SPECTRAL ANALYSIS OF DIRICHLET-NEUMANN OPERATORS AND OPTIMIZED SCHWARZ METHODS WITH ROBIN TRANSMISSION CONDITIONS

doi:10.1137/080713653

	SPECTRAL ANALYSIS OF DIRICHLET-NEUMANN OPERATORS AND OPTIMIZED SCHWARZ METHODS WITH ROBIN TRANSMISSION CONDITIONS
	Xu, Xuejun1 ; Qin, Lizhen 2
	2010
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	47 期号:6 页码:4540-4568
摘要	In this paper, the tight relationship between Dirichlet-Neumann (D-N) operators and optimized Schwarz methods with Robin transmission conditions is disclosed. We describe the spectral distribution of continuous D-N operators and give a rigorous spectral analysis of discrete D-N operators. By these results, we prove that the optimized Schwarz methods with Robin transmission conditions cannot converge geometrically in the case of continuous problems. Furthermore, we get the accurate convergence rate of the two-subdomain case. In addition, an estimation of convergence rate of the optimized Schwarz methods is presented in the general case. Most of our results are asymptotically sharp.
关键词	finite elements optimized Schwarz methods with Robin transmission conditions nonoverlapping domain decomposition convergence rate Dirichlet-Neumann operators
DOI	10.1137/080713653
语种	英语
资助项目	special funds for major state basic research projects (973)[2005CB321701] ; National Science Foundation (NSF) of China[10731060]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000277836100023
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/9409
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Xuejun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 2.Wayne State Univ, Dept Math, Detroit, MI 48202 USA
推荐引用方式 GB/T 7714	Xu, Xuejun,Qin, Lizhen. SPECTRAL ANALYSIS OF DIRICHLET-NEUMANN OPERATORS AND OPTIMIZED SCHWARZ METHODS WITH ROBIN TRANSMISSION CONDITIONS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2010,47(6):4540-4568.
APA	Xu, Xuejun,&Qin, Lizhen.(2010).SPECTRAL ANALYSIS OF DIRICHLET-NEUMANN OPERATORS AND OPTIMIZED SCHWARZ METHODS WITH ROBIN TRANSMISSION CONDITIONS.SIAM JOURNAL ON NUMERICAL ANALYSIS,47(6),4540-4568.
MLA	Xu, Xuejun,et al."SPECTRAL ANALYSIS OF DIRICHLET-NEUMANN OPERATORS AND OPTIMIZED SCHWARZ METHODS WITH ROBIN TRANSMISSION CONDITIONS".SIAM JOURNAL ON NUMERICAL ANALYSIS 47.6(2010):4540-4568.