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

doi:10.1137/080713653

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	SPECTRAL ANALYSIS OF DIRICHLET-NEUMANN OPERATORS AND OPTIMIZED SCHWARZ METHODS WITH ROBIN TRANSMISSION CONDITIONS
	Xu, Xuejun1 ; Qin, Lizhen 2
刊名	SIAM JOURNAL ON NUMERICAL ANALYSIS
	2010
卷号	47 期号:6 页码:4540-4568
关键词	finite elements optimized Schwarz methods with Robin transmission conditions nonoverlapping domain decomposition convergence rate Dirichlet-Neumann operators
ISSN号	0036-1429
DOI	10.1137/080713653
英文摘要	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.
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
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000277836100023
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/9408]
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.