Thin Layer Models For Electromagnetism

Marc Durufle 1, 2 Victor Péron 1, 3 Clair Poignard 2, 4
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
4 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer. These models appear as first order approximations of the electromagnetic field. They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer, that makes possible to replace the thin layer by approximate conditions. We present the advantages and the drawbacks of several approximations together with numerical validations and simulations. The main motivation of this work concerns the computation of electromagnetic field in biological cells. The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane, which provides a specific behavior of the electromagnetic field at low frequencies.
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Marc Durufle, Victor Péron, Clair Poignard. Thin Layer Models For Electromagnetism. Communications in Computational Physics, Global Science Press, 2014, 16, pp.213-238. ⟨10.4208/cicp.120813.100114a ⟩. ⟨hal-00918634⟩

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