Computing estimates on material properties from transmission eigenvalues

Giovanni Giorgi 1, * Houssem Haddar 2
* Corresponding author
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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 farfields measurements. More precisely we are interested in complementing the so called sampling methods, (those methods that enables one to reconstruct just the geometry of the scatterer), by providing estimates on the material properties. We shall use for that purpose the so-called transmission eigenvalues. Our method is based on reformulating the so-called interior transmission eigenvalue problem into an eigenvalue problem for the material coefficients. We shall restrict ourselves to the two dimensional setting of the problem and treat the cases of both TE and TM 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 indexes.
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Giovanni Giorgi, Houssem Haddar. Computing estimates on material properties from transmission eigenvalues. [Research Report] RR-7729, INRIA. 2011. ⟨inria-00619232⟩

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