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A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS
Gong, Wei1; Xie, Hehu2; Yan, Ningning2
2015
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume37Issue:5Pages:A2198-A2221
AbstractWe propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving an optimization problem on the finest finite element space is transformed into a series of solutions of linear boundary value problems by the multigrid method on multilevel meshes and a series of solutions of optimization problems on the coarsest finite element space. Our proposed scheme, instead of solving a large scale optimization problem in the finest finite element space, solves only a series of linear boundary value problems and the optimization problems in a very low dimensional finite element space, and thus can improve the overall efficiency of the solution of optimal control problems governed by PDEs.
Keywordoptimal control problems elliptic equation control constraints finite element method multilevel correction method
DOI10.1137/140990255
Language英语
Funding ProjectNational Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[91330115] ; National Natural Science Foundation of China[91330202] ; National Natural Science Foundation of China[11371026] ; National Natural Science Foundation of China[11001259] ; National Natural Science Foundation of China[11031006] ; National Natural Science Foundation of China[2011CB309703] ; National Natural Science Foundation of China[11171337] ; Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry ; National Center for Mathematics and Interdisciplinary Science, CAS ; President Foundation of AMSS-CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000364457000003
PublisherSIAM PUBLICATIONS
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Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21265
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Gong, Wei,Xie, Hehu,Yan, Ningning. A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2015,37(5):A2198-A2221.
APA Gong, Wei,Xie, Hehu,&Yan, Ningning.(2015).A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,37(5),A2198-A2221.
MLA Gong, Wei,et al."A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 37.5(2015):A2198-A2221.
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