A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation
Leng, Wei1; Ju, Lili2
AbstractIn this paper, we propose and test a novel diagonal sweeping domain decomposition method (DDM) with source transfer for solving the high-frequency Helmholtz equation in R-n. In the method the computational domain is partitioned into overlapping checkerboard subdomains for source transfer with the perfectly matched layer (PML) technique, then a set of diagonal sweeps over the subdomains are specially designed to solve the system efficiently. The method improves the additive overlapping DDM [43] and the L-sweeps method [50] by employing a more efficient subdomain solving order. We show that the method achieves the exact solution of the global PML problem with 2(n) sweeps in the constant medium case. Although the sweeping usually implies sequential subdomain solves, the number of sequential steps required for each sweep in the method is only proportional to the n-th root of the number of subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus it is very suitable for parallel computing of the Helmholtz problem with multiple right-hand sides through the pipeline processing. Extensive numerical experiments in two and three dimensions are presented to demonstrate the effectiveness and efficiency of the proposed method.
KeywordHelmholtz equation domain decomposition method diagonal sweeping perfectly matched layer source transfer parallel computing
Indexed BySCI
Funding ProjectNational Key Research and Development Program of China[2016YFB0201304] ; National Natural Science Foundation of China[11501553] ; National Natural Science Foundation of China[11771440] ; State Key Laboratory of Scientific and Engineering Computing (LSEC) ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS) ; US National Science Foundation[DMS-1818438]
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000596085300002
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Document Type期刊论文
Corresponding AuthorJu, Lili
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. A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2021,29(2):357-398.
APA Leng, Wei,&Ju, Lili.(2021).A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,29(2),357-398.
MLA Leng, Wei,et al."A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 29.2(2021):357-398.
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