The factorization method for cracks in elastic scattering
Jun Guo Qinghua Wu Guozheng Yan
Inverse Problems & Imaging 2018, 12(2): 349-371 doi: 10.3934/ipi.2018016

This paper is concerned with the scattering problems of a crack with Dirichlet or mixed impedance boundary conditions in two dimensional isotropic and linearized elasticity. The well posedness of the direct scattering problems for both situations are studied by the boundary integral equation method. The inverse scattering problems we are dealing with are the shape reconstruction of the crack from the knowledge of far field patterns due to the incident plane compressional and shear waves. We aim at extending the well known factorization method to crack determination in inverse elastic scattering, although it has been proved valid in acoustic and electromagnetic scattering, electrical impedance tomography and so on. The numerical examples are presented to illustrate the feasibility of this method.

keywords: Crack factorization method elastic scattering

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