchor" href="#Increasing-the-sparsity">Increasing the sparsity</a><a id="Increasing-the-sparsity-1"></a><a class="docs-heading-anchor-permalink" href="#Increasing-the-sparsity" title="Permalink"></a></h3><p>By default, when creating a sparsity pattern, it is assumed that each DoF within an element couple with with <em>all</em> other DoFs in the element.</p><div class="admonition is-todo"><header class="admonition-header">Todo</header><div class="admonition-body"><ul><li>Discuss the <code>coupling</code> keyword argument.</li><li>Discuss the <code>keep_constrained</code> keyword argument.</li></ul></div></div><h3 id="Blocked-sparsity-pattern"><a class="docs-heading-anchor" href="#Blocked-sparsity-pattern">Blocked sparsity pattern</a><a id="Blocked-sparsity-pattern-1"></a><a class="docs-heading-anchor-permalink" href="#Blocked-sparsity-pattern" title="Permalink"></a></h3><div class="admonition is-todo"><header class="admonition-header">Todo</header><div class="admonition-body"><p>Discuss <code>BlockSparsityPattern</code> and <code>BlockArrays</code> extension.</p></div></div><h2 id="Instantiating-the-sparse-matrix"><a class="docs-heading-anchor" href="#Instantiating-the-sparse-matrix">Instantiating the sparse matrix</a><a id="Instantiating-the-sparse-matrix-1"></a><a class="docs-heading-anchor-permalink" href="#Instantiating-the-sparse-matrix" title="Permalink"></a></h2><p>As mentioned above, for many simple cases there is no need to work with the sparsity pattern directly and using methods of <a href="../../reference/sparsity_pattern/#Ferrite.allocate_matrix-Tuple{SparsityPattern}"><code>allocate_matrix</code></a> that take the DofHandler as input is enough, for example:</p><pre><code class="language-julia hljs">K = allocate_matrix(dh, ch)</code></pre><p><code>allocate_matrix</code> is also used to instantiate a matrix from a sparsity pattern, for example:</p><pre><code class="language-julia hljs">K = allocate_matrix(sp)</code></pre><div class="admonition is-info"><header class="admonition-header">Multiple matrices with the same pattern</header><div class="admonition-body"><p>For some problems there is a need for multiple matrices with the same sparsity pattern, for example a mass matrix and a stiffness matrix. In this case it is more efficient to create the sparsity pattern once and then instantiate both matrices from it.</p></div></div><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Structurally nonzero means that there is a possibility of a nonzero value even though the computed value might become zero in the end for various reasons.</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>At least for most practical problems using low order interpolations.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../degrees_of_freedom/">« Degrees of Freedom</a><a class="docs-footer-nextpage" href="../assembly/">Assembly »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/computational_homogenization/index.html b/dev/tutorials/computational_homogenization/index.html
index 186e65053a..918e5ddabd 100644
--- a/dev/tutorials/computational_homogenization/index.html
+++ b/dev/tutorials/computational_homogenization/index.html
@@ -471,4 +471,4 @@
write_solution(vtk, dh, uM + u.periodic[i], "_periodic_$i")
write_projection(vtk, projector, σ.periodic[i], "σvM_periodic_$i")
end
-end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../transient_heat_equation/">« Transient heat equation</a><a class="docs-footer-nextpage" href="../stokes-flow/">Stokes flow »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../transient_heat_equation/">« Transient heat equation</a><a class="docs-footer-nextpage" href="../stokes-flow/">Stokes flow »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/dg_heat_equation/index.html b/dev/tutorials/dg_heat_equation/index.html
index 0e772b01a2..6b993c6fea 100644
--- a/dev/tutorials/dg_heat_equation/index.html
+++ b/dev/tutorials/dg_heat_equation/index.html
@@ -297,4 +297,4 @@
u = K \ f;
VTKGridFile("dg_heat_equation", dh) do vtk
write_solution(vtk, dh, u)
-end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linear_shell/">« Linear shell</a><a class="docs-footer-nextpage" href="../../topics/">Topic guide overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linear_shell/">« Linear shell</a><a class="docs-footer-nextpage" href="../../topics/">Topic guide overview »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/heat_equation/index.html b/dev/tutorials/heat_equation/index.html
index b648f764b5..513b911a36 100644
--- a/dev/tutorials/heat_equation/index.html
+++ b/dev/tutorials/heat_equation/index.html
@@ -159,4 +159,4 @@
VTKGridFile("heat_equation", dh) do vtk
write_solution(vtk, dh, u)
-end</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Tutorials overview</a><a class="docs-footer-nextpage" href="../linear_elasticity/">Linear elasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Tutorials overview</a><a class="docs-footer-nextpage" href="../linear_elasticity/">Linear elasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/hyperelasticity.ipynb b/dev/tutorials/hyperelasticity.ipynb
index 1280974cee..c2e3923193 100644
--- a/dev/tutorials/hyperelasticity.ipynb
+++ b/dev/tutorials/hyperelasticity.ipynb
@@ -529,14 +529,14 @@
"-------------------------------------------------------------------------------\n",
" Analysis with 6000 elements Time Allocations \n",
" ----------------------- ------------------------\n",
- " Tot / % measured: 1.99s / 49.6% 145MiB / 44.0% \n",
+ " Tot / % measured: 1.95s / 49.8% 145MiB / 44.0% \n",
"\n",
"Section ncalls time %tot avg alloc %tot avg\n",
"-------------------------------------------------------------------------------\n",
- "export 1 806ms 81.7% 806ms 58.0MiB 90.7% 58.0MiB\n",
- "assemble 6 107ms 10.8% 17.8ms 5.50MiB 8.6% 938KiB\n",
- " element assemble 36.0k 62.5ms 6.3% 1.74μs 0.00B 0.0% 0.00B\n",
- "linear solve 5 74.4ms 7.5% 14.9ms 473KiB 0.7% 94.6KiB\n",
+ "export 1 791ms 81.4% 791ms 58.0MiB 90.7% 58.0MiB\n",
+ "assemble 6 106ms 10.9% 17.6ms 5.50MiB 8.6% 938KiB\n",
+ " element assemble 36.0k 62.1ms 6.4% 1.73μs 0.00B 0.0% 0.00B\n",
+ "linear solve 5 74.5ms 7.7% 14.9ms 473KiB 0.7% 94.6KiB\n",
"-------------------------------------------------------------------------------\n"
]
}
diff --git a/dev/tutorials/hyperelasticity/index.html b/dev/tutorials/hyperelasticity/index.html
index 97f38258df..0d3a0ed0f3 100644
--- a/dev/tutorials/hyperelasticity/index.html
+++ b/dev/tutorials/hyperelasticity/index.html
@@ -246,14 +246,14 @@
<span class="sgr1">-------------------------------------------------------------------------------</span>
<span class="sgr1"> Analysis with 6000 elements </span> Time Allocations
----------------------- ------------------------
