TY - JOUR
T1 - A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations
AU - M. M. Butt & Y. Yuan
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 639
EP - 655
PY - 2017
DA - 2017/10
SN - 10
DO - http://doi.org/10.4208/nmtma.2017.m1637
UR - https://global-sci.org/intro/article_detail/nmtma/12362.html
KW - 
AB - <p style="text-align: justify;">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, forms 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 state- and 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.</p>