This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method.

翻译：本文关注于一个逆弹性散射问题，即识别嵌入在充满均匀各向同性弹性介质的开放空间中的未知刚性障碍物。设计了一种基于边界条件的牛顿型迭代方法来识别障碍物的边界曲线。基于亥姆霍兹分解和傅里叶-贝塞尔展开，我们显式地推导了每个迭代曲线上的近似散射场及其导数。对所提方法给出了严格的数学证明。数值算例验证了所提方法的有效性。