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Greedy Sampling Using Nonlinear Optimization

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2014

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Urban, Karsten
Zeeb, Oliver

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https://doi.org/10.1007/978-3-319-02090-7_5
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QUARTERONI, Alfio, ed. and others. Reduced order methods for modeling and computational reduction. Cham [u.a.]: Springer, 2014, pp. 137-157. Modeling, Simulation & Applications. 9. ISBN 978-3-319-02089-1. Available under: doi: 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.

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510 Mathematik

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ISO 690URBAN, 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, 2014, pp. 137-157. Modeling, Simulation & Applications. 9. ISBN 978-3-319-02089-1. Available under: doi: 10.1007/978-3-319-02090-7_5
BibTex
@incollection{Urban2014Greed-32973,
  year={2014},
  doi={10.1007/978-3-319-02090-7_5},
  title={Greedy Sampling Using Nonlinear Optimization},
  number={9},
  isbn={978-3-319-02089-1},
  publisher={Springer},
  address={Cham [u.a.]},
  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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