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AN ADDITIVE OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION
Leng, Wei1; Ju, Lili2
2019
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume41Issue:2Pages:A1252-A1277
AbstractIn 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.
Keywordadditive domain decomposition method Helmholtz equation perfectly matched layer truncated domain problem error analysis parallel computing
DOI10.1137/18M1196170
Language英语
Funding ProjectNatural 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000469225300023
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34865
Collection计算数学与科学工程计算研究所
Corresponding AuthorLeng, Wei
Affiliation1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
2.Univ South Carolina, Dept Math, Columbia, SC 29208 USA
Recommended Citation
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.
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