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An arbitrary-order Cell Method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations

Authors :
Bernard Kapidani
Lorenzo Codecasa
Joachim Schöberl
Source :
Journal of Computational Physics. 433:110184
Publication Year :
2021
Publisher :
Elsevier BV, 2021.

Abstract

We introduce a new numerical method for the time-dependent Maxwell equations on unstructured meshes in two space dimensions. This relies on the introduction of a new mesh, which is the barycentric-dual cellular complex of the starting simplicial mesh, and on approximating two unknown fields with integral quantities on geometric entities of the two dual complexes. A careful choice of basis-functions yields cheaply invertible block-diagonal system matrices for the discrete time-stepping scheme. The main novelty of the present contribution lies in incorporating arbitrary polynomial degree in the approximating functional spaces, defined through a new reference cell. The presented method, albeit a kind of Discontinuous Galerkin approach, requires neither the introduction of user-tuned penalty parameters for the tangential jump of the fields, nor numerical dissipation to achieve stability. In fact an exact electromagnetic energy conservation law for the semi-discrete scheme is proved and it is shown on several numerical tests that the resulting algorithm provides spurious-free solutions with the expected order of convergence.<br />34 pages, 14 figures, submitted

Details

ISSN :
00219991
Volume :
433
Database :
OpenAIRE
Journal :
Journal of Computational Physics
Accession number :
edsair.doi.dedup.....14369e46f408457152de7be298ccabe5