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Localized Model Reduction in PDE Constrained Optimization

  • Mario Ohlberger
  • Michael Schaefer
  • Felix Schindler
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 169)

Abstract

We present efficient localized model reduction approaches for PDE constraint optimization or optimal control. The first approach focuses on problems where the underlying PDE is given as a locally periodic elliptic multiscale problem. The second approach is more universal and focuses on general underlying multiscale or large scale problems. Both methods make use of reduced basis techniques and rely on efficient a posteriori error estimation for the approximation of the underlying parameterized PDE. The methods are presented and numerical experiments are discussed.

Keywords

Localized model reduction Reduced basis methods Optimal control PDE constrained optimization LRBMS Heterogeneous multiscale method 

Mathematics Subject Classification (2010).

Primary 65K10; Secondary 65N30 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Mario Ohlberger
    • 1
  • Michael Schaefer
    • 1
  • Felix Schindler
    • 1
  1. 1.Applied Mathematics MuensterMünsterGermany

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