On the numerical solution of the heat equation I: Fast solvers in free space

Abstract

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.

DOI: 10.1016/j.jcp.2007.06.021

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@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} }