[Le spectre essentiel de lʼopérateur intégral volumique en diffraction électromagnétique par un corps homogène]
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 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 if and only if the relative permeability and permittivity are both different from 0 and −1.
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@article{CRMATH_2012__350_3-4_193_0,
author = {Costabel, Martin and Darrigrand, Eric and Sakly, Hamdi},
title = {The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body},
journal = {Comptes Rendus. Math\'ematique},
pages = {193--197},
publisher = {Elsevier},
volume = {350},
number = {3-4},
year = {2012},
doi = {10.1016/j.crma.2012.01.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.01.017/}
}
TY - JOUR AU - Costabel, Martin AU - Darrigrand, Eric AU - Sakly, Hamdi TI - The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body JO - Comptes Rendus. Mathématique PY - 2012 SP - 193 EP - 197 VL - 350 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.01.017/ DO - 10.1016/j.crma.2012.01.017 LA - en ID - CRMATH_2012__350_3-4_193_0 ER -
%0 Journal Article %A Costabel, Martin %A Darrigrand, Eric %A Sakly, Hamdi %T The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body %J Comptes Rendus. Mathématique %D 2012 %P 193-197 %V 350 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.01.017/ %R 10.1016/j.crma.2012.01.017 %G en %F CRMATH_2012__350_3-4_193_0
Costabel, Martin; Darrigrand, Eric; Sakly, Hamdi. The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body. Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 193-197. doi : 10.1016/j.crma.2012.01.017. http://www.numdam.org/articles/10.1016/j.crma.2012.01.017/
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