KMS Of Academy of mathematics and systems sciences, CAS
| A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations | |
Butt, M. M.1,2; Yuan, Y.1
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| 2017-08-01 | |
| Source Publication | NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
 |
| ISSN | 1004-8979 |
| Volume | 10Issue:3Pages:639-655 |
| Abstract | A full multigrid method with coarsening by a factor-of-three to distributed control problems constrained by Stokes equations is presented. An optimal control problem with cost functional of velocity and/or pressure tracking-type is considered with Dirichlet boundary conditions. The optimality system that results from a Lagrange multiplier framework, form a linear system connecting the state, adjoint, and control variables. We investigate multigrid methods with finite difference discretization on staggered grids. A coarsening by a factor-of-three is used on staggered grids that results nested hierarchy of staggered grids and simplified the inter-grid transfer operators. A distributive-Gauss-Seidel smoothing scheme is employed to update the stateand adjoint-variables and a gradient update step is used to update the control variables. Numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed multigrid framework to tracking-type optimal control problems. |
| Keyword | PDE-constrained optimization stokes equations multigrid staggered grids finite difference |
| DOI | 10.4208/nmtma.2017.m1637 |
| Language | 英语 |
| Funding Project | CAS President's International Fellowship Initiative (PIFI) |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000403905600007 |
| Publisher | CAMBRIDGE UNIV PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25881 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Butt, M. M. |
| Affiliation | 1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Govt Punjab, Higher Educ Dept, Lahore 54000, Pakistan |
| Recommended Citation GB/T 7714 | Butt, M. M.,Yuan, Y.. A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2017,10(3):639-655. |
| APA | Butt, M. M.,&Yuan, Y..(2017).A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,10(3),639-655. |
| MLA | Butt, M. M.,et al."A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 10.3(2017):639-655. |
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