Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908413085089792 |
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| author | Wirth, Luis |
| author_facet | Wirth, Luis |
| contents | This thesis presents the development of a novel finite element library in Rust based on the principles of Finite Element Exterior Calculus (FEEC). The library solves partial differential equations formulated using differential forms on abstract, coordinate-free simplicial complexes in arbitrary dimensions, employing an intrinsic Riemannian metric derived from edge lengths via Regge Calculus. We focus on solving elliptic Hodge-Laplace eigenvalue and source problems on the nD de Rham complex. We restrict ourselves to first-order Whitney basis functions. The implementation is partially verified through convergence studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes Wirth, Luis Numerical Analysis Analysis of PDEs Algebraic Topology Differential Geometry Functional Analysis This thesis presents the development of a novel finite element library in Rust based on the principles of Finite Element Exterior Calculus (FEEC). The library solves partial differential equations formulated using differential forms on abstract, coordinate-free simplicial complexes in arbitrary dimensions, employing an intrinsic Riemannian metric derived from edge lengths via Regge Calculus. We focus on solving elliptic Hodge-Laplace eigenvalue and source problems on the nD de Rham complex. We restrict ourselves to first-order Whitney basis functions. The implementation is partially verified through convergence studies. |
| title | Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes |
| topic | Numerical Analysis Analysis of PDEs Algebraic Topology Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2506.02429 |