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Journal Articles Journal of Computational Physics Year : 2007

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 O(NMlogN), 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.

Dates and versions

hal-00781132 , version 1 (25-01-2013)

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Jing-Rebecca Li, Leslie Greengard. On the numerical solution of the heat equation I: Fast solvers in free space. Journal of Computational Physics, 2007, 226 (2), pp.1891--1901. ⟨10.1016/j.jcp.2007.06.021⟩. ⟨hal-00781132⟩
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