Latest trends on systems - Wseas.us

LATEST TRENDS on SYSTEMS (Volume I)Plenary Lecture 10Accelerate your Favorite Numerical Integrator with Two Lines of CodeAssistant Professor Houman OwhadiCalifornia Institute of TechnologyPasadena, CAUSAE-Mail: owhadi@caltech.eduAbstract: Dynamical systems (possibly stochastic) with multiple time scales pose a major problem in simulationsbecause the small time steps required for stable integration of the fast motions lead to large numbers of time stepsrequired for the observation of slow degrees of freedom. A general belief has been that with a nonlinear relationbetween original and slow variables, averaging integrators should not work "if the slow variables are not explicitlyidentified and made use of". Furthermore, in recent years, a great deal of attention has been focused on the followingchallenges: 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 (possiblystochastic) 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 largecoefficients 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 andDynamical Systems at California Institute of Technology. His research interests are in homogenization and multiscaleanalysis, probability theory, stochastic mechanics, molecular dynamics and uncertainty quantification. He is the headof the uncertainty quantification group of the Caltech Predictive Science Academic Alliance Program.ISSN: 1792-4235 30 ISBN: 978-960-474-199-1