A multiscale computation for highly oscillatory dynamical systems using two approaches

Applied and Computational Mathematics Seminar
Monday, March 3, 2014 - 2:00pm
1 hour (actually 50 minutes)
Skiles 005
GT Math
In this talk, the two approaches for computing the long time behavior of highly oscillatory dynamical systems will be introduced.  Firstly, a generalization of the backward-forward HMM (BF HMM) will be discussed. It is intended to deal with the multiple time scale (>2) behavior of certain nonlinear systems where the non-linearity is introduced as a perturbation to a primarily linear problem. Focusing on the Fermi-Pasta-Ulam problem, I propose a three-scale version of the BF HMM.  Secondly, I will consider a multiscale method using a signal processingidea. The dynamics on the slow time scale can be approximated by an averaged system gained by fltering out the fast oscillations. An Adaptive Local Iterative Filtering (ALIF) algorithm is used to do such averaging with respect to fast oscillations.