- Tot / % measured: 293ms / 66.8% 29.6MiB / 33.4%
+ Tot / % measured: 323ms / 61.2% 29.7MiB / 33.4%
Section ncalls time %tot avg alloc %tot avg
-------------------------------------------------------------------------------
-assemble 6 107ms 54.4% 17.8ms 5.50MiB 55.5% 938KiB
- element assemble 36.0k 62.0ms 31.6% 1.72μs 0.00B 0.0% 0.00B
-linear solve 5 74.9ms 38.2% 15.0ms 473KiB 4.7% 94.6KiB
-export 1 14.4ms 7.4% 14.4ms 3.94MiB 39.8% 3.94MiB
+assemble 6 109ms 55.1% 18.2ms 5.50MiB 55.5% 938KiB
+ element assemble 36.0k 64.7ms 32.7% 1.80μs 0.00B 0.0% 0.00B
+linear solve 5 74.8ms 37.8% 15.0ms 473KiB 4.7% 94.6KiB
+export 1 14.0ms 7.1% 14.0ms 3.94MiB 39.8% 3.94MiB
<span class="sgr1">-------------------------------------------------------------------------------</span></code></pre><h2 id="Plain-program"><a class="docs-heading-anchor" href="#Plain-program">Plain program</a><a id="Plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#Plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../hyperelasticity.jl"><code>hyperelasticity.jl</code></a>.</p><pre><code class="language-julia hljs">using Ferrite, Tensors, TimerOutputs, ProgressMeter, IterativeSolvers
struct NeoHooke
@@ -463,4 +463,4 @@
return u
end
-u = solve();</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../incompressible_elasticity/">« Incompressible elasticity</a><a class="docs-footer-nextpage" href="../plasticity/">Von Mises plasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+u = solve();</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../incompressible_elasticity/">« Incompressible elasticity</a><a class="docs-footer-nextpage" href="../plasticity/">Von Mises plasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/incompressible_elasticity/index.html b/dev/tutorials/incompressible_elasticity/index.html
index e785b4c3af..33feada659 100644
--- a/dev/tutorials/incompressible_elasticity/index.html
+++ b/dev/tutorials/incompressible_elasticity/index.html
@@ -443,4 +443,4 @@
quadratic_u = Lagrange{RefTriangle, 2}()^2
u1 = solve(0.5, linear_u, linear_p);
-u2 = solve(0.5, quadratic_u, linear_p);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linear_elasticity/">« Linear elasticity</a><a class="docs-footer-nextpage" href="../hyperelasticity/">Hyperelasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+u2 = solve(0.5, quadratic_u, linear_p);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linear_elasticity/">« Linear elasticity</a><a class="docs-footer-nextpage" href="../hyperelasticity/">Hyperelasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Tutorials</a></li><li class="is-active"><a href>Tutorials overview</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Tutorials overview</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/tutorials/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Tutorials"><a class="docs-heading-anchor" href="#Tutorials">Tutorials</a><a id="Tutorials-1"></a><a class="docs-heading-anchor-permalink" href="#Tutorials" title="Permalink"></a></h1><p>On this page you find an overview of Ferrite tutorials. The tutorials explain and show how Ferrite can be used to solve a wide range of problems. See also the <a href="../gallery/">Code gallery</a> for more examples.</p><p>The tutorials all follow roughly the same structure:</p><ul><li><strong>Introduction</strong> introduces the problem to be solved and discusses the learning outcomes of the tutorial.</li><li><strong>Commented program</strong> is the code for solving the problem with explanations and comments.</li><li><strong>Plain program</strong> is the raw source code of the program.</li></ul><p>When studying the tutorials it is a good idea to obtain a local copy of the code and run it on your own machine as you read along. Some of the tutorials also include suggestions for tweaks to the program that you can try out on your own.</p><h3 id="Tutorial-index"><a class="docs-heading-anchor" href="#Tutorial-index">Tutorial index</a><a id="Tutorial-index-1"></a><a class="docs-heading-anchor-permalink" href="#Tutorial-index" title="Permalink"></a></h3><p>The tutorials are listed in roughly increasing order of complexity. However, since they focus on different aspects, and solve different problems, it is suggested to have a look at the brief descriptions below to get an idea about what you will learn from each tutorial.</p><p>If you are new to Ferrite then Tutorial 1 - Tutorial 6 is the best place to start. These tutorials introduces and teaches most of the basic finite element techniques (e.g. linear and non-linear problems, scalar- and vector-valued problems, Dirichlet and Neumann boundary conditions, mixed finite elements, time integration, direct and iterative linear solvers, etc). In particular the very first tutorial is essential in order to be able to follow any of the other tutorials. The remaining tutorials discuss more advanced topics.</p><hr/><h5 id="[Tutorial-1:-Heat-equation](heat_equation.md)"><a class="docs-heading-anchor" href="#[Tutorial-1:-Heat-equation](heat_equation.md)"><a href="heat_equation/">Tutorial 1: Heat equation</a></a><a id="[Tutorial-1:-Heat-equation](heat_equation.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-1:-Heat-equation](heat_equation.md)" title="Permalink"></a></h5><p>This tutorial guides you through the process of solving the linear stationary heat equation (i.e. Poisson's equation) on a unit square with homogeneous Dirichlet boundary conditions. This tutorial introduces and teaches many important parts of Ferrite: problem setup, degree of freedom management, assembly procedure, boundary conditions, solving the linear system, visualization of the result). <em>Understanding this tutorial is essential to follow more complex tutorials.</em></p><p><strong>Keywords</strong>: scalar-valued solution, Dirichlet boundary conditions.</p><hr/><h5 id="[Tutorial-2:-Linear-elasticity](linear_elasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-2:-Linear-elasticity](linear_elasticity.md)"><a href="linear_elasticity/">Tutorial 2: Linear elasticity</a></a><a id="[Tutorial-2:-Linear-elasticity](linear_elasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-2:-Linear-elasticity](linear_elasticity.md)" title="Permalink"></a></h5><p>TBW.</p><p><strong>Keywords</strong>: vector-valued solution, Dirichlet and Neumann boundary conditions.</p><hr/><h5 id="[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)"><a href="incompressible_elasticity/">Tutorial 3: Incompressible elasticity</a></a><a id="[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)" title="Permalink"></a></h5><p>This tutorial focuses on a mixed formulation of linear elasticity, with (vector) displacement and (scalar) pressure as the two unknowns, suitable for incompressibility. Thus, this tutorial guides you through the process of solving a problem with two unknowns from two coupled weak forms. The problem that is studied is Cook's membrane in the incompressible limit.