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OVERLAPPING DOMAIN DECOMPOSITION PRECONDITIONERS FOR UNCONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS
Tan, Zhiyu1; Gong, Wei2; Yan, Ningning3
2017
Source PublicationINTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
ISSN1705-5105
Volume14Issue:4-5Pages:550-570
AbstractIn 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.
KeywordOverlapping domain decomposition method elliptic optimal control problem preconditioned MINRES method preconditioned GMRES method
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000408158100005
PublisherISCI-INST SCIENTIFIC COMPUTING & INFORMATION
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26493
Collection计算数学与科学工程计算研究所
系统科学研究所
Corresponding AuthorTan, Zhiyu
Affiliation1.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
Recommended Citation
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.
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