Aded Firedrake, some pictures and a video

docs/requirements.txt

@@ -81,6 +81,7 @@ sphinxcontrib-jsmath
 sphinxcontrib-qthelp
 sphinxcontrib-serializinghtml
 sphinx-autoapi
+sphinxcontrib-video
 stack-data==0.6.2
 tbb==2021.9.0
 tinycss2==1.2.1

docs/src/PETScSNES/hyperelasticity.py.rst

@@ -91,4 +91,9 @@ We compare the performance of the `PETSc SNES` solvers and the one of `NGSolve`
    * - PETSc SNES
      - 10
 
-This suggests that while NGS non-linear solver when finely tuned performs as well as PETSc SNES, it is more sensitive to the choice of the damping factor. In this case, a damping factor of 0.3 was found to be the best choice.
+This suggests that while NGSolve's non-linear solver when finely tuned performs as well as PETSc SNES, it is more sensitive to the choice of the damping factor. In this case, a damping factor of 0.3 was found to be the best choice.
+
+.. video:: ./twistedBeam.mp4
+    :width: 600
+    :height: 400
+    :loop:

docs/src/conf.py

@@ -20,7 +20,7 @@
 # -- General configuration ---------------------------------------------------
 # https://www.sphinx-doc.org/en/master/usage/configuration.html#general-configuration
 
-extensions = ['sphinx.ext.autodoc', 'sphinx_autodoc_typehints',"sphinx.ext.mathjax","sphinx.ext.todo",
+extensions = ['sphinx.ext.autodoc', 'sphinxcontrib.video', 'sphinx_autodoc_typehints',"sphinx.ext.mathjax","sphinx.ext.todo",
               "IPython.sphinxext.ipython_console_highlighting", "IPython.sphinxext.ipython_directive",
               "nbsphinx", 'sphinx.ext.autodoc', "autoapi.extension"]
 autosummary_generate = True  # Turn on sphinx.ext.autosummary]

docs/src/index.rst

@@ -45,6 +45,13 @@ Welcome to ngsPETSc's documentation!
 
    SLEPcEPS/poisson.py
 
+.. toctree::
+   :maxdepth: 1
+   :caption: Firedrake
+
+   utils/firedrake/lomesh.py
+   utils/firedrake/homesh.py
+
 Indices and tables
 ==================
 

docs/src/install.rst

@@ -89,7 +89,7 @@ We are now fianlly ready to install ngsPETSc:
 Authors
 ----------
 
-Stefano Zampini, Umberto Zerbinati
+Patrick E. Farrell, Stefano Zampini, Umberto Zerbinati
 
 License
 ---------------

docs/src/utils/firedrake/homesh.py.rst

@@ -0,0 +1,86 @@
+High-order meshes 
+==================
+
+This tutorial is an improved version of the Netgen tutorial available in the Firedrake documentation, which can be found `here <https://www.firedrakeproject.org/demos/netgen_mesh.py.html>`__.
+It is possible to construct high-order meshes for a geometry constructed in Netgen.
+In order to do so we need to use the `curve_field` method of a Firedrake `Mesh` object generated from a Netgen mesh.
+In particular, we need to pass the degree of the polynomial field we want to use to parametrise the coordinates of the domain to the `curve_field` method, which will return a `Function` constructed on a DG space for this purpose. ::
+
+   from firedrake import *
+   from netgen.occ import WorkPlane, OCCGeometry
+   import netgen
+   from mpi4py import MPI
+
+   wp = WorkPlane()
+   if COMM_WORLD.rank == 0:
+       for i in range(6):
+           wp.Line(0.6).Arc(0.4, 60)
+       shape = wp.Face()
+       ngmesh = OCCGeometry(shape,dim=2).GenerateMesh(maxh=1.)
+   else:
+       ngmesh = netgen.libngpy._meshing.Mesh(2)
+   mesh = Mesh(Mesh(ngmesh, comm=COMM_WORLD).curve_field(4))
+   VTKFile("output/MeshExample5.pvd").write(mesh)
+
+.. figure:: Example5.png
+   :align: center
+   :alt: Example of a curved mesh of order 4 generated from a geometry described using Open Cascade WorkPlane.
+
+High-order meshes are also supported in three dimensions; we just need to specify the correct dimension when constructing the OCCGeometry object.
+We will now show how to solve the Poisson problem on a high-order mesh, of order 3, for the unit sphere. ::
+
+   from netgen.occ import Sphere, Pnt
+   import netgen
+   from mpi4py import MPI
+
+   if COMM_WORLD.rank == 0:
+       shape = Sphere(Pnt(0,0,0), 1)
+       ngmesh = OCCGeometry(shape,dim=3).GenerateMesh(maxh=1.)
+   else:
+       ngmesh = netgen.libngpy._meshing.Mesh(3)
+   mesh = Mesh(Mesh(ngmesh).curve_field(3))
+   # Solving the Poisson problem
+   VTKFile("output/MeshExample6.pvd").write(mesh)
+   x, y, z = SpatialCoordinate(mesh)
+   V = FunctionSpace(mesh, "CG", 3)
+   f = Function(V).interpolate(1+0*x)
+   u = TrialFunction(V)
+   v = TestFunction(V)
+   a = inner(grad(u), grad(v)) * dx
+   l = inner(f, v) * dx
+
+   sol = Function(V)
+
+   bc = DirichletBC(V, 0.0, [1])
+   A = assemble(a, bcs=bc)
+   b = assemble(l)
+   bc.apply(b)
+   solve(A, sol, b, solver_parameters={"ksp_type": "cg", "pc_type": "lu"})
+
+   VTKFile("output/Sphere.pvd").write(sol)
+
+.. figure:: Example6.png
+   :align: center
+   :alt: The solution of the Poisson problem solved on a mesh of order 3 for the unit sphere.
+
+It is also possible to construct high-order meshes using the `SplineGeometry`, `CSG2d` and `CSG` classes. ::
+
+   from netgen.geom2d import CSG2d, Circle, Rectangle
+   import netgen
+   from mpi4py import MPI
+
+   if COMM_WORLD.rank == 0:
+      geo = CSG2d()
+      circle = Circle(center=(1,1), radius=0.1, bc="curve").Maxh(0.01)
+      rect = Rectangle(pmin=(0,1), pmax=(1,2),
+                       bottom="b", left="l", top="t", right="r")
+      geo.Add(rect-circle)
+      ngmesh = geo.GenerateMesh(maxh=0.2)
+   else:
+       ngmesh = netgen.libngpy._meshing.Mesh(2)
+   mesh = Mesh(Mesh(ngmesh,comm=COMM_WORLD).curve_field(2))
+   VTKFile("output/MeshExample7.pvd").write(mesh)
+
+.. figure:: Example7.png
+   :align: center
+   :alt: Example of a curved mesh of order 2 generated from a geometry described using Netgen CSG2d.