Greedy Sampling Using Nonlinear Optimization

Publikationstyp: Beitrag zu einem Sammelband
Publikationsstatus: Published
Autor/innen: Urban, Karsten; Volkwein, Stefan; Zeeb, Oliver
Erscheinungsjahr: 2014
Erschienen in: Reduced order methods for modeling and computational reduction / Quarteroni, Alfio et al. (Hrsg.). - Cham [u.a.] : Springer, 2014. - (Modeling, Simulation & Applications ; 9). - S. 137-157. - ISBN 978-3-319-02089-1
DOI (zitierfähiger Link): https://dx.doi.org/10.1007/978-3-319-02090-7_5
Zusammenfassung:
We consider the reduced basis generation in the offline stage. As an alternative for standard Greedy-training methods based upon a-posteriori error estimates on a training subset of the parameter set, we consider a nonlinear optimization combined with a Greedy method. We define an optimization problem for selecting a new parameter value on a given reduced space. This new parameter is then used -in a Greedy fashion- to determine the corresponding snapshot and to update the reduced basis. We show the well-posedness of this nonlinear optimization problem and derive first- and second-order optimality conditions. Numerical comparisons with the standard Greedy-training method are shown.
Fachgebiet (DDC): 510 Mathematik
Universitätsbibliographie: Ja

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URBAN, Karsten, Stefan VOLKWEIN, Oliver ZEEB, 2014. Greedy Sampling Using Nonlinear Optimization. In: QUARTERONI, Alfio, ed. and others. Reduced order methods for modeling and computational reduction. Cham [u.a.]:Springer, pp. 137-157. ISBN 978-3-319-02089-1. Available under: doi: 10.1007/978-3-319-02090-7_5

@incollection{Urban2014Greed-32973, title={Greedy Sampling Using Nonlinear Optimization}, year={2014}, doi={10.1007/978-3-319-02090-7_5}, number={9}, isbn={978-3-319-02089-1}, address={Cham [u.a.]}, publisher={Springer}, series={Modeling, Simulation & Applications}, booktitle={Reduced order methods for modeling and computational reduction}, pages={137--157}, editor={Quarteroni, Alfio}, author={Urban, Karsten and Volkwein, Stefan and Zeeb, Oliver} }

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