formoniq

This library is being developed as part of the bachelor thesis of Luis Wirth at ETH Zurich.

Formoniq is a Rust implementation of the Finite Element Method (FEM) for solving partial differential equations (PDEs) in arbitrarily high spatial dimensions, using the theory of Exterior Calculus of Differential Forms.

This particular formulation of FEM is known as Finite Element Exterior Calculus (FEEC). It allows for a unified treatment of scalar- and vector-valued PDEs by treating general differential k-forms as solutions.

This framework unifies multiple Finite Element Spaces (Lagrangian, Raviart-Thomas, and Nédélec) into one: the FE space of Whitney forms, by identifying scalar and vector fields through Hodge duality. Additionally, it extends these spaces from 3D to higher dimensions.

Our primary focus is solving elliptic Hodge-Laplace problems on simplicial meshes with first-order Whitney forms.

Example

The following animation shows a solution to the wave equation, solved using formoniq.

It's the result of the wave example and the corresponding wave plot script.