| Issue |
ESAIM: M2AN
Volume 44, Number 3, May-June 2010
|
|
|---|---|---|
| Page(s) | 509 - 529 | |
| DOI | https://doi.org/10.1051/m2an/2010011 | |
| Published online | 04 February 2010 | |
Optimal snapshot location for computing POD basis functions
1
University of Graz,
Institute for Mathematics and Scientific Computing,
Heinrichstrasse 36, 8010 Graz, Austria. karl.kunisch@uni-graz.at
2
University of Constance,
Department for Mathematics and Statistics,
Universitätsstraße 10, 78464 Konstanz, Germany. stefan.volkwein@uni-konstanz.de
Received:
10
September
2008
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.
Mathematics Subject Classification: 49J20 / 49K20 / 49M15 / 90C53
Key words: Proper orthogonal decomposition / optimal snapshot locations / first and second order optimality conditions
© EDP Sciences, SMAI, 2010
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