A new version of the fast Gauss transform and the simulation of diffusion in complex geometries

Abstract: We will review the state of the art in fast algorithms for the solution of the heat equation in moving geometries, using integral equation methods. Such methods achieve optimal complexity and, in the homogeneous case, require the discretization of the space-time boundary alone. They achieve high order accuracy with suitable quadratures and are straightforward to implement adaptively in space-time. This set of tools has direct application to biophysical modeling, reaction-diffusion systems, and computational fluid dynamics.