On simultaneous identification of a scatterer and its generalized impedance boundary condition

Laurent Bourgeois 1 Nicolas Chaulet 2 Houssem Haddar 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We consider the inverse scattering problem consisting in the identification of both an obstacle and two functional coefficients of a generalized boundary condition prescribed on its boundary, from far--fields due to several plane waves. After proving a uniqueness result for such inverse problem, we define and compute appropriate derivative of the far--field with respect to an obstacle with non constant impedances. A steepest descent method is then applied to retrieve both the obstacle and the functional impedances from the measured far--fields. The feasability of the method is demonstrated with the help of some 2D numerical experiments.
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Laurent Bourgeois, Nicolas Chaulet, Houssem Haddar. On simultaneous identification of a scatterer and its generalized impedance boundary condition. [Research Report] RR-7645, INRIA. 2011, pp.28. ⟨inria-00599567⟩

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