Electromagnetic inverse shape problem for coated obstacles

Nicolas Chaulet 1 Houssem Haddar 1
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We address the inverse problem of retrieving the shape of an obstacle with impedance in the form of a surface wave operator using the knowledge of electromagnetic scattering amplitude at a fixed frequency. We prove unique reconstructions from infinitely many measures. We then provide a characterization of the scattering amplitude derivative with respect to the obstacle shape. This derivative includes the case of shape dependent impedance parameters. We then employ a gradient-descent algorithm with H 1 boundary regularisation of the descent direction to numerically solve the inverse problem. The procedure is validated for three dimensional geometries using synthetic data.
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Nicolas Chaulet, Houssem Haddar. Electromagnetic inverse shape problem for coated obstacles. Advances in Computational Mathematics, Springer Verlag, 2014, pp.21. ⟨hal-01110003⟩

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