KMS Of Academy of mathematics and systems sciences, CAS
| Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems | |
| Huang, Na1,2; Ma, Chang-Feng2 | |
| 2017-11-15 | |
| Source Publication | COMPUTERS & MATHEMATICS WITH APPLICATIONS
 |
| ISSN | 0898-1221 |
| Volume | 74Issue:10Pages:2423-2437 |
| Abstract | By using the Galerkin finite element method, the distributed control problems can be discretized into a saddle point problem with a coefficient matrix of block three-by-three, which can be reduced to a linear system with lower order. We first introduce a class of inexact block diagonal preconditioners and estimate the lower and upper bounds of positive and negative eigenvalues of the preconditioned matrices, respectively. Based on the Cholesky decomposition of the known matrices, we also analyze a lower triangular preconditioner to accelerate the minimal residual method for the reduced linear system and discuss its real and complex eigenvalues respectively. Moreover, these bounds do not rely on the regularization parameter and the eigenvalues of the matrices in the discrete system. Numerical experiments are also presented to demonstrate the effectiveness and robustness of the two new preconditioners. (C) 2017 Elsevier Ltd. All rights reserved. |
| Keyword | PDE-constrained optimization Saddle point matrices Preconditioner Cholesky decomposition Spectral bound |
| DOI | 10.1016/j.camwa.2017.07.018 |
| Language | 英语 |
| Funding Project | National Postdoctoral Program for Innovative Talents[BX201600182] ; China Postdoctoral Science Foundation[2016M600141] ; National Natural Science Foundation of China[11071041] ; Fujian Natural Science Foundation[02016J01005] ; Fujian Natural Science Foundation[2015J01578] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000415908400015 |
| Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/123 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Ma, Chang-Feng |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China 2.Fujian Normal Univ, Coll Math & Informat, Fujian Key Lab Math Anal & Applicat, Fuzhou 350117, Fujian, Peoples R China |
| Recommended Citation GB/T 7714 | Huang, Na,Ma, Chang-Feng. Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,74(10):2423-2437. |
| APA | Huang, Na,&Ma, Chang-Feng.(2017).Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems.COMPUTERS & MATHEMATICS WITH APPLICATIONS,74(10),2423-2437. |
| MLA | Huang, Na,et al."Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems".COMPUTERS & MATHEMATICS WITH APPLICATIONS 74.10(2017):2423-2437. |
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| 1-s2.0-S089812211730（577KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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