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Optimal snapshot location for computingPOD basis functions

Published online by Cambridge University Press:  04 February 2010

Karl Kunisch  and
Stefan Volkwein
Karl Kunisch
Affiliation:
University of Graz, Institute for Mathematics and Scientific Computing, Heinrichstrasse 36, 8010 Graz, Austria. karl.kunisch@uni-graz.at
Stefan Volkwein
Affiliation:
University of Constance, Department for Mathematics and Statistics, Universitätsstraße 10, 78464 Konstanz, Germany. stefan.volkwein@uni-konstanz.de
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Abstract

The construction of reduced order models for dynamical systems using proper orthogonal decomposition (POD) is based on the information contained in so-called snapshots. These provide the spatial distribution of the dynamical system at discrete time instances. This work is devoted to optimizing the choice of these time instances in such a manner that the error between the POD-solution and the trajectory of the dynamical system is minimized. First and second order optimality systems are given. Numerical examples illustrate that the proposed criterion is sensitive with respect to the choice of the time instances and further they demonstrate the feasibility of the method in determining optimal snapshot locations for concrete diffusion equations.

Keywords

Proper orthogonal decompositionoptimal snapshot locationsfirst and second order optimality conditions
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 3 , May 2010 , pp. 509 - 529
Copyright
© EDP Sciences, SMAI, 2010

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