Fast computation of time convolutions: the heat equation and applications

Abstract: I will describe a fast method to compute time convolutions, with the goal of numerically solving diffusion-type equations in a way that is computationally efficient in time and memory.

The method is Fourier-based, the practical implementation of which requires several recently developed sub-algorithms. These include the Fast Gauss Transform, the Non-uniform Fast Fourier Transform, spectral approximation of the heat kernel, and high order quadratures for heat layer potentials.

I will show the application of this method to the modeling of crystal growth and briefly touch upon the extension of this work to fractional integral and differential equations.

This is joint work with Leslie Greengard, Donna Calhoun, and Lucien Brush.

Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge).