MOR Seminar

The next MOR Seminar will be held by Fredrik Ekre from the Technische Universität Braunschweig.

Topic: Numerical model reduction with error control for multiscale modeling of porous media

Abstract: Computational homogenization can be used in order to model the effective mechanical behavior of fluid saturated porous media with heterogeneous properties. A standard approach is the "finite element squared" (FE2) procedure, where a new boundary value problem for the coupled porous media problem is defined on a Representative Volume Element (RVE). The effective macroscopic response is obtained from solving the RVE problem. The FE2 strategy can be computationally expensive and it is therefore of interest to reduce the cost of solving the individual RVE problems by introducing a reduced basis. A well known method for identifying a reduced basis is Proper Orthogonal Decomposition (POD). Typically POD basis reduction can be split into an "offline" stage and an "online" stage. During the offline stage a set of training computations are performed in order to collect snapshots of the system. These snapshots are then used to construct a POD basis. In the online stage the simulation is accelerated by using the reduced basis. Naturally the accuracy of the online simulation depends on how well the reduced basis can capture also the new conditions. In this presentation we will present a POD-reduced model for solving the RVE problem, together with an a posteriori error estimator. We will also present some initial work towards an adaptive method, where the reduced basis is updated during the online stage to better capture new, previously unseen, loading.

The presentations are announced some days in advance via the mor-seminar mailing list of the University of Stuttgart.In case of interest to join this mailing list, please contact the organizers or register at

https://listserv.uni-stuttgart.de/mailman/listinfo/mor-seminar