2020/02/20 by Bernard Kapidani, Joachim Schöberl, Kapidani, Bernard +1 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #65M60 #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Basis function #Block matrix #Computational Physics (physics.comp-ph) #Computer science #Covariant transformation #Curl (programming language) #Diagonal #Diagonal matrix #Discontinuous Galerkin method #Eigenvalues and eigenvectors #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Finite element method #Galerkin method #Geometry #Mass matrix #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Maxwell's equations #Numerical Analysis (math.NA) #Numerical methods in engineering #Physics #Simplex #cs.NA #math.NA #msc:65M60 #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.2002.08733
published in arXiv (Cornell University) (Cornell University) · 9 pages (double column), 7 figures
arxiv created 2020/02/20 · openalex publication_date 2020/02/20 · arxiv updated 2020/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Discontinuous Galerkin (DG) Finite Element Method (FEM) approach for the 3D time dependent Maxwell equations in unbounded domains is presented. The method (implemented in the FEM library NGsolve) is based on the covariant transformation of a modal orthogonal polynomial basis, originally defined on a reference simplex. The approach leads to an explicit time stepping scheme for which the mass matrix to be inverted is at most d × d block-diagonal (in d = 2,3 spatial dimensions) while the matrix which discretizes the curl operators on the right-hand side of the system is a small reference matrix, independent from geometric properties of mesh elements. Furthermore, we show that the introduced optimizations are preserved when unbounded domains are also included in the formulation through a complex-stretching based approach.