Preprint of the project: SFB 701: Spectral Structures and Topological Methods in Mathematics - Project A2

Numerical analysis of high-dimensional transfer operators

08-118 Jens Kemper.
Computing invariant measures with dimension reduction methods

We present an algorithm to compute invariant measures in high dimensions, e.g. in discretizations of scalar reaction diffusion equations. The algorithm combines subdivision techniques developed by Dellnitz, Junge and co-authors with Proper Orthogonal Decomposition as a model reduction method. Since the algorithm computes discrete measures with support in a low dimensional subspace of the state space we present methods for representing and comparing such measures. One such method aims at a discretization of the Prohorov metric. The paper also contains numerical results of the algorithms.