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

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  • Oliver Lass
  • Stefan Volkwein

Abstract

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Oliver Lass & Stefan Volkwein, 2014. "Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location," Computational Optimization and Applications, Springer, vol. 58(3), pages 645-677, July.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:3:p:645-677
    DOI: 10.1007/s10589-014-9646-z
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    References listed on IDEAS

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    1. S. Volkwein, 2010. "Admittance Identification from Point-wise Sound Pressure Measurements Using Reduced-order Modelling," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 169-193, October.
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    Cited by:

    1. Karasözen, Bülent & Akkoyunlu, Canan & Uzunca, Murat, 2015. "Model order reduction for nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 509-519.

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