A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS
文献类型：期刊论文
| 作者 | Gong, Wei1 ; Xie, Hehu2; Yan, Ningning2
|
| 刊名 | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| 出版日期 | 2015 |
| 卷号 | 37期号:5页码:A2198-A2221 |
| 关键词 | optimal control problems elliptic equation control constraints finite element method multilevel correction method |
| ISSN号 | 1064-8275 |
| DOI | 10.1137/140990255 |
| 英文摘要 | We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving an optimization problem on the finest finite element space is transformed into a series of solutions of linear boundary value problems by the multigrid method on multilevel meshes and a series of solutions of optimization problems on the coarsest finite element space. Our proposed scheme, instead of solving a large scale optimization problem in the finest finite element space, solves only a series of linear boundary value problems and the optimization problems in a very low dimensional finite element space, and thus can improve the overall efficiency of the solution of optimal control problems governed by PDEs. |
| 资助项目 | National Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[91330115] ; National Natural Science Foundation of China[91330202] ; National Natural Science Foundation of China[11371026] ; National Natural Science Foundation of China[11001259] ; National Natural Science Foundation of China[11031006] ; National Natural Science Foundation of China[2011CB309703] ; National Natural Science Foundation of China[11171337] ; Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry ; National Center for Mathematics and Interdisciplinary Science, CAS ; President Foundation of AMSS-CAS |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000364457000003 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/21264]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Gong, Wei |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Gong, Wei,Xie, Hehu,Yan, Ningning. A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2015,37(5):A2198-A2221. |
| APA | Gong, Wei,Xie, Hehu,&Yan, Ningning.(2015).A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,37(5),A2198-A2221. |
| MLA | Gong, Wei,et al."A MULTILEVEL CORRECTION METHOD FOR OPTIMAL CONTROLS OF ELLIPTIC EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 37.5(2015):A2198-A2221. |
入库方式： OAI收割
来源：数学与系统科学研究院
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