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A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations

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Abstract

Trefftz methods are known to be very efficient to reduce the numerical pollution when associated to plane wave basis. However, these local basis functions are not adapted to the computation of evanescent modes or corner singularities. In this article, we consider a two dimensional time-harmonic Maxwell system and we propose a formulation which allows to design an electromagnetic Trefftz formulation associated to local Galerkin basis computed thanks to an auxiliary Nédélec finite element method. The results are illustrated with numerous numerical examples. The considered test cases reveal that the short range and long range propagation phenomena are both well taken into account.

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Notes

  1. All along this paper, bold terms refer to either vectors or vectorial functions.

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Authors and Affiliations

  1. ONERA, DTIS, 2 avenue Edouard Belin, 31000, Toulouse, France

    Håkon Sem Fure, Sébastien Pernet & Margot Sirdey

  2. Universite de Pau et des Pays de l’Adour, E2S-UPPA, CNRS, INRIA, équipe Magique 3D, LMAP, Pau, France

    Margot Sirdey & Sébastien Tordeux

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  1. Håkon Sem Fure
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  2. Sébastien Pernet
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  4. Sébastien Tordeux
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Correspondence to Sébastien Tordeux.

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This article is part of the topical collection "Waves 2019–invited papers" edited by Manfred Kaltenbacher and Markus Melenk.

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Fure, H.S., Pernet, S., Sirdey, M. et al. A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations. SN Partial Differ. Equ. Appl. 1, 23 (2020). https://doi.org/10.1007/s42985-020-00024-0

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