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Large-Scale PDE-Constrained Optimization pp 268–280Cite as

Reduced Order Modelling Approaches to PDE-Constrained Optimization Based on Proper Orthogonal Decomposition

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 30))

Abstract

Reduced order modelling techniques can be used in order to circumvent computational difficulties due to large-scale state equations related to PDE-constrained optimization problems. However, if reduced order modelling based on the Proper Orthogonal Decomposition (POD) is performed, it is necessary to include an update mechanism into the optimization procedure in order to guarantee reliable reduced order state solutions during the course of the optimization. Furthermore, specific modelling issues should be taken into account such that sufficiently accurate gradient information is obtained during the optimization process. In this context, we discuss some relevant topics arising from the POD based reduced order modelling approach.

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Author information

Authors and Affiliations

  1. Fachbereich IV — Mathematik, Universität Trier, D-54286, Trier, Germany

    Marco Fahl & Ekkehard W. Sachs

  2. Department of Mathematics, Virginia Polytechnic Institute and State University, ICAM, Blacksburg, VA, 24060, USA

    Ekkehard W. Sachs

Authors
  1. Marco Fahl
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  2. Ekkehard W. Sachs
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Lorenz T. Biegler

  2. Department of Computational and Applied Mathematics, Rice University, 6100 S. Main Street — MS134, Houston, TX, 77005, USA

    Matthias Heinkenschloss

  3. Department of Biomedical Engineering and Civil & Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Omar Ghattas

  4. Optimization & Uncertainty Estimation Dept., Sandia National Laboratories — MS 0847, P.O. Box 5800, Albuquerque, NM, 87185, USA

    Bart van Bloemen Waanders

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© 2003 Springer-Verlag Berlin Heidelberg

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Fahl, M., Sachs, E.W. (2003). Reduced Order Modelling Approaches to PDE-Constrained Optimization Based on Proper Orthogonal Decomposition. In: Biegler, L.T., Heinkenschloss, M., Ghattas, O., van Bloemen Waanders, B. (eds) Large-Scale PDE-Constrained Optimization. Lecture Notes in Computational Science and Engineering, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55508-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-55508-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05045-2

  • Online ISBN: 978-3-642-55508-4

  • eBook Packages: Springer Book Archive

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