×

zbMATH — the first resource for mathematics

The factorization method applied to cracks with impedance boundary conditions. (English) Zbl 1302.35430
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.

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
Citations:
Zbl 0968.35129
PDF BibTeX XML Cite
Full Text: DOI