</p><p><strong>Keywords</strong>: mixed finite elements, Dirichlet and Neumann boundary conditions.</p><hr/><h4 id="[Tutorial-4:-Hyperelasticity](hyperelasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-4:-Hyperelasticity](hyperelasticity.md)"><a href="hyperelasticity/">Tutorial 4: Hyperelasticity</a></a><a id="[Tutorial-4:-Hyperelasticity](hyperelasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-4:-Hyperelasticity](hyperelasticity.md)" title="Permalink"></a></h4><p>In this tutorial you will learn how to solve a non-linear finite element problem. In particular, a hyperelastic material model, in a finite strain setting, is used to solve the rotation of a cube. Automatic differentiatio (AD) is used for the consitutive relations. Newton's method is used for the non-linear iteration, and a conjugate gradient (CG) solver is used for the linear solution of the increment.</p><p><strong>Keywords</strong>: non-linear finite element, finite strain, automatic differentiation (AD), Newton's method, conjugate gradient (CG).</p><hr/><h4 id="[Tutorial-5:-von-Mises-Plasticity](plasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-5:-von-Mises-Plasticity](plasticity.md)"><a href="plasticity/">Tutorial 5: von Mises Plasticity</a></a><a id="[Tutorial-5:-von-Mises-Plasticity](plasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-5:-von-Mises-Plasticity](plasticity.md)" title="Permalink"></a></h4><p>This tutorial revisits the cantilever beam problem from <a href="linear_elasticity/">Tutorial 2: Linear elasticity</a>, but instead of linear elasticity a plasticity model is used for the constitutive relation. You will learn how to solve a problem which require the solution of a local material problem, and the storage of material state, in each quadrature point. Newton's method is used both locally in the material routine, and globally on the finite element level.</p><p><strong>Keywords</strong>: non-linear finite element, plasticity, material modeling, state variables, Newton’s method.</p><hr/><h4 id="[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)"><a class="docs-heading-anchor" href="#[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)"><a href="transient_heat_equation/#tutorial-transient-heat-equation">Tutorial 6: Transient heat equation</a></a><a id="[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)" title="Permalink"></a></h4><p>In this tutorial the transient heat equation is solved on the unit square. The problem to be solved is thus similar to the one solved in the first tutorial, <a href="heat_equation/">Heat equation</a>, but with time-varying boundary conditions. In particular you will learn how to solve a time dependent problem with an implicit Euler scheme for the time integration.</p><p><strong>Keywords</strong>: time dependent finite elements, implicit Euler time integration.</p><hr/><h4 id="[Tutorial-7:-Computational-homogenization](computational_homogenization.md)"><a class="docs-heading-anchor" href="#[Tutorial-7:-Computational-homogenization](computational_homogenization.md)"><a href="computational_homogenization/">Tutorial 7: Computational homogenization</a></a><a id="[Tutorial-7:-Computational-homogenization](computational_homogenization.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-7:-Computational-homogenization](computational_homogenization.md)" title="Permalink"></a></h4><p>This tutorial guides you through computational homogenization of an representative volume element (RVE) consisting of a soft matrix material with stiff inclusions. The computational mesh is read from an external mesh file generated with Gmsh. Dirichlet and periodic boundary conditions are used.</p><p><strong>Keywords</strong>: Gmsh mesh reading, Dirichlet and periodic boundary conditions</p><hr/><h4 id="[Tutorial-8:-Stokes-flow](stokes-flow.md)"><a class="docs-heading-anchor" href="#[Tutorial-8:-Stokes-flow](stokes-flow.md)"><a href="stokes-flow/">Tutorial 8: Stokes flow</a></a><a id="[Tutorial-8:-Stokes-flow](stokes-flow.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-8:-Stokes-flow](stokes-flow.md)" title="Permalink"></a></h4><p>In this tutorial Stokes flow with (vector) velocity and (scalar) pressure is solved on on a quarter circle. Rotationally periodic boundary conditions is used for the inlet/outlet coupling. To obtain a unique solution, a mean value constraint is applied on the pressure using an affine constraint. The computational mesh is generated directly using the Gmsh API.</p><p><strong>Keywords</strong>: periodic boundary conditions, mean value constraint, mesh generation with Gmsh.</p><hr/><h4 id="[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)"><a class="docs-heading-anchor" href="#[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)"><a href="porous_media/">Tutorial 9: Porous media (SubDofHandler)</a></a><a id="[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)" title="Permalink"></a></h4><p>This tutorial introduces how to solve a complex linear problem, where there are different fields on different subdomains, and different cell types in the grid. This requires using the <code>SubDofHandler</code> interface.</p><p><strong>Keywords</strong>: Mixed grids, multiple fields, porous media, <code>SubDofHandler</code></p><hr/><h4 id="[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)"><a class="docs-heading-anchor" href="#[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)"><a href="ns_vs_diffeq/">Tutorial 10: Incompressible Navier-Stokes equations</a></a><a id="[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)" title="Permalink"></a></h4><p>In this tutorial the incompressible Navier-Stokes equations are solved. The domain is discretized in space with Ferrite as usual, and then forumalated in a way to be compatible with the <a href="https://docs.sciml.ai/OrdinaryDiffEq/">OrdinaryDiffEq.jl</a> package, which is used for the time-integration.</p><p><strong>Keywords</strong>: non-linear time dependent problem</p><hr/><h4 id="[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)"><a class="docs-heading-anchor" href="#[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)"><a href="reactive_surface/#tutorial-reactive-surface">Tutorial 10: Reactive surface</a></a><a id="[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)" title="Permalink"></a></h4><p>In this tutorial a reaction diffusion system on a sphere surface embedded in 3D is solved. Ferrite is used to assemble the diffusion operators and the mass matrices. The problem is solved by using the usual first order reaction diffusion operator splitting.