Localized Model Reduction in PDE Constrained Optimization

Ohlberger Mario, Schaefer Michael, Schindler Felix

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.