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

作　　者：Yuqing Hu 

机构地区：[1]School of Science,Jinling Institute of Technology,Nanjing,Jiangsu 211169,China

出　　处：《Advances in Applied Mathematics and Mechanics》2021年第6期1558-1574,共17页应用数学与力学进展（英文）

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

摘　　要：Consider the inverse scattering problem in terms of Helmholtz equation.We study a simply connected domain with oblique derivative boundary condition.In the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field data.We propose a Newton method which is based on the nonlinear boundary integral equation.After 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 problem.We conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.

关 键 词：Helmholtz equation oblique derivative problem nonlinear integral equation iterative solution numerics. 

分 类 号：O17[理学—数学]