Preprint of the project:
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.
