Boukari, Yosra; Haddar, Houssem The factorization method applied to cracks with impedance boundary conditions. (English) Zbl 1302.35430 Inverse Probl. Imaging 7, No. 4, 1123-1138 (2013). Summary: 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 A. Kirsch and S. Ritter [Inverse Probl. 16, No. 1, 89–105 (2000; Zbl 0968.35129)] 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. Cited in 27 Documents MSC: 35R30 Inverse problems for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory Keywords:inverse scattering problems; sampling methods for cracks; impedance boundary conditions; the factorization method Citations:Zbl 0968.35129 PDFBibTeX XMLCite \textit{Y. Boukari} and \textit{H. Haddar}, Inverse Probl. Imaging 7, No. 4, 1123--1138 (2013; Zbl 1302.35430) Full Text: DOI