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Application of the linear sampling method to identify cracks with impedance boundary conditions. (English) Zbl 1267.78036
Summary: 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, Inverse Probl. 19, No. 2, 279–295 (2003; Zbl 1171.35487)] 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.

MSC:
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
Citations:
Zbl 1171.35487
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