Discretization of transfer operators using a sparse hierarchical tensor basis - the Sparse Ulam method

Details Discretization of transfer operators using a sparse hierarchical tensor basis - the Sparse Ulam method Discretization of transfer operators using a sparse hierarchical tensor basis - the Sparse Ulam method

2008-02-27

arxiv.org/abs/0802.4006v1

Mathematics

Numerical Analysis

Scientific paper

The global macroscopic behaviour of a dynamical system is encoded in the eigenfunctions of a certain transfer operator associated to it. For systems with low dimensional long term dynamics, efficient techniques exist for a numerical approximation of the most important eigenfunctions, cf. DeJu99a. They are based on a projection of the operator onto a space of piecewise constant functions supported on a neighborhood of the attractor - Ulam's method. In this paper we develop a numerical technique which makes Ulam's approach applicable to systems with higher dimensional long term dynamics. It is based on ideas for the treatment of higher dimensional partial differential equations using sparse grids. We develop the technique, establish statements about its complexity and convergence and present two numerical examples.

Affiliated with

Also associated with

No associations

Rating

Discretization of transfer operators using a sparse hierarchical tensor basis - the Sparse Ulam method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Discretization of transfer operators using a sparse hierarchical tensor basis - the Sparse Ulam method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discretization of transfer operators using a sparse hierarchical tensor basis - the Sparse Ulam method will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-25829