The Mathematical Institute, University of Oxford, Eprints Archive

Preconditioning iterative methods for the optimal control of the Stokes equation

Rees, Tyrone and Wathen, A. J. (2010) Preconditioning iterative methods for the optimal control of the Stokes equation. Technical Report. SICS. (Submitted)

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Abstract

Solving problems regarding the optimal control of partial differential equations (PDEs) – also known as PDE-constrained optimization – is a frontier area of numerical analysis. Of particular interest is the problem of flow control, where one would like to effect some desired flow by exerting, for example, an external force. The bottleneck in many current algorithms is the solution of the optimality system – a system of equations in saddle point form that is usually very large and ill-conditioned. In this paper we describe two preconditioners – a block-diagonal preconditioner for the minimal residual method and a block-lower triangular preconditioner for a non-standard conjugate gradient method – which can be effective when applied to such problems where the PDEs are the Stokes equations. We consider only distributed control here, although other problems – for example boundary control – could be treated in the same way. We give numerical results, and compare these with those obtained by solving the equivalent forward problem using similar techniques

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:937
Deposited By:Lotti Ekert
Deposited On:24 Jul 2010 08:18
Last Modified:24 Jul 2010 08:18

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