distributed control problems
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2017 ◽  
Vol 10 (3) ◽  
pp. 639-655 ◽  
Author(s):  
M. M. Butt ◽  
Y. Yuan

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 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.


2017 ◽  
Vol 62 (1) ◽  
pp. 206-221 ◽  
Author(s):  
Ghazal Fazelnia ◽  
Ramtin Madani ◽  
Abdulrahman Kalbat ◽  
Javad Lavaei

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