The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body

Martin Costabel; Eric Darrigrand; Hamdi Sakly

doi:10.1016/j.crma.2012.01.017

Partial Differential Equations/Functional Analysis

The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body
[Le spectre essentiel de lʼopérateur intégral volumique en diffraction électromagnétique par un corps homogène]

Présenté par : Olivier Pironneau

Martin Costabel ¹ ; Eric Darrigrand ¹ ; Hamdi Sakly ¹

¹ IRMAR, université de Rennes 1, campus de Beaulieu, 35042 Rennes, France

Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 193-197.

Résumé
Abstract

Nous étudions le spectre essentiel de lʼopérateur intégral volumique fortement singulier décrivant la diffraction dʼondes électromagnétiques. Dans le cas de coefficients constants par morceaux et pour une interface régulière nous démontrons quʼil est fini et que lʼopérateur intégral est Fredholm dʼindice zéro dans $H (curl)$ si et seulement si les perméabilité et permittivité relatives sont différentes de 0 et de −1.

We study the strongly singular volume integral operator that describes the scattering of time-harmonic electromagnetic waves. For the case of piecewise constant material coefficients and smooth interfaces, we determine the essential spectrum. We show that it is a finite set and that the operator is Fredholm of index zero in $H (curl)$ if and only if the relative permeability and permittivity are both different from 0 and −1.

Reçu le : 2011-11-24
Accepté le : 2012-01-23
Publié le : 2012-02-01

DOI : 10.1016/j.crma.2012.01.017

Affiliations des auteurs :

Martin Costabel ¹ ; Eric Darrigrand ¹ ; Hamdi Sakly ¹

¹ IRMAR, université de Rennes 1, campus de Beaulieu, 35042 Rennes, France

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     title = {The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body},
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Martin Costabel; Eric Darrigrand; Hamdi Sakly. The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 193-197. doi : 10.1016/j.crma.2012.01.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.017/

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