</p><p><strong>Keywords</strong>: embedded elements, operator splitting, gmsh</p><hr/><h4 id="[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)"><a class="docs-heading-anchor" href="#[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)"><a href="linear_shell/#tutorial-linear-shell">Tutorial 11: Linear shell</a></a><a id="[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)" title="Permalink"></a></h4><p>In this tutorial a linear shell element formulation is set up as a two-dimensional domain embedded in three-dimensional space. This will teach, and perhaps inspire, you on how Ferrite can be used for non-standard things and how to add "hacks" that build on top of Ferrite.</p><p><strong>Keywords</strong>: shell elements, automatic differentiation</p><hr/><h4 id="[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)"><a class="docs-heading-anchor" href="#[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)"><a href="dg_heat_equation/#tutorial-dg-heat-equation">Tutorial 12: Discontinuous Galerkin heat equation</a></a><a id="[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)" title="Permalink"></a></h4><p>This tutorial guides you through the process of solving the linear stationary heat equation (i.e. Poisson's equation) on a unit square with inhomogeneous Dirichlet and Neumann boundary conditions using the interior penalty discontinuous Galerkin method. This tutorial follows the <a href="heat_equation/#tutorial-heat-equation">heat equation tutorial</a>, introducing face and interface iterators, jump and average operators, and cross-element coupling in sparsity patterns. This example was developed as part of the <em>Google Summer of Code</em> funded project <a href="https://summerofcode.withgoogle.com/programs/2023/projects/SLGbRNI5">"Discontinuous Galerkin Infrastructure For the finite element toolbox Ferrite.jl"</a>.</p><p><strong>Keywords</strong>: scalar-valued solution, Dirichlet boundary conditions, Discontinuous Galerkin, Interior penalty</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../changelog/">« Changelog</a><a class="docs-footer-nextpage" href="heat_equation/">Heat equation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. 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href="https://github.com/Ferrite-FEM/Ferrite.jl/blob/master/docs/src/tutorials/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Tutorials"><a class="docs-heading-anchor" href="#Tutorials">Tutorials</a><a id="Tutorials-1"></a><a class="docs-heading-anchor-permalink" href="#Tutorials" title="Permalink"></a></h1><p>On this page you find an overview of Ferrite tutorials. The tutorials explain and show how Ferrite can be used to solve a wide range of problems. See also the <a href="../gallery/">Code gallery</a> for more examples.</p><p>The tutorials all follow roughly the same structure:</p><ul><li><strong>Introduction</strong> introduces the problem to be solved and discusses the learning outcomes of the tutorial.</li><li><strong>Commented program</strong> is the code for solving the problem with explanations and comments.</li><li><strong>Plain program</strong> is the raw source code of the program.</li></ul><p>When studying the tutorials it is a good idea to obtain a local copy of the code and run it on your own machine as you read along. Some of the tutorials also include suggestions for tweaks to the program that you can try out on your own.</p><h3 id="Tutorial-index"><a class="docs-heading-anchor" href="#Tutorial-index">Tutorial index</a><a id="Tutorial-index-1"></a><a class="docs-heading-anchor-permalink" href="#Tutorial-index" title="Permalink"></a></h3><p>The tutorials are listed in roughly increasing order of complexity. However, since they focus on different aspects, and solve different problems, it is suggested to have a look at the brief descriptions below to get an idea about what you will learn from each tutorial.</p><p>If you are new to Ferrite then Tutorial 1 - Tutorial 6 is the best place to start. These tutorials introduces and teaches most of the basic finite element techniques (e.g. linear and non-linear problems, scalar- and vector-valued problems, Dirichlet and Neumann boundary conditions, mixed finite elements, time integration, direct and iterative linear solvers, etc). In particular the very first tutorial is essential in order to be able to follow any of the other tutorials. The remaining tutorials discuss more advanced topics.</p><hr/><h5 id="[Tutorial-1:-Heat-equation](heat_equation.md)"><a class="docs-heading-anchor" href="#[Tutorial-1:-Heat-equation](heat_equation.md)"><a href="heat_equation/">Tutorial 1: Heat equation</a></a><a id="[Tutorial-1:-Heat-equation](heat_equation.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-1:-Heat-equation](heat_equation.md)" title="Permalink"></a></h5><p>This tutorial guides you through the process of solving the linear stationary heat equation (i.e. Poisson's equation) on a unit square with homogeneous Dirichlet boundary conditions. This tutorial introduces and teaches many important parts of Ferrite: problem setup, degree of freedom management, assembly procedure, boundary conditions, solving the linear system, visualization of the result). <em>Understanding this tutorial is essential to follow more complex tutorials.</em></p><p><strong>Keywords</strong>: scalar-valued solution, Dirichlet boundary conditions.</p><hr/><h5 id="[Tutorial-2:-Linear-elasticity](linear_elasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-2:-Linear-elasticity](linear_elasticity.md)"><a href="linear_elasticity/">Tutorial 2: Linear elasticity</a></a><a id="[Tutorial-2:-Linear-elasticity](linear_elasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-2:-Linear-elasticity](linear_elasticity.md)" title="Permalink"></a></h5><p>TBW.</p><p><strong>Keywords</strong>: vector-valued solution, Dirichlet and Neumann boundary conditions.</p><hr/><h5 id="[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)"><a href="incompressible_elasticity/">Tutorial 3: Incompressible elasticity</a></a><a id="[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-3:-Incompressible-elasticity](incompressible_elasticity.md)" title="Permalink"></a></h5><p>This tutorial focuses on a mixed formulation of linear elasticity, with (vector) displacement and (scalar) pressure as the two unknowns, suitable for incompressibility. Thus, this tutorial guides you through the process of solving a problem with two unknowns from two coupled weak forms. The problem that is studied is Cook's membrane in the incompressible limit.</p><p><strong>Keywords</strong>: mixed finite elements, Dirichlet and Neumann boundary conditions.