Abstract: Dynamical systems (possibly stochastic) with multiple time scales pose a major problem in simulations because the small time steps required for stable integration of the fast motions lead to large numbers of time steps required for the observation of slow degrees of freedom. A general belief has been that with a nonlinear relation between original and slow variables, averaging integrators should not work "if the slow variables are not explicitly identified and made use of". Furthermore, in recent years, a great deal of attention has been focused on the following challenges: How to accelerate a legacy code (used as black box) for stiff ODEs or SDEs while, at the same time, preserving all of its nice properties? How to obtain explicit structure/symmetry-preserving integrators for (possibly stochastic) mechanical (molecular) systems with non quadratic stiff-potentials? etc...
In this talk, we show that these problems have a surprisingly simple common solution: turning on and off large coefficients in the legacy code. This a joint work with J. Marsden and M. Tao.

Brief Biography of the Speaker:
Houman Owhadi PhD is an assistant professor of Applied and Computational Mathematics and Control and Dynamical Systems at California Institute of Technology. His research interests are in homogenization and multiscale analysis, probability theory, stochastic mechanics, molecular dynamics and uncertainty quantification. He is the head of the uncertainty quantification group of the Caltech Predictive Science Academic Alliance Program.