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

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Abstract
In this manuscript, we describe effective solvers for the optimal control of stabilized convectiondiffusion problems. We employ the local projection stabilization, which we show to give the same matrix system whether the discretizethenoptimize or optimizethendiscretize 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 BramblePasciak 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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