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 PDEconstrained 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 illconditioned. In this paper we describe two preconditioners – a blockdiagonal preconditioner for the minimal residual method and a blocklower triangular preconditioner for a nonstandard 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 07:18 
Last Modified:  29 May 2015 18:37 
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