https://github.com/inducer/modepy

Modes and nodes for high-order discretizations
https://github.com/inducer/modepy

Last synced: 10 months ago
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Modes and nodes for high-order discretizations

• Host: GitHub
• URL: https://github.com/inducer/modepy
• Owner: inducer
• License: other
• Created: 2013-05-03T22:38:03.000Z (over 12 years ago)
• Default Branch: main
• Last Pushed: 2025-03-14T19:27:46.000Z (10 months ago)
• Last Synced: 2025-03-20T01:02:26.833Z (10 months ago)
• Language: Python
• Size: 1.4 MB
• Stars: 17
• Watchers: 5
• Forks: 7
• Open Issues: 5
• Metadata Files:
  • Readme: README.rst
  • License: LICENSE
  • Citation: CITATION.cff

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README

          
modepy: Basis Functions, Node Sets, Quadratures

===============================================

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    :target: https://zenodo.org/doi/10.5281/zenodo.11105051

``modepy`` helps you create well-behaved high-order discretizations on

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. 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

- Tools to construct new quadrature rules:

    - A basic iterative Gauss-Newton process to optimize/tighten rules

    - Vioreanu-Rokhlin node initial generation based on multiplication operators

- 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 `_

but much has been added beyond that basic functionality.

Resources:

* `documentation `_

* `wiki home page `_

* `source code via git `_