Regularization-robust preconditioners for time-dependent PDE constrained optimization problems / John W. Pearson, Martin Stoll, Andy Wathen
Anzeigen / Download1023.68 KB
Discovery
870175599
URN
urn:nbn:de:gbv:3:2-63825
DOI
ISBN
ISSN
Autorin / Autor
Beiträger
Erschienen
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, September 14, 2011
Umfang
1 Online-Ressource (26 Seiten = 0,99 MB) : Diagramme
Ausgabevermerk
Sprache
eng
Anmerkungen
Inhaltliche Zusammenfassung
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.
Schriftenreihe
Max Planck Institute Magdeburg Preprints ; 11-05 ppn:870173030