Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations

doi:10.1016/j.apnum.2021.01.011

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	Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations
	Bai, Zhong-Zhi 1,2; Lu, Kang-Ya 3
	2021-05-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	163 页码:126-146
摘要	For a class of optimal control problems constrained with certain timeand space-fractional diffusive equations, by making use of mixed discretizations of temporal finite-difference and spatial finite-element schemes along with Lagrange multiplier approach, we obtain specially structured block two-by-two linear systems. We demonstrate positive definiteness of the coefficient matrices of these discrete linear systems, construct rotated block diagonal preconditioning matrices, and analyze spectral properties of the corresponding preconditioned matrices. Both theoretical analysis and numerical experiments show that the preconditioned Krylov subspace iteration methods, when incorporated with these rotated block-diagonal preconditioners, can exhibit optimal convergence property in the sense that their convergence rates are independent of both discretization stepsizes and problem parameters, and their computational workloads are linearly proportional with the number of discrete unknowns. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
关键词	Fractional optimal control problem Numerical discretizations Block two-by-two linear system Preconditioning Spectral bounds Krylov subspace iteration methods Convergence property
DOI	10.1016/j.apnum.2021.01.011
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China, P.R. China[11671393] ; National Natural Science Foundation of China, P.R. China[12071472] ; National Natural Science Foundation of China, P.R. China[12001048] ; Government of the Russian Federation, Russia[075-15-2019-1928] ; China-Russia (NSFC-RFBR) International Cooperative Research Project[11911530082] ; China-Russia (NSFC-RFBR) International Cooperative Research Project[19-51-53013] ; Science and Technology Planning Projects of Beijing Municipal Education Commission, P.R. China[KM202011232019]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000620660200009
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58183
专题	中国科学院数学与系统科学研究院
通讯作者	Bai, Zhong-Zhi
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China 2.Southern Fed Univ, II Vorovich Inst Math Mech & Comp Sci, Lab Computat Mech, Rostov Na Donu 344090, Russia 3.Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing 100192, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Lu, Kang-Ya. Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations[J]. APPLIED NUMERICAL MATHEMATICS,2021,163:126-146.
APA	Bai, Zhong-Zhi,&Lu, Kang-Ya.(2021).Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations.APPLIED NUMERICAL MATHEMATICS,163,126-146.
MLA	Bai, Zhong-Zhi,et al."Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations".APPLIED NUMERICAL MATHEMATICS 163(2021):126-146.