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Thin Layer Models for Electromagnetism

Published online by Cambridge University Press:  03 June 2015

Marc Duruflé ,
Victor Péron  and
Clair Poignard
Marc Duruflé*
Affiliation:
Team Magique-3D, INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251 & Université de Bordeaux1, 351 cours de la Libération, 33405 Talence Cedex, France
Victor Péron*
Affiliation:
Team Magique-3D, INRIA Bordeaux-Sud-Ouest, LMAP CNRS UMR 5142 & Université de Pau et des Pays de l’Adour, France
Clair Poignard*
Affiliation:
Team MC2, INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251 & Université de Bordeaux1, 351 cours de la Libération, 33405 Talence Cedex, France
*
Email:marc.durufle@inria.fr
Email:victor.peron@inria.fr
Corresponding author.Email:clair.poignard@inria.fr
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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.

Keywords

34E0534E1058J37Asymptoticstime-harmonic Maxwell’s equationsfinite element methodedge elements.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 1 , July 2014 , pp. 213 - 238
Copyright
Copyright © Global Science Press Limited 2014

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