A low-rank in time approach to PDE-constrained optimization / Martin Stoll, Tobias Breiten
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870490702
URN
urn:nbn:de:gbv:3:2-64210
DOI
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Autorin / Autor
Beiträger
Erschienen
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, June 26, 2013
Umfang
1 Online-Ressource (26 Seiten = 1,03 MB) : Diagramme
Ausgabevermerk
Sprache
eng
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Inhaltliche Zusammenfassung
Abstract: The solution of time-dependent PDE-constrained optimization problems is a challenging task in numerical analysis and applied mathematics. All-at-once discretizations and corresponding solvers provide efficient methods to robustly solve the arising discretized equations. One of the drawbacks of this approach is the high storage demand for the vectors representing the discrete space-time cylinder. We here introduce a low-rank in time technique that exploits the low-rank nature of the solution. The theoretical foundations for this approach originate in the numerical treatment of matrix equations and can be carried over to PDE-constrained optimization. We illustrate how three different problems can be rewritten and used within a low-rank Krylov subspace solver with appropriate preconditioning.
Schriftenreihe
Max Planck Institute Magdeburg Preprints ; 13-08 ppn:870173030