volume | PIER Journals

Abstract

This paper presents a numerical approach for solving the magnetic diffusion equation using structure-preserving discretization methods, like Discrete Exterior Calculus (DEC) and Finite Element Exterior Calculus (FEEC). A detailed derivation of the DEC operators is provided, also their geometric foundation and relevance for discretizing differential forms on meshes. Furthermore, the paper includes an explicit introduction to the finite element exterior calculus framework, with a concise overview of the underlying functional spaces. The proposed formulations aim to preserve the topological and metric structure inherent in Maxwell's equation system. Numerical examples illustrate the stability and convergence of both methods, while also comparing their treatment of boundary conditions and discrete Hodge star construction which makes DEC and FEEC solvers spurious free and efficient useful for complex geometries.

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Dr. Lukas Schöppner

Mr. Matthias Friedrich