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Stefan Ulbrich
Multilevel Methods for PDE-Constrained Optimization Based on Adaptive Discretizations and Reduced Order Models

Dolivostr 15
64293 Darmstadt
Germany
ulbrich@mathematik.tu-darmstadt.de
Stefan Ulbrich
Stefanie Bott

In this talk we discuss recent developments for multilevel optimization methods. In particular, we propose a multilevel optimization approach that generates a hierarchy of adaptive discretizations during the optimization iteration using adaptive finite-element approximations and reduced order models such as POD. The adaptive refinement strategy is based on a posteriori error estimators for the PDE-constraint, the adjoint equation and the criticality measure. The resulting optimization method allows to use existing adaptive PDE-solvers and error estimators in a modular way. By combining Moreau-Yosida regularization techniques with the multilevel approach the method is able to handle state constraints. We demonstrate the efficiency of the approach by numerical examples.





Copper Mountain 2014-02-23