On a parallel Robin-type nonoverlapping domain decomposition method

doi:10.1137/05063790X

	On a parallel Robin-type nonoverlapping domain decomposition method
	Qin, Lizhen; Xu, Xuejun
	2006
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	44 期号:6 页码:2539-2558
摘要	In recent years, a nonoverlapping Robin-type domain decomposition method (DDM) for the finite element discretization systems of the second order elliptic equations, which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces, has been developed and analyzed since it was first proposed by P. L. Lions in [On the Schwarz alternating method III: A variant for nonoverlapping subdomains, in Proceedings of the 3rd International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1990, pp. 202 - 223]. However, the convergence rate of this DDM with many subdomains remains open when the lower term of equations vanishes. This open problem will be considered in this paper. The convergence rate is almost 1 - O(h(1/2)H-(1/2)) in certain cases - for example, the case of a small number of subdomains, where h is the mesh size and H is the size of subdomain. In order to get the desirous convergence results, two mathematics skills are introduced in this paper; one is complexification of real linear space and the other is the spectral radius formula.
关键词	nonconforming finite elements nonoverlapping domain decomposition convergence rate geometric convergence
DOI	10.1137/05063790X
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000243968000013
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/3747
专题	计算数学与科学工程计算研究所
通讯作者	Qin, Lizhen
作者单位	Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100864, Peoples R China
推荐引用方式 GB/T 7714	Qin, Lizhen,Xu, Xuejun. On a parallel Robin-type nonoverlapping domain decomposition method[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2006,44(6):2539-2558.
APA	Qin, Lizhen,&Xu, Xuejun.(2006).On a parallel Robin-type nonoverlapping domain decomposition method.SIAM JOURNAL ON NUMERICAL ANALYSIS,44(6),2539-2558.
MLA	Qin, Lizhen,et al."On a parallel Robin-type nonoverlapping domain decomposition method".SIAM JOURNAL ON NUMERICAL ANALYSIS 44.6(2006):2539-2558.