可穿透无穷曲面反散射问题的非线性积分方程方法  

A nonlinear integral equation method for the inverse scattering problem by penetrable infinite interfaces

作　　者：黎雪健 李雪年 李建樑 LI Xuejian;LI Xuenian;LI Jianliang(School of Mathematics and Statistics,Changsha University of Technology,Changsha 410004,China)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410114

出　　处：《湘潭大学学报（自然科学版）》2022年第5期32-49,共18页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金(12171057);湖南省教育厅项目(21B0299)。

摘　　要：该文研究了二维空间中利用无穷界面上下方近场的测量数据重构可穿透无穷界面位置和形状的反散射问题.基于散射场和透射场的积分表示,发展了求解该问题的非线性积分方程方法,其主要思想是建立散射问题和一个积分系统的等价性,通过求解积分系统来求解反散射问题.最后通过数值实验证明了非线性积分方程方法的有效性.In this paper,the inverse problem of reconstructing the location and shape of a penetrable infinite interface using the measurement data of the near-field above and below the infinite interface in two-dimensional space is studied.Based on the integral representation of the scattered and transmitted fields,develop a nonlinear integral equation method for this problem.The main idea is to establish the equivalence of the scattering problem and an integral system,and solve the inverse scattering problem by solving the integral system.Finally,numerical experiments are carried out to show the validity of the inversion algorithm.

关 键 词：反散射问题 可穿透无穷界面 近场数据 非线性积分方程方法 

分 类 号：O241.8[理学—计算数学]