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Non-conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE Constrained Optimization

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Book cover Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems (FVCA 2017)

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Abstract

We propose a new non-conforming localized model reduction paradigm for efficient solution of large scale or multiscale PDE constrained optimization problems. The new conceptual approach goes beyond the classical offline/online splitting of traditional projection based model order reduction approaches for the underlying state equation, such as the reduced basis method. Instead of first constructing a surrogate model that has globally good approximation quality with respect to the whole parameter range, we propose an iterative enrichment procedure that refines and locally adapts the surrogate model specifically for the parameters that are depicted during the outer optimization loop.

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Authors and Affiliations

  1. Applied Mathematics, Center for Nonlinear Sciences and Center for Multiscale Theory and Computation, University of Muenster, Einsteinstr. 62, 48149, Münster, Germany

    Mario Ohlberger

  2. Applied Mathematics and Center for Nonlinear Sciences, University of Muenster, Einsteinstr. 62, 48149, Münster, Germany

    Felix Schindler

Authors
  1. Mario Ohlberger
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  2. Felix Schindler
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Correspondence to Mario Ohlberger .

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Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Ohlberger, M., Schindler, F. (2017). Non-conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE Constrained Optimization. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_38

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