Rees, Tyrone and Dollar, H. Sue and Wathen, A. J. (2008) Optimal solvers for PDEConstrained Optimization. Technical Report. Unspecified. (Submitted)

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Abstract
Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The solution of such PDEconstrained optimization problems is usually a major computational task. Here we consider simple problems of this type: distributed control problems in which the 2 and 3dimensional Poisson problem is the PDE. The large dimensional linear systems which result from discretization and which need to be solved are of saddlepoint type. We introduce two optimal preconditioners for these systems which lead to convergence of symmetric Krylov subspace iterative methods in a number of iterations which does not increase with the dimension of the discrete problem. These preconditioners are block structured and involve standard multigrid cycles. The optimality of the preconditioned iterative solver is proved theoretically and verified computationally in several test cases. The theoretical proof indicates that these approaches may have much broader applicability for other partial differential equations.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1068 
Deposited By:  Lotti Ekert 
Deposited On:  21 Apr 2011 07:33 
Last Modified:  29 May 2015 18:45 
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