Abstract: Stefan Ulbrich

TU Darmstadt

Adaptive Multilevel Methods for PDE-Constrained Optimization Based on Adaptive Finite Element or Reduced Order Approximations

We present an adaptive multilevel generalized SQP-method for optimal control problems governed by nonlinear PDEs with control constraints. During the optimization iteration the algorithm generates a hierarchy of adaptively refined discretizations, which can be based on adaptive finite element approximations or on reduced order methods like Reduced Basis Methods or POD. The adaptive refinement strategy is based on error estimators for the PDE, adjoint PDE and a criticality measure. We consider first the case of an adaptive finite element discretization and discuss then the extension of the algorithm to adaptive approximations by reduced order models. We conclude the talk by showing numerical results.

Joint work with J. Carsten Ziems, Department of Mathematics, TU Darmstadt.


Aachen Institute for Advanced Study in Computational Engineering Science (AICES)
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