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

  • Marco Fahl
  • Ekkehard W. Sachs
Part of the Lecture Notes in Computational Science and Engineering book series (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.

Keywords

Proper Orthogonal Decomposition Reduce Order Model Adjoint Equation Trust Region Method Proper Orthogonal Decomposition Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Marco Fahl
    • 1
  • Ekkehard W. Sachs
    • 1
    • 2
  1. 1.Fachbereich IV — MathematikUniversität TrierTrierGermany
  2. 2.Department of MathematicsVirginia Polytechnic Institute and State University, ICAMBlacksburgUSA

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