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A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations
Butt, M. M.1,2; Yuan, Y.1
2017-08-01
Source PublicationNUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN1004-8979
Volume10Issue:3Pages:639-655
AbstractA 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.
KeywordPDE-constrained optimization stokes equations multigrid staggered grids finite difference
DOI10.4208/nmtma.2017.m1637
Language英语
Funding ProjectCAS President's International Fellowship Initiative (PIFI)
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000403905600007
PublisherCAMBRIDGE UNIV PRESS
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25881
Collection计算数学与科学工程计算研究所
Affiliation1.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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