A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations

doi:10.4208/nmtma.2017.m1637

	A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations
	Butt, M. M.1,2; Yuan, Y.1
	2017-08-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	10 期号:3 页码:639-655
摘要	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.
关键词	PDE-constrained optimization stokes equations multigrid staggered grids finite difference
DOI	10.4208/nmtma.2017.m1637
语种	英语
资助项目	CAS President's International Fellowship Initiative (PIFI)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000403905600007
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25881
专题	计算数学与科学工程计算研究所
通讯作者	Butt, M. M.
作者单位	1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Govt Punjab, Higher Educ Dept, Lahore 54000, Pakistan
推荐引用方式 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.