Low-rank solutions to an optimization problem constrained by the Navier-Stokes equations / Sergey Dolgov, Martin Stoll
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Low-rank solutions to an optimization problem constrained by the Navier-Stokes equations
Discovery
870922998
URN
urn:nbn:de:gbv:3:2-64817
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Publication history
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, September 18, 2015
Content
1 Online-Ressource (33 Seiten = 0,62 MB) : Diagramme
Edition
Language
eng
Comment
Abstract
Abstract: The numerical solution of PDE-constrained optimization problems subject to the non-stationary Navier-Stokes equation is a challenging task. While space-time approaches often show favorable convergence properties they often suffer from storage problems. We here propose to approximate the solution to the optimization problem in a low-rank from, which is similar to the Model Order Reduction (MOR) approach. However, in contrast to classical MOR schemes we do not compress the full solution at the end of the algorithm but start our algorithm with low-rank data and maintain this form throughout the iteration. Theoretical results and numerical experiments indicate that this approach reduces the computational costs by two orders of magnitude.
Series
Max Planck Institute Magdeburg Preprints ; 15-15 ppn:870173030