Trace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: Algorithms and convergence analysis

doi:10.1016/j.jcp.2022.110980

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	Trace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: Algorithms and convergence analysis
	Leng, Wei 1; Ju, Lili 2
	2022-04-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	455 页码:29
摘要	By utilizing the perfectly matched layer (PML) and source transfer techniques, the diagonal sweeping domain decomposition method (DDM) was recently developed for solving the high-frequency Helmholtz equation in R-n, which uses 2(n) sweeps along respective diagonal directions with checkerboard domain decomposition. Although this diagonal sweeping DDM is essentially multiplicative, it is highly suitable for parallel computing of the Helmholtz problem with multiple right-hand sides when combined with the pipeline processing since the number of sequential steps in each sweep is much smaller than the number of subdomains. In this paper, we propose and analyze a trace transfer-based diagonal sweeping DDM. A major advantage of changing from source transfer to trace transfer for information passing between neighbor subdomains is that the resulting diagonal sweeps become easier to analyze and implement and more efficient, since the transferred traces have only 2n cardinal directions between neighbor subdomains while the transferred sources come from a total of 3(n) - 1 cardinal and corner directions. We rigorously prove that the proposed diagonal sweeping DDM not only gives the exact solution of the global PML problem in the constant medium case but also does it with at most one extra round of diagonal sweeps in the two-layered media case, which lays down the theoretical foundation of the method. Performance and parallel scalability of the proposed DDM as direct solver or preconditioner are also numerically demonstrated through extensive experiments in two and three dimensions. (C) 2022 Elsevier Inc. All rights reserved.
关键词	Domain decomposition method Diagonal sweeping Helmholtz equation Perfectly matched layer Trace transfer Parallel computing
DOI	10.1016/j.jcp.2022.110980
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12171464] ; National Natural Science Foundation of China[11771440] ; National Key R&D Program of China[2020YFA0711904] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB 41000000] ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS) ; U.S. National Science Foundation[DMS-1818438] ; U.S. National Science Foundation[DMS-2109633]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000762463300014
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60101
专题	中国科学院数学与系统科学研究院
通讯作者	Ju, Lili
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. Trace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: Algorithms and convergence analysis[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,455:29.
APA	Leng, Wei,&Ju, Lili.(2022).Trace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: Algorithms and convergence analysis.JOURNAL OF COMPUTATIONAL PHYSICS,455,29.
MLA	Leng, Wei,et al."Trace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: Algorithms and convergence analysis".JOURNAL OF COMPUTATIONAL PHYSICS 455(2022):29.