Tuesday, 15:15 - 15:40 h, Room: MA 415


Stefan Ulbrich
Multilevel optimization based on adaptive discretizations and reduced order models for engineering applications

Coauthor: J. Carsten Ziems


We consider optimization problems governed by partial differential
equations. Multilevel techniques use a hierarchy of approximations to
this infinite dimensional problem and offer the potential to carry out
most optimization iterations on comparably coarse discretizations.
Motivated by engineering applications we discuss the efficient interplay between the optimization method, adaptive discretizations of the PDE, reduced order models derived from these discretizations, and error estimators.
To this end, we describe an adaptive multilevel SQP method 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 methods allows to use existing adaptive PDE-solvers and error estimators in a modular way.
We demonstrate the efficiency of the approach by numerical examples for engineering applications.


Talk 1 of the invited session Tue.3.MA 415
"Optimization applications in industry II" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]


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