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Revamp README to better advertise capabilities
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inducer committed Jun 7, 2024
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modepy: Basis Functions and Node Sets for Interpolation
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modepy: Basis Functions, Node Sets, Quadratures
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.. image:: https://gitlab.tiker.net/inducer/modepy/badges/main/pipeline.svg
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simplices (i.e. segments, triangles and tetrahedra) and tensor products of
simplices (i.e. squares, cubes, prisms, etc.). These are a key building block
for high-order unstructured discretizations, as often used in a finite
element context. It closely follows the approach taken in the book
element context. Features include:

- Support for simplex and tensor product elements in any dimension.
- Orthogonal bases:
- Jacobi polynomials with derivatives
- Orthogonal polynomials for simplices up to 3D and tensor product elements
and their derivatives.
- All bases permit symbolic evaluation, for code generation.
- Access to numerous quadrature rules:
- Jacobi-Gauss, Jacobi-Gauss-Lobatto in 1D
(includes Legendre, Chebyshev, ultraspherical, Gegenbauer)
- Clenshaw-Curtis and Fejér in 1D
- Grundmann-Möller on the simplex
- Xiao-Gimbutas on the simplex
- Vioreanu-Rokhlin on the simplex
- Jaśkowiec-Sukumar on the tetrahedron
- Witherden-Vincent on the hypercube
- Generic tensor products built on the above, e.g. for prisms and hypercubes
- Matrices for FEM, usable across all element types:
- generalized Vandermonde,
- mass matrices (including lumped diagonal),
- face mass matrices,
- differentiation matrices, and
- resampling matrices.
- Objects to represent 'element shape' and 'function space',
generic node/mode/quadrature retrieval based on them.

Its roots closely followed the approach taken in the book

Hesthaven, Jan S., and Tim Warburton. "Nodal Discontinuous Galerkin Methods:
Algorithms, Analysis, and Applications". 1st ed. Springer, 2007.
`Book web page <http://nudg.org>`_

but much has been added beyond that basic functionality.

Resources:

* `documentation <http://documen.tician.de/modepy>`_
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