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Optimal snapshot locationfor 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. [email protected]
Stefan Volkwein
Affiliation:
University of Constance, Department for Mathematics and Statistics, Universitätsstraße 10, 78464 Konstanz, Germany. [email protected]
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Abstract

The construction of reduced order models for dynamical systems usingproper orthogonal decomposition (POD) is based on the informationcontained in so-called snapshots. These provide the spatialdistribution of the dynamical system at discrete time instances.This work is devoted to optimizing the choice of these timeinstances in such a manner that the error between the POD-solutionand the trajectory of the dynamical system is minimized. First andsecond order optimality systems are given. Numerical examplesillustrate that the proposed criterion is sensitive with respect tothe choice of the time instances and further they demonstrate thefeasibility of the method in determining optimal snapshot locationsfor concrete diffusion equations.

Keywords

Proper orthogonal decompositionoptimal snapshotlocationsfirst 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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