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Generalized Multilevel SQP-methods for PDAE-constrained Optimization Based on Space-Time Adaptive PDAE Solvers

  • Debora CleverEmail author
  • Jens Lang
  • Stefan Ulbrich
  • Carsten Ziems
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 160)

Abstract

In this work, we present an all-in-one optimization approach suitable to solve complex optimal control problems with time-dependent nonlinear partial differential algebraic equations and point-wise control constraints. A newly developed generalized SQP-method is combined with an error based multilevel strategy and the state-of-the-art software package Kardos to allow the efficient resolution of different space and time scales in an adaptive manner. The numerical performance of the method is demonstrated and analyzed for a real-life two-dimensional radiative heat transfer problem modelling the optimal boundary control for a cooling process in glass manufacturing.

Keywords

Adaptivemultilevel finite elements Rosenbrock method, glass cooling radiation multilevel optimization generalized SQP method control constraints trust region methods PDAE constrained optimization 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Debora Clever
    • 1
    Email author
  • Jens Lang
    • 1
  • Stefan Ulbrich
    • 1
  • Carsten Ziems
    • 2
  1. 1.Department of Mathematics and Graduate School of Computational EngineeringTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of MathematicsTechnische Universität DarmstadtDarmstadtGermany

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