</p><hr/><h4 id="[Tutorial-4:-Hyperelasticity](hyperelasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-4:-Hyperelasticity](hyperelasticity.md)"><a href="hyperelasticity/">Tutorial 4: Hyperelasticity</a></a><a id="[Tutorial-4:-Hyperelasticity](hyperelasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-4:-Hyperelasticity](hyperelasticity.md)" title="Permalink"></a></h4><p>In this tutorial you will learn how to solve a non-linear finite element problem. In particular, a hyperelastic material model, in a finite strain setting, is used to solve the rotation of a cube. Automatic differentiatio (AD) is used for the consitutive relations. Newton's method is used for the non-linear iteration, and a conjugate gradient (CG) solver is used for the linear solution of the increment.</p><p><strong>Keywords</strong>: non-linear finite element, finite strain, automatic differentiation (AD), Newton's method, conjugate gradient (CG).</p><hr/><h4 id="[Tutorial-5:-von-Mises-Plasticity](plasticity.md)"><a class="docs-heading-anchor" href="#[Tutorial-5:-von-Mises-Plasticity](plasticity.md)"><a href="plasticity/">Tutorial 5: von Mises Plasticity</a></a><a id="[Tutorial-5:-von-Mises-Plasticity](plasticity.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-5:-von-Mises-Plasticity](plasticity.md)" title="Permalink"></a></h4><p>This tutorial revisits the cantilever beam problem from <a href="linear_elasticity/">Tutorial 2: Linear elasticity</a>, but instead of linear elasticity a plasticity model is used for the constitutive relation. You will learn how to solve a problem which require the solution of a local material problem, and the storage of material state, in each quadrature point. Newton's method is used both locally in the material routine, and globally on the finite element level.</p><p><strong>Keywords</strong>: non-linear finite element, plasticity, material modeling, state variables, Newton’s method.</p><hr/><h4 id="[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)"><a class="docs-heading-anchor" href="#[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)"><a href="transient_heat_equation/#tutorial-transient-heat-equation">Tutorial 6: Transient heat equation</a></a><a id="[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-6:-Transient-heat-equation](@ref-tutorial-transient-heat-equation)" title="Permalink"></a></h4><p>In this tutorial the transient heat equation is solved on the unit square. The problem to be solved is thus similar to the one solved in the first tutorial, <a href="heat_equation/">Heat equation</a>, but with time-varying boundary conditions. In particular you will learn how to solve a time dependent problem with an implicit Euler scheme for the time integration.</p><p><strong>Keywords</strong>: time dependent finite elements, implicit Euler time integration.</p><hr/><h4 id="[Tutorial-7:-Computational-homogenization](computational_homogenization.md)"><a class="docs-heading-anchor" href="#[Tutorial-7:-Computational-homogenization](computational_homogenization.md)"><a href="computational_homogenization/">Tutorial 7: Computational homogenization</a></a><a id="[Tutorial-7:-Computational-homogenization](computational_homogenization.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-7:-Computational-homogenization](computational_homogenization.md)" title="Permalink"></a></h4><p>This tutorial guides you through computational homogenization of an representative volume element (RVE) consisting of a soft matrix material with stiff inclusions. The computational mesh is read from an external mesh file generated with Gmsh. Dirichlet and periodic boundary conditions are used.</p><p><strong>Keywords</strong>: Gmsh mesh reading, Dirichlet and periodic boundary conditions</p><hr/><h4 id="[Tutorial-8:-Stokes-flow](stokes-flow.md)"><a class="docs-heading-anchor" href="#[Tutorial-8:-Stokes-flow](stokes-flow.md)"><a href="stokes-flow/">Tutorial 8: Stokes flow</a></a><a id="[Tutorial-8:-Stokes-flow](stokes-flow.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-8:-Stokes-flow](stokes-flow.md)" title="Permalink"></a></h4><p>In this tutorial Stokes flow with (vector) velocity and (scalar) pressure is solved on on a quarter circle. Rotationally periodic boundary conditions is used for the inlet/outlet coupling. To obtain a unique solution, a mean value constraint is applied on the pressure using an affine constraint. The computational mesh is generated directly using the Gmsh API.</p><p><strong>Keywords</strong>: periodic boundary conditions, mean value constraint, mesh generation with Gmsh.</p><hr/><h4 id="[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)"><a class="docs-heading-anchor" href="#[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)"><a href="porous_media/">Tutorial 9: Porous media (SubDofHandler)</a></a><a id="[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-9:-Porous-media-(SubDofHandler)](porous_media.md)" title="Permalink"></a></h4><p>This tutorial introduces how to solve a complex linear problem, where there are different fields on different subdomains, and different cell types in the grid. This requires using the <code>SubDofHandler</code> interface.</p><p><strong>Keywords</strong>: Mixed grids, multiple fields, porous media, <code>SubDofHandler</code></p><hr/><h4 id="[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)"><a class="docs-heading-anchor" href="#[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)"><a href="ns_vs_diffeq/">Tutorial 10: Incompressible Navier-Stokes equations</a></a><a id="[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-10:-Incompressible-Navier-Stokes-equations](ns_vs_diffeq.md)" title="Permalink"></a></h4><p>In this tutorial the incompressible Navier-Stokes equations are solved. The domain is discretized in space with Ferrite as usual, and then forumalated in a way to be compatible with the <a href="https://docs.sciml.ai/OrdinaryDiffEq/">OrdinaryDiffEq.jl</a> package, which is used for the time-integration.</p><p><strong>Keywords</strong>: non-linear time dependent problem</p><hr/><h4 id="[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)"><a class="docs-heading-anchor" href="#[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)"><a href="reactive_surface/#tutorial-reactive-surface">Tutorial 10: Reactive surface</a></a><a id="[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-10:-Reactive-surface](@ref-tutorial-reactive-surface)" title="Permalink"></a></h4><p>In this tutorial a reaction diffusion system on a sphere surface embedded in 3D is solved. Ferrite is used to assemble the diffusion operators and the mass matrices. The problem is solved by using the usual first order reaction diffusion operator splitting.