The Mathematical Institute, University of Oxford, Eprints Archive

Regularization-robust preconditioners for time-dependent PDE constrained optimization problems

Pearson, John W. and Stoll, Martin and Wathen, A. J. (2011) Regularization-robust preconditioners for time-dependent PDE constrained optimization problems. Technical Report. SIAM. (Submitted)

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Abstract

In this article, we motivate, derive and test effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two different functionals, and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the effectiveness of our preconditioners in each case is an effective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are effective for a wide range of regularization parameter values, as well as mesh sizes and time-steps.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Fluid mechanics
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1398
Deposited By:Lotti Ekert
Deposited On:15 Sep 2011 07:30
Last Modified:15 Sep 2011 07:30

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