Reconstruction of discontinuous parameters in a second order impedance boundary operator

Slim Chaabane 1, 2 Bilel Charfi 2, 1 Houssem Haddar 3
3 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We consider the inverse problem of retrieving the coefficients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the differentiability of the Khon-Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of unknown number of discontinuity points.
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Slim Chaabane, Bilel Charfi, Houssem Haddar. Reconstruction of discontinuous parameters in a second order impedance boundary operator. Inverse Problems, IOP Publishing, 2016, 32 (10), ⟨10.1088/0266-5611/32/10/105004⟩. ⟨hal-01349696⟩

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