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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 impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the analysis for the generalized impedance boundary conditions, since classical compactness arguments are no longer possible. Our new analysis is based on the use of Rellich-type estimates and boundedness of L2 solution operators. We also discuss some numerical experiments concerning these boundary conditions.

Keywords

Scattering problemsunbounded domainsasymptotic modelsgeneralized impedance boundary conditionshigh conductivity
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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