The factorization method for cracks in elastic scattering
Jun Guo Qinghua Wu Guozheng Yan

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
The factorization method for a partially coated cavity in inverse scattering
Qinghua Wu Guozheng Yan
We consider the interior inverse scattering problem of recovering the shape of an impenetrable partially coated cavity. The scattered fields incited by point source waves are measured on a closed curve inside the cavity. We prove the validity of the factorization method for reconstructing the shape of the cavity. However, we are not able to apply the basic theorem introduced by Kirsch and Grinberg to treat the key operator directly, and some auxiliary operators have to be considered. In this paper, we provide theoretical validation of the factorization method to the problem, and some numerical results are presented to show the viability of our method.
keywords: inverse scattering problem Factorization method partially coated acoustic and electromagnetic wave. cavity

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