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Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location

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2014

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https://doi.org/10.1007/s10589-014-9646-z
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Computational Optimization and Applications. 2014, 58(3), pp. 645-677. ISSN 0926-6003. eISSN 1573-2894. Available under: doi: 10.1007/s10589-014-9646-z

Zusammenfassung

The construction of reduced-order models for parametrized partial differential systems using proper orthogonal decomposition (POD) is based on the information of the so-called snapshots. These provide the spatial distribution of the nonlinear system at discrete parameter and/or time instances. In this work a strategy is used, where the POD reduced-order model is improved by choosing additional snapshot locations in an optimal way; see Kunisch and Volkwein (ESAIM: M2AN, 44:509–529, 2010). These optimal snapshot locations influences the POD basis functions and therefore the POD reduced-order model. This strategy is used to build up a POD basis on a parameter set in an adaptive way. The approach is illustrated by the construction of the POD reduced-order model for the complex-valued Helmholtz equation.

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510 Mathematik

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ISO 690LASS, Oliver, Stefan VOLKWEIN, 2014. Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location. In: Computational Optimization and Applications. 2014, 58(3), pp. 645-677. ISSN 0926-6003. eISSN 1573-2894. Available under: doi: 10.1007/s10589-014-9646-z
BibTex
@article{Lass2014Adapt-32340,
  year={2014},
  doi={10.1007/s10589-014-9646-z},
  title={Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location},
  number={3},
  volume={58},
  issn={0926-6003},
  journal={Computational Optimization and Applications},
  pages={645--677},
  author={Lass, Oliver and Volkwein, Stefan}
}
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