Geodesic
Optimal snapshot location for computing POD basis functions
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 3, pp. 509-529

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/m2an/2010011
Classification : 49J20, 49K20, 49M15, 90C53
Keywords: 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: Mathematical Modelling and Numerical Analysis },
     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://geodesic.mathdoc.fr/articles/10.1051/m2an/2010011/}
}
TY  - JOUR
AU  - Kunisch, Karl
AU  - Volkwein, Stefan
TI  - Optimal snapshot location for computing POD basis functions
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2010
SP  - 509
EP  - 529
VL  - 44
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
%D 2010
%P 509-529
%V 44
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 3, pp. 509-529. doi: 10.1051/m2an/2010011

Cité par Sources :