Abstract

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

中文翻译：

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不可穿透的障碍物和裂缝的逆弹性散射

摘要

本文涉及混合型散射体对时谐弹性波的逆散射问题，它是由不可穿透的障碍物和裂纹的结合给出的。我们开发了改进的因子分解方法，以根据远场数据确定混合型散射体的形状。然而，远场算子$ F $的因式分解与边界积分矩阵算子$ A $有关，这是在直接散射问题的研究中获得的。因此，在第一部分中，我们通过边界积分方程方法展示了直接散射问题的适定性。最后，通过数值算例说明了逆算法的可行性和有效性。