Wess, M., Kapidani, B., Codecasa, L., & Schöberl, J. (2024). Mass lumping the dual cell method to arbitrary polynomial degree for acoustic and electromagnetic waves. Journal of Computational Physics, 513, Article 113196. https://doi.org/10.1016/j.jcp.2024.113196
E101-03-1 - Forschungsgruppe Computational Mathematics in Engineering
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Zeitschrift:
Journal of Computational Physics
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ISSN:
0021-9991
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Datum (veröffentlicht):
15-Sep-2024
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Umfang:
19
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Verlag:
ACADEMIC PRESS INC ELSEVIER SCIENCE
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Peer Reviewed:
Ja
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Keywords:
Time-domain Maxwell equations; Cell method; Discontinuous Galerkin; Dual grids; Mass lumping; High-order finite elements
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Abstract:
We present a fundamental improvement of a high polynomial degree time domain cell method recently introduced by the last three authors. The published work introduced a method featuring block-diagonal system matrices where the block size and conditioning scaled poorly with respect to polynomial degree. The issue is herein bypassed by the construction of new basis functions exploiting quadrature rule based mass lumping techniques for arbitrary polynomial degrees in two dimensions for the Maxwell equations and the acoustic wave equation in the first order velocity pressure formulation. We characterize the degrees of freedom of all new discrete approximation spaces we employ for differential forms and show that the resulting block diagonal (inverse) mass matrices have block sizes independent of the polynomial degree. We demonstrate on an extensive number of examples how the new technique is applicable and efficient for large scale computations.