Application of the linear sampling method to identify cracks with impedance boundary conditions
DOI: 10.1080/17415977.2012.686997
Title: Application of the linear sampling method to identify cracks with impedance boundary conditions
Journal Title: Inverse Problems in Science and Engineering
Volume: Volume 21
Issue: Issue 2
Publication Date: March 2013
Start Page: 210
End Page: 234
Published online: 8 Feb 2013
ISSN: 1741-5977
Author: Fahmi Ben Hassena, Yosra Boukariab* & Houssem Haddarb
Affiliations:
a ENIT-LAMSIN , Université de Tunis el-Manar , BP 37, 1002 Tunis , Tunisia
b INRIA Saclay Ile de France/CMAP Ecole Polytechnique , Route de Saclay, 91128 Palaiseau Cedex , France
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.
Accepted: 17 Apr 2012

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