Numerical methods for highly oscillatory dynamical systems using multiscale structure

Applied and Computational Mathematics Seminar
Monday, September 9, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 005
GT Math
The main aim of this talk is to design efficient and novel numerical algorithms for highly oscillatory dynamical systems with multiple time scales. Classical numerical methods for such problems need temporal resolution to resolve the finest scale and become very inefficient when the longer time intervals are of interest.  In order to accelerate computations and improve the long time accuracy of numerical schemes, we take advantage of various multiscale structures established from a separation of time scales.  The framework of the heterogeneous multiscale method (HMM) will be considered as a general strategy both for the design and for the analysis of  multiscale methods.(Keywords: Multiscale oscillatory dynamical systems, numerical averaging methods.)