The Mathematical Institute, University of Oxford, Eprints Archive

Fast iterative solvers for convection-diffusion control problems

Pearson, John W. and Wathen, A. J. (2011) Fast iterative solvers for convection-diffusion control problems. Technical Report. ETNA. (Submitted)

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Abstract

In this manuscript, we describe effective solvers for the optimal control of stabilized convection-diffusion problems. We employ the local projection stabilization, which we show to give the same matrix system whether the discretize-then-optimize or optimize-then-discretize approach for this problem is used. We then derive two effective preconditioners for this problem, the �first to be used with MINRES and the second to be used with the Bramble-Pasciak Conjugate Gradient method. The key components of both preconditioners are an accurate mass matrix approximation, a good approximation of the Schur complement, and an appropriate multigrid process to enact this latter approximation. We present numerical results to demonstrate that these preconditioners result in convergence in a small number of iterations, which is robust with respect to the mesh size h, and the regularization parameter β, for a range of problems.

Item Type:Technical Report (Technical Report)
Subjects:A - C > Calculus of variations and optimal control
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1410
Deposited By: Lotti Ekert
Deposited On:03 Nov 2011 09:04
Last Modified:29 May 2015 19:06

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