Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media  

作　　者：Yu Du Haijun Wu 

机构地区：[1]School of Mathematics and Computational science,Xiangtan University,Hunan 411105,P.R.China [2]Department of Mathematics,Nanjing University,Jiangsu,210093,P.R.China

出　　处：《Communications in Computational Physics》2023年第10期1247-1276,共30页计算物理通讯（英文）

基　　金：funded by the Natural Science Foundation of China under grants 12071401,12171238,12261160361,and 11525103;the science and technology innovation Program of Hunan Province 2022RC1191.

摘　　要：We extend the pure source transfer domain decomposition method(PSTDDM)to solve the perfectly matched layer approximation of Helmholtz scattering problems in heterogeneous media.We first propose some new source transfer operators,and then introduce the layer-wise and block-wise PSTDDMs based on these operators.In particular,it is proved that the solution obtained by the layer-wise PSTDDM in R2 coincides with the exact solution to the heterogeneous Helmholtz problem in the computational domain.Second,we propose the iterative layer-wise and blockwise PSTDDMs,which are designed by simply iterating the PSTDDM alternatively over two staggered decompositions of the computational domain.Finally,extensive numerical tests in two and three dimensions show that,as the preconditioner for the GMRES method,the iterative PSTDDMs are more robust and efficient than PSTDDMs for solving heterogeneous Helmholtz problems.

关 键 词：Helmholtz equation large wave number perfectly matched layer source transfer domain decomposition method PRECONDITIONER heterogeneous problem 

分 类 号：O17[理学—数学]