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

  • Authors:

  • Jing-Rebecca Li;Leslie Greengard

  • Affiliations:

  • INRIA-Rocquencourt, Projet POEMS, Domaine de Voluceau - Rocquencour, 78153 Le Chesnay Cedex, France;INRIA-Rocquencourt, Projet POEMS, Domaine de Voluceau - