Computing estimates of material properties from transmission eigenvalues

Giovanni Giorgi 1, 2 Houssem Haddar 1
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : This work is motivated by inverse scattering problems, those problems where one is interested in reconstructing the shape and the material properties of an inclusion from electromagnetic farfield measurements. More precisely, we are interested in complementing the so-called sampling methods by providing an estimate of the material properties of the sought inclusion. We use for this purpose a measure of the first transmission eigenvalue. Our method is then based on computing the desired estimate by reformulating the so-called interior transmission eigenvalue problem as an eigenvalue problem for the material coefficients. We will restrict ourselves to the two-dimensional setting of the problem and treat the cases of both transverse electric and transverse magnetic polarizations. We present a number of numerical experiments that validate our methodology for homogeneous and inhomogeneous inclusions and backgrounds. We also treat the case of a background with absorption and the case of scatterers with multiple connected components of different refractive indices.
Type de document :
Article dans une revue
Inverse Problems, IOP Publishing, 2012, 28 (5), pp.055009, 23. 〈10.1088/0266-5611/28/5/055009〉
Liste complète des métadonnées
Contributeur : Houssem Haddar <>
Soumis le : dimanche 21 octobre 2012 - 22:58:54
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14




Giovanni Giorgi, Houssem Haddar. Computing estimates of material properties from transmission eigenvalues. Inverse Problems, IOP Publishing, 2012, 28 (5), pp.055009, 23. 〈10.1088/0266-5611/28/5/055009〉. 〈hal-00743910〉



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