Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes
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.
Keywords
Cite
@article{arxiv.2506.02429,
title = {Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes},
author = {Luis Wirth},
journal= {arXiv preprint arXiv:2506.02429},
year = {2025}
}
Comments
This report was created as part of a BSc thesis project under the supervision of Prof. Dr. Ralf Hiptmair, for Computational Science and Engineering at ETH Z\"urich