KMS Of Academy of mathematics and systems sciences, CAS
| Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations | |
| Bai, Zhong-Zhi1,2; Lu, Kang-Ya3 | |
| 2021-05-01 | |
| Source Publication | APPLIED NUMERICAL MATHEMATICS
 |
| ISSN | 0168-9274 |
| Volume | 163Pages:126-146 |
| Abstract | 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. |
| Keyword | 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 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000620660200009 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58183 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Bai, Zhong-Zhi |
| Affiliation | 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 |
| Recommended Citation 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. |
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