AN ADDITIVE OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION

doi:10.1137/18M1196170

	AN ADDITIVE OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION
	Leng, Wei1 ; Ju, Lili 2
	2019
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	41 期号:2 页码:A1252-A1277
摘要	In this paper, we propose and analyze an additive domain decomposition method (DDM) for solving the Helmholtz equation with the Sommerfeld radiation condition. In the proposed method, the computational domain is partitioned into structured subdomains along all spatial directions, and each of the subdomains contains an overlapping region for source transferring through the perfectly matched layer (PML) technique. At each step all subdomain PML problems are solved concurrently, and then the horizontal, vertical, and corner directional residuals on each subdomain are passed to their corresponding neighbor subdomains as the sources for the next step. This DDM is efficient in nature and theoretically shown to produce the exact solution for the PML problem with constant medium defined in the whole two-dimensional space. A slightly modified version of the method for bounded truncated domains is next developed for its use in practice and an error estimate is rigorously proved. Various numerical experiments in two and three dimensions are conducted on the supercomputer Tianhe-2 Cluster to verify the theoretical results and demonstrate excellent performance of the proposed method as an iterative solver or a preconditioner.
关键词	additive domain decomposition method Helmholtz equation perfectly matched layer truncated domain problem error analysis parallel computing
DOI	10.1137/18M1196170
语种	英语
资助项目	Natural Science Foundation of China[11501553] ; Natural Science Foundation of China[11771440] ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences ; US National Science Foundation[DMS-1521965] ; US National Science Foundation[DMS-1818438]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000469225300023
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34865
专题	计算数学与科学工程计算研究所
通讯作者	Leng, Wei
作者单位	1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China 2.Univ South Carolina, Dept Math, Columbia, SC 29208 USA
推荐引用方式 GB/T 7714	Leng, Wei,Ju, Lili. AN ADDITIVE OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(2):A1252-A1277.
APA	Leng, Wei,&Ju, Lili.(2019).AN ADDITIVE OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(2),A1252-A1277.
MLA	Leng, Wei,et al."AN ADDITIVE OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.2(2019):A1252-A1277.