Mathematisches Kolloquium

The next talk in the mathematical colloquium will take place Friday, 14th of January 2022, 2:15 pm  via Zoom.

Title:  (Localized) Model Reduction with Adaptive Enrichment for PDE Constrained Optimization
Speaker: Prof. Dr. Mario Ohlberger (Universität Münster)

Model order reduction is a very active research field that has seen tremendous development in recent years, both from a theoretical and application point of view.
A particular promising model reduction approach for parameterized partial differential equations (pPDEs) is the Reduced Basis (RB) Method that  relies on the approximation of the solution manifold of pPDEs by low dimensional linear spaces that are spanned from  suitably selected particular solutions, called snapshots.
While RB methods are meanwhile very well established and analyzed for scalar coercive problems, there are still major challenges for problems with a slow convergence of the Kolmogorov N-width.
Particular promising approaches for high dimensional parameter dependence or for multiscale problems are localized model reduction approaches.
Based on efficient a posteriori error control and online enrichment, these methods overcome traditional offline/online splitting and are thus particularly well suited for applications in optimization or inverse problems. In this talk we investigate model reduction with adaptive basis enrichment within an Trust Region  RB approach that updates the reduced model during the trust region iterations.
We discuss a posteriori error estimation, convergence of the overall method as well as numerical experiments that demonstrate the efficiency of the approach.

This is joint work with Tim Keil, Luca Mechelli, Felix Schindler, Stephan Rave, and Stefan Volkwein.