Regularization-robust preconditioners for time-dependent PDE constrained optimization problems / John W. Pearson, Martin Stoll, Andy Wathen
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Regularization-robust preconditioners for time-dependent PDE constrained optimization problems
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870175599
URN
urn:nbn:de:gbv:3:2-63825
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Publication history
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, September 14, 2011
Content
1 Online-Ressource (26 Seiten = 0,99 MB) : Diagramme
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Language
eng
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Abstract
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.
Series
Max Planck Institute Magdeburg Preprints ; 11-05 ppn:870173030