Geodesic
Two-scale simulation of Maxwell's equations
Hyam Abboud1 ; Sébastien Jund2 ; Stéphanie Salmon2 ; Eric Sonnendrücker2 ; Hamdi Zorgati3
1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (Paris 6), Boîte Courrier 187, 4, place Jussieu, 75252 Paris cedex 05, France. Faculté des Sciences, Université Saint-Joseph,B.P 11-514 Riad El Solh, Beyrouth 1107 2050, Liban.
2 Institut de Recherche Mathématiques Avancées, Université Louis Pasteur, Strasbourg, France.
3 CEREMADE, CNRS UMR 7534, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris, France.
ESAIM. Proceedings, Tome 16 (2007), pp. 211-223.

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We develop a numerical method for solving Maxwell's equations on a grid involving zones with cells of very different sizes, in order for example to compute sources coming from particles which need to be resolved on a very fine grid. The method is based on domain decomposition techniques which lead us to introduce two auxiliary problems and show theoretically how they allow us to calculate the solution of the initial problem. These two auxiliary problems are discretized using Edge Finite Elements introduced by Nedelec on two different scales which introduce some errors that we correct by setting to zero an operator we know has to be zero in the theoretical study.

DOI : 10.1051/proc:2007001

Hyam Abboud 1 ; Sébastien Jund 2 ; Stéphanie Salmon 2 ; Eric Sonnendrücker 2 ; Hamdi Zorgati 3

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (Paris 6), Boîte Courrier 187, 4, place Jussieu, 75252 Paris cedex 05, France. Faculté des Sciences, Université Saint-Joseph,B.P 11-514 Riad El Solh, Beyrouth 1107 2050, Liban.
2 Institut de Recherche Mathématiques Avancées, Université Louis Pasteur, Strasbourg, France.
3 CEREMADE, CNRS UMR 7534, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris, France. 
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     title = {Two-scale simulation of {Maxwell's} equations},
     journal = {ESAIM. Proceedings},
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Hyam Abboud; Sébastien Jund; Stéphanie Salmon; Eric Sonnendrücker; Hamdi Zorgati. Two-scale simulation of Maxwell's equations. ESAIM. Proceedings, Tome 16 (2007), pp. 211-223. doi : 10.1051/proc:2007001. http://geodesic.mathdoc.fr/articles/10.1051/proc:2007001/

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