A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems
文献类型：期刊论文
| 作者 | Gong, Wei1 ; Tan, Zhiyu2; Zhang, Shuo1
|
| 刊名 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
 |
| 出版日期 | 2018 |
| 卷号 | 25期号:1页码:17 |
| 关键词 | elliptic equation mixed finite element method optimal control problem optimal preconditioner |
| ISSN号 | 1070-5325 |
| DOI | 10.1002/nla.2129 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000417585300008 |
| 出版者 | WILEY |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26998]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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