## UC Berkeley / Lawrence Berkeley Laboratory

#### Multiscale Geometric Integration and Analysis of Deterministic and Stochastic Systems

**Molei Tao, Caltech**

##### November 30th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

In order to accelerate computations, improve long time accuracy of numerical
simulations, and sample statistics distribution by dynamics, we develop
multiscale geometric integrators. Most of the talk will be focused on the
description of FLow AVeraging integratORs (FLAVORs), which apply to general
multiscale stiff ODEs, SDEs, and PDEs. These integrators employ coarse
integration steps that do not resolve the fast timescale in the dynamics;
nevertheless, they capture the correct effective contribution of the fast
dynamics. Distinct from existing approaches, an identification of the
underlying slow variables (or process) is not required, and intrinsic geometric
structures (*e.g.* symplecticity, conservation laws) can be preserved by the
multiscale simulation.