# Optimal snapshot location for computing POD basis functions

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topKunisch, 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 -

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