</p><p><strong>Keywords</strong>: embedded elements, operator splitting, gmsh</p><hr/><h4 id="[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)"><a class="docs-heading-anchor" href="#[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)"><a href="linear_shell/#tutorial-linear-shell">Tutorial 11: Linear shell</a></a><a id="[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-11:-Linear-shell](@ref-tutorial-linear-shell)" title="Permalink"></a></h4><p>In this tutorial a linear shell element formulation is set up as a two-dimensional domain embedded in three-dimensional space. This will teach, and perhaps inspire, you on how Ferrite can be used for non-standard things and how to add "hacks" that build on top of Ferrite.</p><p><strong>Keywords</strong>: shell elements, automatic differentiation</p><hr/><h4 id="[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)"><a class="docs-heading-anchor" href="#[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)"><a href="dg_heat_equation/#tutorial-dg-heat-equation">Tutorial 12: Discontinuous Galerkin heat equation</a></a><a id="[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)-1"></a><a class="docs-heading-anchor-permalink" href="#[Tutorial-12:-Discontinuous-Galerkin-heat-equation](@ref-tutorial-dg-heat-equation)" title="Permalink"></a></h4><p>This tutorial guides you through the process of solving the linear stationary heat equation (i.e. Poisson's equation) on a unit square with inhomogeneous Dirichlet and Neumann boundary conditions using the interior penalty discontinuous Galerkin method. This tutorial follows the <a href="heat_equation/#tutorial-heat-equation">heat equation tutorial</a>, introducing face and interface iterators, jump and average operators, and cross-element coupling in sparsity patterns. This example was developed as part of the <em>Google Summer of Code</em> funded project <a href="https://summerofcode.withgoogle.com/programs/2023/projects/SLGbRNI5">"Discontinuous Galerkin Infrastructure For the finite element toolbox Ferrite.jl"</a>.</p><p><strong>Keywords</strong>: scalar-valued solution, Dirichlet boundary conditions, Discontinuous Galerkin, Interior penalty</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../changelog/">« Changelog</a><a class="docs-footer-nextpage" href="heat_equation/">Heat equation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/linear_elasticity/index.html b/dev/tutorials/linear_elasticity/index.html
index d948f8d829..ae691e118a 100644
--- a/dev/tutorials/linear_elasticity/index.html
+++ b/dev/tutorials/linear_elasticity/index.html
@@ -290,4 +290,4 @@
end
write_projection(vtk, proj, stress_field, "stress field")
Ferrite.write_cellset(vtk, grid)
-end</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../heat_equation/">« Heat equation</a><a class="docs-footer-nextpage" href="../incompressible_elasticity/">Incompressible elasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../heat_equation/">« Heat equation</a><a class="docs-footer-nextpage" href="../incompressible_elasticity/">Incompressible elasticity »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/linear_shell/index.html b/dev/tutorials/linear_shell/index.html
index 11c95eebdc..e6026e78c8 100644
--- a/dev/tutorials/linear_shell/index.html
+++ b/dev/tutorials/linear_shell/index.html
@@ -182,4 +182,4 @@
ke .+= B'*data.C*B * dV
end
end
-end;</code></pre><p>Run everything:</p><pre><code class="language-julia hljs">main()</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">VTKGridFile for the closed file "linear_shell.vtu".</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reactive_surface/">« Reactive surface</a><a class="docs-footer-nextpage" href="../dg_heat_equation/">Discontinuous Galerkin heat equation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end;</code></pre><p>Run everything:</p><pre><code class="language-julia hljs">main()</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">VTKGridFile for the closed file "linear_shell.vtu".</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reactive_surface/">« Reactive surface</a><a class="docs-footer-nextpage" href="../dg_heat_equation/">Discontinuous Galerkin heat equation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/ns_vs_diffeq/index.html b/dev/tutorials/ns_vs_diffeq/index.html
index db3beca71b..7cb153b347 100644
--- a/dev/tutorials/ns_vs_diffeq/index.html
+++ b/dev/tutorials/ns_vs_diffeq/index.html
@@ -546,4 +546,4 @@
pvd[t] = vtk
end
end
-vtk_save(pvd);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../porous_media/">« Porous media</a><a class="docs-footer-nextpage" href="../reactive_surface/">Reactive surface »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+vtk_save(pvd);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../porous_media/">« Porous media</a><a class="docs-footer-nextpage" href="../reactive_surface/">Reactive surface »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/plasticity.ipynb b/dev/tutorials/plasticity.ipynb
index 0b0e87eb7d..b0ffbbf91b 100644
--- a/dev/tutorials/plasticity.ipynb
+++ b/dev/tutorials/plasticity.ipynb
@@ -720,182 +720,182 @@
"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600\" height=\"400\" viewBox=\"0 0 2400 1600\">\n",
"<defs>\n",
- " <clipPath id=\"clip900\">\n",
+ " <clipPath id=\"clip510\">\n",
" <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"/>\n",
" </clipPath>\n",
"</defs>\n",
- "<path clip-path=\"url(#clip900)\" d=\"M0 1600 L2400 1600 L2400 0 L0 0 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+ "<path clip-path=\"url(#clip510)\" d=\"M0 1600 L2400 1600 L2400 0 L0 0 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<defs>\n",
- " <clipPath id=\"clip901\">\n",
+ " <clipPath id=\"clip511\">\n",
" <rect x=\"480\" y=\"0\" width=\"1681\" height=\"1600\"/>\n",
" </clipPath>\n",
"</defs>\n",
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"<defs>\n",
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+ " <clipPath id=\"clip512\">\n",
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diff --git a/dev/tutorials/plasticity/index.html b/dev/tutorials/plasticity/index.html
index a4e89bd6c3..0d3d840fc4 100644
--- a/dev/tutorials/plasticity/index.html
+++ b/dev/tutorials/plasticity/index.html
@@ -346,7 +346,7 @@
markershape = :auto
)
ylabel!("Traction [Pa]")
-xlabel!("Maximum deflection [m]")</code></pre><img src="3e25d0a4.svg" alt="Example block output"/><p><em>Figure 2.</em> Load-displacement-curve for the beam, showing a clear decrease in stiffness as more material starts to yield.</p><h2 id="plasticity-plain-program"><a class="docs-heading-anchor" href="#plasticity-plain-program">Plain program</a><a id="plasticity-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#plasticity-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../plasticity.jl"><code>plasticity.jl</code></a>.</p><pre><code class="language-julia hljs">using Ferrite, Tensors, SparseArrays, LinearAlgebra, Printf
