This repository contains the Typst source files for the Bachelor's Thesis of Luis Wirth under the supervision of Prof. Dr. Ralf Hiptmair, for Computational Science and Engineering at ETH Zürich. Compiled thesis as PDF available under GitHub releases. For the implementation itself, see Formoniq.
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 verified through convergence studies using manufactured solutions, demonstrating expected theoretical accuracy.