Optimal snapshot location for computing POD basis functions

Karl Kunisch; Stefan Volkwein

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 3, page 509-529
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Kunisch, Karl, and Volkwein, Stefan. "Optimal snapshot location for computing POD basis functions." ESAIM: Mathematical Modelling and Numerical Analysis 44.3 (2010): 509-529. <http://eudml.org/doc/250703>.

@article{Kunisch2010,
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. },
author = {Kunisch, Karl, Volkwein, Stefan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Proper orthogonal decomposition; optimal snapshot locations; first and second order optimality conditions; proper orthogonal decomposition (POD); optimal time snapshot locations; optimality conditions},
language = {eng},
month = {4},
number = {3},
pages = {509-529},
publisher = {EDP Sciences},
title = {Optimal snapshot location for computing POD basis functions},
url = {http://eudml.org/doc/250703},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Kunisch, Karl
AU - Volkwein, Stefan
TI - Optimal snapshot location for computing POD basis functions
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/4//
PB - EDP Sciences
VL - 44
IS - 3
SP - 509
EP - 529
AB - 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.
LA - eng
KW - Proper orthogonal decomposition; optimal snapshot locations; first and second order optimality conditions; proper orthogonal decomposition (POD); optimal time snapshot locations; optimality conditions
UR - http://eudml.org/doc/250703
ER -

References

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