Asymptotic models for scattering from unbounded media with high conductivity
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 6, p. 1295-1317

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.

DOI : https://doi.org/10.1051/m2an/2010029
Classification:  35C20,  78A40
Keywords: scattering problems, unbounded domains, asymptotic models, generalized impedance boundary conditions, high conductivity
@article{M2AN_2010__44_6_1295_0,
     author = {Haddar, Houssem and Lechleiter, Armin},
     title = {Asymptotic models for scattering from unbounded media with high conductivity},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {6},
     year = {2010},
     pages = {1295-1317},
     doi = {10.1051/m2an/2010029},
     zbl = {1206.35066},
     mrnumber = {2769059},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_6_1295_0}
}
Haddar, Houssem; Lechleiter, Armin. Asymptotic models for scattering from unbounded media with high conductivity. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 6, pp. 1295-1317. doi : 10.1051/m2an/2010029. http://www.numdam.org/item/M2AN_2010__44_6_1295_0/

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