Integral Equation Method for Inverse Scattering Problem from the Far-Field Data

作     者：Yuqing Hu 

作者机构：School of ScienceJinling Institute of TechnologyNanjingJiangsu 211169China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2021年第13卷第6期

页      面：1558-1574页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：foundation of Jinling Institute of Technology(No.jit-b-201524) the Science Foundation of Jinling Institute of Technology(No.Jit-fhxm-201809) 

主　　题：Helmholtz equation oblique derivative problem nonlinear integral equation iterative solution numerics. 

摘      要：Consider the inverse scattering problem in terms of Helmholtz *** study a simply connected domain with oblique derivative boundary *** the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field *** propose a Newton method which is based on the nonlinear boundary integral *** computing the Fr´echet derivatives with respect to the unknown boundary,the nonlinear equation is transformed to its linear form,then we show the iteration scheme for the inverse *** conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.