Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes

Luis Wirth

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arXiv · 2506.02429

Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes

Luis Wirth

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Abstract

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.

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Luis Wirth. 2025-06-03. Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes. https://arxiv.org/abs/2506.02429

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