+xlabel!("Maximum deflection [m]")</code></pre><img src="d0ba011e.svg" alt="Example block output"/><p><em>Figure 2.</em> Load-displacement-curve for the beam, showing a clear decrease in stiffness as more material starts to yield.</p><h2 id="plasticity-plain-program"><a class="docs-heading-anchor" href="#plasticity-plain-program">Plain program</a><a id="plasticity-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#plasticity-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../plasticity.jl"><code>plasticity.jl</code></a>.</p><pre><code class="language-julia hljs">using Ferrite, Tensors, SparseArrays, LinearAlgebra, Printf
struct J2Plasticity{T, S <: SymmetricTensor{4, 3, T}}
G::T # Shear modulus
@@ -649,4 +649,4 @@
markershape = :auto
)
ylabel!("Traction [Pa]")
-xlabel!("Maximum deflection [m]")</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../hyperelasticity/">« Hyperelasticity</a><a class="docs-footer-nextpage" href="../transient_heat_equation/">Transient heat equation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+xlabel!("Maximum deflection [m]")</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../hyperelasticity/">« Hyperelasticity</a><a class="docs-footer-nextpage" href="../transient_heat_equation/">Transient heat equation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/porous_media/index.html b/dev/tutorials/porous_media/index.html
index 13605465b2..3004128a3d 100644
--- a/dev/tutorials/porous_media/index.html
+++ b/dev/tutorials/porous_media/index.html
@@ -478,4 +478,4 @@
end;
dh, ch, domains = setup_problem()
-solve(dh, ch, domains);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../stokes-flow/">« Stokes flow</a><a class="docs-footer-nextpage" href="../ns_vs_diffeq/">Incompressible Navier-Stokes equations via DifferentialEquations.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+solve(dh, ch, domains);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../stokes-flow/">« Stokes flow</a><a class="docs-footer-nextpage" href="../ns_vs_diffeq/">Incompressible Navier-Stokes equations via DifferentialEquations.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/reactive_surface.ipynb b/dev/tutorials/reactive_surface.ipynb
index 0c4f473045..95ff569920 100644
--- a/dev/tutorials/reactive_surface.ipynb
+++ b/dev/tutorials/reactive_surface.ipynb
@@ -332,10 +332,10 @@
"text": [
"Info : Meshing 1D...\n",
"Info : [ 40%] Meshing curve 2 (Circle)\n",
- "Info : Done meshing 1D (Wall 9.4327e-05s, CPU 9.5e-05s)\n",
+ "Info : Done meshing 1D (Wall 0.000103574s, CPU 0.000104s)\n",
"Info : Meshing 2D...\n",
"Info : Meshing surface 1 (Sphere, Frontal-Delaunay)\n",
- "Info : Done meshing 2D (Wall 0.00963593s, CPU 0.009618s)\n",
+ "Info : Done meshing 2D (Wall 0.00984966s, CPU 0.009832s)\n",
"Info : 160 nodes 328 elements\n",
"Info : Refining mesh...\n",
"Info : Meshing order 2 (curvilinear on)...\n",
@@ -345,8 +345,8 @@
"Info : [ 70%] Meshing surface 1 order 2\n",
"Info : [ 90%] Meshing volume 1 order 2\n",
"Info : Surface mesh: worst distortion = 0.970866 (0 elements in ]0, 0.2]); worst gamma = 0.433887\n",
- "Info : Done meshing order 2 (Wall 0.00114026s, CPU 0.00114s)\n",
- "Info : Done refining mesh (Wall 0.00146305s, CPU 0.001463s)\n",
+ "Info : Done meshing order 2 (Wall 0.00116066s, CPU 0.00116s)\n",
+ "Info : Done refining mesh (Wall 0.00149942s, CPU 0.001499s)\n",
"Info : Refining mesh...\n",
"Info : Meshing order 2 (curvilinear on)...\n",
"Info : [ 0%] Meshing curve 1 order 2\n",
@@ -355,8 +355,8 @@
"Info : [ 70%] Meshing surface 1 order 2\n",
"Info : [ 90%] Meshing volume 1 order 2\n",
"Info : Surface mesh: worst distortion = 0.992408 (0 elements in ]0, 0.2]); worst gamma = 0.421451\n",
- "Info : Done meshing order 2 (Wall 0.0043544s, CPU 0.004353s)\n",
- "Info : Done refining mesh (Wall 0.00560651s, CPU 0.005606s)\n",
+ "Info : Done meshing order 2 (Wall 0.00442149s, CPU 0.004421s)\n",
+ "Info : Done refining mesh (Wall 0.00570811s, CPU 0.005707s)\n",
"Info : Refining mesh...\n",
"Info : Meshing order 2 (curvilinear on)...\n",
"Info : [ 0%] Meshing curve 1 order 2\n",
@@ -365,8 +365,8 @@
"Info : [ 70%] Meshing surface 1 order 2\n",
"Info : [ 90%] Meshing volume 1 order 2\n",
"Info : Surface mesh: worst distortion = 0.998082 (0 elements in ]0, 0.2]); worst gamma = 0.418317\n",
- "Info : Done meshing order 2 (Wall 0.0166962s, CPU 0.016695s)\n",
- "Info : Done refining mesh (Wall 0.0218316s, CPU 0.021831s)\n"
+ "Info : Done meshing order 2 (Wall 0.0167681s, CPU 0.016767s)\n",
+ "Info : Done refining mesh (Wall 0.0219069s, CPU 0.021906s)\n"
]
}
],
diff --git a/dev/tutorials/reactive_surface/index.html b/dev/tutorials/reactive_surface/index.html
index e1292f22be..0bb0487a74 100644
--- a/dev/tutorials/reactive_surface/index.html
+++ b/dev/tutorials/reactive_surface/index.html
@@ -222,10 +222,10 @@
material = GrayScottMaterial(0.00016, 0.00008, 0.06, 0.062)
gray_scott_on_sphere(material, 10.0, 32000.0, 3)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Info : Meshing 1D...
Info : [ 40%] Meshing curve 2 (Circle)
-Info : Done meshing 1D (Wall 8.9588e-05s, CPU 9e-05s)
+Info : Done meshing 1D (Wall 9.8384e-05s, CPU 0.0001s)
Info : Meshing 2D...
Info : Meshing surface 1 (Sphere, Frontal-Delaunay)
-Info : Done meshing 2D (Wall 0.00949275s, CPU 0.009474s)
+Info : Done meshing 2D (Wall 0.00923319s, CPU 0.009215s)
Info : 160 nodes 328 elements
Info : Refining mesh...
Info : Meshing order 2 (curvilinear on)...
@@ -235,8 +235,8 @@
Info : [ 70%] Meshing surface 1 order 2
Info : [ 90%] Meshing volume 1 order 2
Info : Surface mesh: worst distortion = 0.970866 (0 elements in ]0, 0.2]); worst gamma = 0.433887
-Info : Done meshing order 2 (Wall 0.0012175s, CPU 0.001217s)
-Info : Done refining mesh (Wall 0.00156364s, CPU 0.001564s)
+Info : Done meshing order 2 (Wall 0.00114717s, CPU 0.001132s)
+Info : Done refining mesh (Wall 0.00149521s, CPU 0.001475s)
Info : Refining mesh...
Info : Meshing order 2 (curvilinear on)...
Info : [ 0%] Meshing curve 1 order 2
@@ -245,8 +245,8 @@
Info : [ 70%] Meshing surface 1 order 2
Info : [ 90%] Meshing volume 1 order 2
Info : Surface mesh: worst distortion = 0.992408 (0 elements in ]0, 0.2]); worst gamma = 0.421451
-Info : Done meshing order 2 (Wall 0.00447432s, CPU 0.004474s)
-Info : Done refining mesh (Wall 0.00579685s, CPU 0.005797s)
+Info : Done meshing order 2 (Wall 0.00463219s, CPU 0.004623s)
+Info : Done refining mesh (Wall 0.00615366s, CPU 0.006145s)
Info : Refining mesh...
Info : Meshing order 2 (curvilinear on)...
