Inverse Elastic Scattering for Multiscale Rigid Bodies with a Single Far-Field Pattern
Inverse Elastic Scattering for Multiscale Rigid Bodies with a Single Far-Field Pattern
复制标题
具有单一远场模式的多尺度刚体的逆弹性散射
DOI：
10.1137/130944187
复制
发表时间：
2014
影响因子：
2.1
通讯作者：
Sun Hongpeng
中科院分区：
文献类型：
--
作者：
Hu Guanghui;Li Jingzhi;Liu Hongyu;Sun Hongpeng
我们开发了三种逆弹性散射方案，分别用于定位多个小型、扩展和多尺度刚体。所提出的方法有一些突出的和有前途的功能。这些方案的核心是某些指示函数，这些指示函数是通过仅使用压力（纵向）波或剪切（横向）波或总波场的单个远场图案来获得的。虽然逆散射问题是已知的非线性和不适定的，所提出的重建方法是完全“直接”的，没有反演。因此，该方法对噪声数据非常有效和鲁棒。在我们的研究中，严格的数学证明和数值模拟。
We develop three inverse elastic scattering schemes for locating multiple small, extended, and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of these schemes are certain indicator functions, which are obtained by using only a single far-field pattern of the pressure (longitudinal) wave, or the shear (transversal) wave, or the total wave field. Though the inverse scattering problem is known to be nonlinear and ill-posed, the proposed reconstruction methods are totally “direct," and there are no inversions involved. Hence, the methods are very efficient and robust against noisy data. Both rigorous mathematical justifications and numerical simulations are presented in our study.