Modélisation mathématique de phénomènes électromagnétiques dans des matériaux à fort contraste

Abstract : This work consists in the study of transmission problems of electromagnetic waves in high contrast media, like a highly conducting body embedded in an insulating medium. We perform an accurate analysis of the skin effect by the way of the asymptotic analysis and numerical simulations. We derive a scaled asymptotic expansion in the three dimensionnal cae of the harmonic Maxwell equations with high conductivity. We prove uniform estimates with respect to the high conductivity in polyhedral domains with Lipschitz boundaries. These estimates motive the study of a scalar transmission problem, in which case a priori estimates are obtained by the way of an asymptotic expansion. Numerical simulations in axisymetric geometry highlight the skin effect and show the expansion accuracy.

Next, 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.
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https://tel.archives-ouvertes.fr/tel-00421736
Contributor : Victor Péron <>
Submitted on : Friday, October 2, 2009 - 6:38:10 PM
Last modification on : Wednesday, June 19, 2019 - 11:42:08 AM
Long-term archiving on : Tuesday, October 16, 2012 - 11:45:10 AM

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  • HAL Id : tel-00421736, version 1

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Victor Peron. Modélisation mathématique de phénomènes électromagnétiques dans des matériaux à fort contraste. Mathématiques [math]. Université Rennes 1, 2009. Français. ⟨tel-00421736⟩

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