Two-scale simulation of Maxwell's equations

Hyam Abboud (1) , Sébastien Jund (2) , Stéphanie Salmon (2) , Eric Sonnendrücker (2) , Hamdi Zorgati (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 IRMA - Institut de Recherche Mathématique Avancée
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Analyse numérique [math.NA]

Hyam Abboud, Sébastien Jund, Stéphanie Salmon, Eric Sonnendrücker, Hamdi Zorgati. Two-scale simulation of Maxwell's equations. Feb 2007, pp.211-223, ⟨10.1051/proc:2007001⟩. ⟨hal-00139181⟩