A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation

doi:10.4208/cicp.OA-2020-0169

	A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation
	Leng, Wei 1; Ju, Lili 2
刊名	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
	2021-02-01
卷号	29 期号:2 页码:357-398
关键词	Helmholtz equation domain decomposition method diagonal sweeping perfectly matched layer source transfer parallel computing
ISSN号	1815-2406
DOI	10.4208/cicp.OA-2020-0169
英文摘要	In 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.
资助项目	National 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研究方向	Physics
语种	英语
出版者	GLOBAL SCIENCE PRESS
WOS记录号	WOS:000596085300002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/57849]
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. 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.