A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS

doi:10.1137/140990255

	A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS
	Gong, Wei1 ; Xie, Hehu2 ; Yan, Ningning2
	2015
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	37 期号:5 页码:A2198-A2221
摘要	We 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.
关键词	optimal control problems elliptic equation control constraints finite element method multilevel correction method
DOI	10.1137/140990255
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000364457000003
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/21265
专题	计算数学与科学工程计算研究所
通讯作者	Gong, Wei
作者单位	1.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
推荐引用方式 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.