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.
Mots clés : proper orthogonal decomposition, optimal snapshot locations, first and second order optimality conditions
@article{M2AN_2010__44_3_509_0,
author = {Kunisch, Karl and Volkwein, Stefan},
title = {Optimal snapshot location for computing {POD} basis functions},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {509--529},
publisher = {EDP-Sciences},
volume = {44},
number = {3},
year = {2010},
doi = {10.1051/m2an/2010011},
mrnumber = {2666653},
zbl = {1193.65113},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010011/}
}
TY - JOUR AU - Kunisch, Karl AU - Volkwein, Stefan TI - Optimal snapshot location for computing POD basis functions JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 509 EP - 529 VL - 44 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010011/ DO - 10.1051/m2an/2010011 LA - en ID - M2AN_2010__44_3_509_0 ER -
%0 Journal Article %A Kunisch, Karl %A Volkwein, Stefan %T Optimal snapshot location for computing POD basis functions %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 509-529 %V 44 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010011/ %R 10.1051/m2an/2010011 %G en %F M2AN_2010__44_3_509_0
Kunisch, Karl; Volkwein, Stefan. Optimal snapshot location for computing POD basis functions. ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 3, pp. 509-529. doi : 10.1051/m2an/2010011. http://www.numdam.org/articles/10.1051/m2an/2010011/
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