Leslie Greengard, Courant Department of Mathematics, New York University
Adaptive methods for the simulation of diffusion and fluid flow in complex geometries
We will review the state of the art in integral equation methods for the solution of the heat equation and fluid flow in moving geometries. With suitable fast algorithms, 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. We will discuss applications to biophysical modeling, reaction-diffusion systems, and incompressible fluid dynamics.