Approximate transmission conditions for time-harmonic Maxwell equations in a domain with thin layer

Victor Peron 1 Clair Poignard 2, 3, *
* Corresponding author
2 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : We study the behavior of the electromagnetic field in a biological cell modelized by a medium surrounded by a thin layer and embedded in an ambient medium. We derive approximate transmission conditions in order to replace the membrane by these conditions on the boundary of the interior domain. Our approach is essentially geometric and based on a suitable change of variables in the thin layer. Few notions of differential calculus are given in order to obtain our asymptotic conditions in a simple way. This paper extends to time-harmonic Maxwell equations the previous works of C.Poignard. Asymptotic transmission conditions at any order are given in Appendix~1.
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Victor Peron, Clair Poignard. Approximate transmission conditions for time-harmonic Maxwell equations in a domain with thin layer. [Research Report] RR-6775, INRIA. 2008, pp.37. ⟨inria-00347971v3⟩

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