Geodesic
Ultra-weak variational formulation for heterogeneous Maxwell problem in the context of high performance computing
Sebastien Pernet1 ; Margot Sirdey2, 1 ; Sebastien Tordeux2
1 DTIS, ONERA
2 Makutu, EPC INRIA, e2s-UPPA, LMAP UMR CNRS 5142
ESAIM. Proceedings, Tome 75 (2023), pp. 96-121.

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Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks to a left preconditioner. The considered numerical cases illustrate the performance of this basis reduction, which leads to the consideration of an industrial case of more than 750 millions of degrees of freedom.
DOI : 10.1051/proc/202375096

Sebastien Pernet 1 ; Margot Sirdey 2, 1 ; Sebastien Tordeux 2

1 DTIS, ONERA
2 Makutu, EPC INRIA, e2s-UPPA, LMAP UMR CNRS 5142 
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     title = {Ultra-weak variational formulation for heterogeneous {Maxwell} problem in the context of high performance computing},
     journal = {ESAIM. Proceedings},
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     doi = {10.1051/proc/202375096},
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Sebastien Pernet; Margot Sirdey; Sebastien Tordeux. Ultra-weak variational formulation for heterogeneous Maxwell problem in the context of high performance computing. ESAIM. Proceedings, Tome 75 (2023), pp. 96-121. doi : 10.1051/proc/202375096. http://geodesic.mathdoc.fr/articles/10.1051/proc/202375096/

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