2025/06/03 by Luis Wirth, Wirth, Luis
Computer Science · #Graph Theory and Algorithms #Computational Geometry and Mesh Generation #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2506.02429
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.