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:03 Nov 2011 09:05

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