A Transmission Problem in Electromagnetism with a Singular Interface

Gabriel Caloz 1 Monique Dauge 1 Erwan Faou 1, 2 Victor Peron 3, 4 Clair Poignard 3, 4
2 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
3 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : We investigate a scalar interface problem originating from a skin effect model in electromagnetism. The problem is posed in a domain made of two materials, dielectric and highly conducting. We focus on the case of a corner interface between the two subdomains. In this context, we present a multi-scale expansion for the solution of the transmission problem at high conductivity. For a smooth interface, boundary layers are present close to the surface of the conductor. For a corner interface, singularities appear in the dielectric part, and generate corner layers in the conducting part. Numerical simulations will be presented. This work is a collaboration with G. Caloz, M. Dauge, E. Faou, and C. Poignard.
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https://hal.inria.fr/inria-00528523
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Submitted on : Friday, October 22, 2010 - 7:19:11 PM
Last modification on : Wednesday, June 19, 2019 - 11:42:09 AM
Long-term archiving on : Sunday, January 23, 2011 - 2:41:31 AM

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  • HAL Id : inria-00528523, version 1

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Gabriel Caloz, Monique Dauge, Erwan Faou, Victor Peron, Clair Poignard. A Transmission Problem in Electromagnetism with a Singular Interface. 6th Singular Days on Asymptotic Methods for PDEs, Apr 2010, Berlin, Germany. ⟨inria-00528523⟩

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