Highly Influenced

4 Excerpts

- Published 2007 in J. Comput. Physics

We describe a fast solver for the inhomogeneous heat equation in free space, following the time evolution of the solution in the Fourier domain. It relies on a recently developed spectral approximation of the free-space heat kernel coupled with the non-uniform fast Fourier transform. Unlike finite difference and finite element techniques, there is no need for artificial boundary conditions on a finite computational domain. The method is explicit, unconditionally stable, and requires an amount of work of the order OðNM logNÞ, where N is the number of discretization points in physical space and M is the number of time steps. We refer to the approach as the fast recursive marching (FRM) method. 2007 Elsevier Inc. All rights reserved.

@article{Li2007OnTN,
title={On the numerical solution of the heat equation I: Fast solvers in free space},
author={Jing-Rebecca Li and Leslie Greengard},
journal={J. Comput. Physics},
year={2007},
volume={226},
pages={1891-1901}
}