An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media  

作　　者：Haixia Dong Wenjun Ying Jiwei Zhang 

机构地区：[1]MOE-LCSM,School ofMathematics and Statistics,Hunan Normal University,Changsha,Hunan 410081,P.R.China [2]School of Mathematical Sciences,MOE-LSC and Institute of Natural Sciences,Shanghai Jiao Tong University,Minhang,Shanghai 200240,P.R.China [3]School of Mathematics and Statistics,Hubei Key Laboratory of Computational Science,Wuhan University,Wuhan 430072,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第2期541-564,共24页高等学校计算数学学报（英文版）

基　　金：supported by the NSFC(Grant No.12001193),by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.20B376);by the Key Projects of Hunan Provincial Department of Education(Grant No.22A033);by the Changsha Municipal Natural Science Foundation(Grant Nos.kq2014073,kq2208158).W.Ying is supported by the NSFC(Grant No.DMS-11771290);by the Science Challenge Project of China(Grant No.TZ2016002);by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA25000400).J.Zhang was partially supported by the National Natural Science Foundation of China(Grant No.12171376);by the Fundamental Research Funds for the Central Universities(Grant No.2042021kf0050);by the Natural Science Foundation of Hubei Province(Grant No.2019CFA007).

摘　　要：Boundary integral equations provide a powerful tool for the solution of scattering problems.However,often a singular kernel arises,in which case the standard quadratures will give rise to unavoidable deteriorations in numerical precision,thus special treatment is needed to handle the singular behavior.Especially,for inhomogeneous media,it is difficult if not impossible to find out an analytical expression for Green’s function.In this paper,an efficient fourth-order accurate Cartesian grid-based method is proposed for the two-dimensional Helmholtz scattering and transmission problems with inhomogeneous media.This method provides an alternative approach to indirect integral evaluation by solving equivalent interface problems on Cartesian grid with a modified fourth-order accurate compact finite difference scheme and a fast Fourier transform preconditioned conjugate gradient(FFT-PCG)solver.A remarkable point of this method is that there is no need to know analytical expressions for Green’s function.Numerical experiments are provided to demonstrate the advantage of the current approach,including its simplicity in implementation,its high accuracy and efficiency.

关 键 词：Transmission problem inhomogeneous media Cartesian grid-based method modified fourth-order compact difference scheme fast Fourier transform preconditioned conjugate gradient solver. 

分 类 号：O157.5[理学—数学]