Application of the linear sampling method to identify cracks with impedance boundary conditions

Fahmi Ben Hassen 1 Yosra Boukari 1, 2 Houssem Haddar 2
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : We use the linear sampling method (LSM) to identify a crack with impedance boundary conditions from far-field measurements at a fixed frequency. This article extends the work of Cakoni-Colton [F. Cakoni and D. Colton, The linear sampling method for cracks, Inverse Probl. 19 (2003), pp. 279-295] where LSM has been used to reconstruct a crack with impedance boundary conditions on one side of the crack and a Dirichlet boundary condition on the other one. In addition, we present two methods to also reconstruct the impedance parameters whence the geometry is known. The first one is based on the interpretation of the indicator function produced by the LSM, while the second one is a natural approach based on the integral representation of the far-field in terms of densities on the crack geometry. The performance of the different reconstruction methods is illustrated through numerical examples in a 2D setting of the scattering problem.
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Article dans une revue
Inverse Problems in Science and Engineering, Taylor & Francis, 2012, pp.1-25. 〈10.1080/17415977.2012.686997〉
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https://hal.inria.fr/hal-00743816
Contributeur : Houssem Haddar <>
Soumis le : samedi 20 octobre 2012 - 21:20:41
Dernière modification le : jeudi 10 mai 2018 - 02:05:48

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Fahmi Ben Hassen, Yosra Boukari, Houssem Haddar. Application of the linear sampling method to identify cracks with impedance boundary conditions. Inverse Problems in Science and Engineering, Taylor & Francis, 2012, pp.1-25. 〈10.1080/17415977.2012.686997〉. 〈hal-00743816〉

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