A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems

doi:10.1002/nla.2129

	A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems
	Gong, Wei1 ; Tan, Zhiyu 2; Zhang, Shuo1
	2018
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
卷号	25 期号:1 页码:17
摘要	In this paper, we consider the efficient solving of the resulting algebraic system for elliptic optimal control problems with mixed finite element discretization. We propose a block-diagonal preconditioner for the symmetric and indefinite algebraic system solved with minimum residual method, which is proved to be robust and optimal with respect to both the mesh size and the regularization parameter. The block-diagonal preconditioner is constructed based on an isomorphism between appropriately chosen solution space and its dual for a general control problem with both state and gradient state observations in the objective functional. Numerical experiments confirm the efficiency of our proposed preconditioner.
关键词	elliptic equation mixed finite element method optimal control problem optimal preconditioner
DOI	10.1002/nla.2129
语种	英语
资助项目	National Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11571356] ; National Natural Science Foundation of China[11471026]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000417585300008
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26999
专题	计算数学与科学工程计算研究所
通讯作者	Zhang, Shuo
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS,LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gong, Wei,Tan, Zhiyu,Zhang, Shuo. A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2018,25(1):17.
APA	Gong, Wei,Tan, Zhiyu,&Zhang, Shuo.(2018).A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,25(1),17.
MLA	Gong, Wei,et al."A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 25.1(2018):17.