OVERLAPPING DOMAIN DECOMPOSITION PRECONDITIONERS FOR UNCONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS

	OVERLAPPING DOMAIN DECOMPOSITION PRECONDITIONERS FOR UNCONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS
	Tan, Zhiyu 1; Gong, Wei2 ; Yan, Ningning3
	2017
发表期刊	INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
ISSN	1705-5105
卷号	14 期号:4-5 页码:550-570
摘要	In this paper, we propose several overlapping domain decomposition preconditioners for solving the unconstrained elliptic optimal control problem, based on the two level additive Schwarz algorithm. We consider the cases with controls on the whole domain and controls from a local subset. The latter case can be viewed as the subproblems when we solve the control-constrained control problem by using semi-smooth Newton method. When the controls act on the whole domain, we construct a symmetric and positive definite preconditioner which is proved to be robust combined with preconditioned MINRES method, and a symmetric and indefinite preconditioner which can be used in the preconditioned GMRES method and shows better numerical performance than the positive definite one. When the controls act on a local subset, we also construct a similar symmetric and indefinite preconditioner, the numerical experiments show its efficiency when combined with preconditioned GMRES method.
关键词	Overlapping domain decomposition method elliptic optimal control problem preconditioned MINRES method preconditioned GMRES method
语种	英语
资助项目	National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11571356]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000408158100005
出版者	ISCI-INST SCIENTIFIC COMPUTING & INFORMATION
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26493
专题	计算数学与科学工程计算研究所系统科学研究所
通讯作者	Tan, Zhiyu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Tan, Zhiyu,Gong, Wei,Yan, Ningning. OVERLAPPING DOMAIN DECOMPOSITION PRECONDITIONERS FOR UNCONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,2017,14(4-5):550-570.
APA	Tan, Zhiyu,Gong, Wei,&Yan, Ningning.(2017).OVERLAPPING DOMAIN DECOMPOSITION PRECONDITIONERS FOR UNCONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS.INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,14(4-5),550-570.
MLA	Tan, Zhiyu,et al."OVERLAPPING DOMAIN DECOMPOSITION PRECONDITIONERS FOR UNCONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS".INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING 14.4-5(2017):550-570.