# American Institute of Mathematical Sciences

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November  2013, 7(4): 1123-1138. doi: 10.3934/ipi.2013.7.1123

## The factorization method applied to cracks with impedance boundary conditions

 1 INRIA Saclay Ile de France/Ecole Polytechnique, CMAP, Route de Saclay, 91128 Palaiseau Cedex, France 2 INRIA Saclay Ile de France / CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex

Received  August 2012 Revised  June 2013 Published  November 2013

We use the Factorization method to retrieve the shape of cracks with impedance boundary conditions from farfields associated with incident plane waves at a fixed frequency. This work is an extension of the study initiated by Kirsch and Ritter [Inverse Problems, 16, pp. 89-105, 2000] where the case of sound soft cracks is considered. We address here the scalar problem and provide theoretical validation of the method when the impedance boundary conditions hold on both sides of the crack. We then deduce an inversion algorithm and present some validating numerical results in the case of simply and multiply connected cracks.
Citation: Yosra Boukari, Houssem Haddar. The factorization method applied to cracks with impedance boundary conditions. Inverse Problems & Imaging, 2013, 7 (4) : 1123-1138. doi: 10.3934/ipi.2013.7.1123
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