Info : [ 0%] Meshing curve 1 order 2
@@ -255,8 +255,8 @@
Info : [ 70%] Meshing surface 1 order 2
Info : [ 90%] Meshing volume 1 order 2
Info : Surface mesh: worst distortion = 0.998082 (0 elements in ]0, 0.2]); worst gamma = 0.418317
-Info : Done meshing order 2 (Wall 0.0171863s, CPU 0.017184s)
-Info : Done refining mesh (Wall 0.0228193s, CPU 0.022819s)</code></pre><h2 id="reactive_surface-plain-program"><a class="docs-heading-anchor" href="#reactive_surface-plain-program">Plain program</a><a id="reactive_surface-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#reactive_surface-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../reactive_surface.jl"><code>reactive_surface.jl</code></a>.</p><pre><code class="language-julia hljs">using Ferrite, FerriteGmsh
+Info : Done meshing order 2 (Wall 0.017739s, CPU 0.017738s)
+Info : Done refining mesh (Wall 0.0239097s, CPU 0.023908s)</code></pre><h2 id="reactive_surface-plain-program"><a class="docs-heading-anchor" href="#reactive_surface-plain-program">Plain program</a><a id="reactive_surface-plain-program-1"></a><a class="docs-heading-anchor-permalink" href="#reactive_surface-plain-program" title="Permalink"></a></h2><p>Here follows a version of the program without any comments. The file is also available here: <a href="../reactive_surface.jl"><code>reactive_surface.jl</code></a>.</p><pre><code class="language-julia hljs">using Ferrite, FerriteGmsh
using BlockArrays, SparseArrays, LinearAlgebra, WriteVTK
struct GrayScottMaterial{T}
@@ -484,4 +484,4 @@
# This parametrization gives the spot pattern shown in the gif above.
material = GrayScottMaterial(0.00016, 0.00008, 0.06, 0.062)
- gray_scott_on_sphere(material, 10.0, 32000.0, 3)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ns_vs_diffeq/">« Incompressible Navier-Stokes equations via DifferentialEquations.jl</a><a class="docs-footer-nextpage" href="../linear_shell/">Linear shell »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ gray_scott_on_sphere(material, 10.0, 32000.0, 3)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ns_vs_diffeq/">« Incompressible Navier-Stokes equations via DifferentialEquations.jl</a><a class="docs-footer-nextpage" href="../linear_shell/">Linear shell »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/stokes-flow/index.html b/dev/tutorials/stokes-flow/index.html
index 604fc3a93b..f21e8504a2 100644
--- a/dev/tutorials/stokes-flow/index.html
+++ b/dev/tutorials/stokes-flow/index.html
@@ -482,4 +482,4 @@
return
end
-main()</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../computational_homogenization/">« Computational homogenization</a><a class="docs-footer-nextpage" href="../porous_media/">Porous media »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+main()</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../computational_homogenization/">« Computational homogenization</a><a class="docs-footer-nextpage" href="../porous_media/">Porous media »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/transient_heat_equation/index.html b/dev/tutorials/transient_heat_equation/index.html
index 3a6c41a25f..a0c4a2e5dd 100644
--- a/dev/tutorials/transient_heat_equation/index.html
+++ b/dev/tutorials/transient_heat_equation/index.html
@@ -233,4 +233,4 @@
uₙ .= u
end
-vtk_save(pvd);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../plasticity/">« Von Mises plasticity</a><a class="docs-footer-nextpage" href="../computational_homogenization/">Computational homogenization »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:47">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+vtk_save(pvd);</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../plasticity/">« Von Mises plasticity</a><a class="docs-footer-nextpage" href="../computational_homogenization/">Computational homogenization »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 10 January 2025 11:48">Friday 10 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/vortex-street.pvd b/dev/tutorials/vortex-street.pvd
index 91ea81106e..db1e99e661 100755
--- a/dev/tutorials/vortex-street.pvd
+++ b/dev/tutorials/vortex-street.pvd
@@ -3,37 +3,37 @@
<Collection>
<DataSet timestep="0.0" part="0" file="vortex-street-1.vtu"/>
<DataSet timestep="0.1" part="0" file="vortex-street-2.vtu"/>
- <DataSet timestep="0.14596645898489624" part="0" file="vortex-street-3.vtu"/>
- <DataSet timestep="0.22438131462649163" part="0" file="vortex-street-4.vtu"/>
- <DataSet timestep="0.2871602254543282" part="0" file="vortex-street-5.vtu"/>
- <DataSet timestep="0.36440118484370215" part="0" file="vortex-street-6.vtu"/>
- <DataSet timestep="0.44164214423307613" part="0" file="vortex-street-7.vtu"/>
- <DataSet timestep="0.5189083098837332" part="0" file="vortex-street-8.vtu"/>
- <DataSet timestep="0.5961744755343902" part="0" file="vortex-street-9.vtu"/>
- <DataSet timestep="0.6734406411850472" part="0" file="vortex-street-10.vtu"/>
- <DataSet timestep="0.7507068068357042" part="0" file="vortex-street-11.vtu"/>
- <DataSet timestep="0.8279729724863613" part="0" file="vortex-street-12.vtu"/>
- <DataSet timestep="0.9052391381370183" part="0" file="vortex-street-13.vtu"/>
- <DataSet timestep="0.9825053037876753" part="0" file="vortex-street-14.vtu"/>
+ <DataSet timestep="0.14597505895698665" part="0" file="vortex-street-3.vtu"/>
+ <DataSet timestep="0.2244069890488254" part="0" file="vortex-street-4.vtu"/>
+ <DataSet timestep="0.2871966083231415" part="0" file="vortex-street-5.vtu"/>
+ <DataSet timestep="0.36446694274162084" part="0" file="vortex-street-6.vtu"/>
+ <DataSet timestep="0.44173727716010025" part="0" file="vortex-street-7.vtu"/>
+ <DataSet timestep="0.5190294900449979" part="0" file="vortex-street-8.vtu"/>
+ <DataSet timestep="0.5963217029298955" part="0" file="vortex-street-9.vtu"/>
+ <DataSet timestep="0.6736139158147931" part="0" file="vortex-street-10.vtu"/>
+ <DataSet timestep="0.7509061286996908" part="0" file="vortex-street-11.vtu"/>
+ <DataSet timestep="0.8281983415845884" part="0" file="vortex-street-12.vtu"/>
+ <DataSet timestep="0.905490554469486" part="0" file="vortex-street-13.vtu"/>
+ <DataSet timestep="0.9827827673543836" part="0" file="vortex-street-14.vtu"/>
<DataSet timestep="1.0" part="0" file="vortex-street-15.vtu"/>
- <DataSet timestep="1.0433164070930814" part="0" file="vortex-street-16.vtu"/>
- <DataSet timestep="1.0669706472570621" part="0" file="vortex-street-17.vtu"/>
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- <DataSet timestep="1.131488811754707" part="0" file="vortex-street-19.vtu"/>
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