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Asymptotic models for scattering from unbounded media with high conductivity

Published online by Cambridge University Press:  15 April 2010

Houssem Haddar and
Armin Lechleiter
Houssem Haddar
Affiliation:
INRIA Saclay Île-de-France/École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France. haddar@cmap.polytechnique.fr; alechle@cmap.polytechnique.fr
Armin Lechleiter
Affiliation:
INRIA Saclay Île-de-France/École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France. haddar@cmap.polytechnique.fr; alechle@cmap.polytechnique.fr
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Abstract

We analyze the accuracy and well-posedness of generalized impedanceboundary value problems in the framework of scattering problemsfrom unbounded highly absorbing media. We restrict ourselves in this first workto the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficultiesin the analysis for the generalized impedance boundary conditions, sinceclassical compactness arguments are no longer possible. Our new analysisis based on the use of Rellich-type estimates and boundedness of L2solution operators. We also discuss some numerical experimentsconcerning these boundary conditions.

Keywords

Scattering problemsunbounded domainsasymptotic modelsgeneralized impedance boundary conditionshigh conductivity

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 6 , November 2010, pp. 1295 - 1317
Copyright
© EDP Sciences, SMAI, 2010

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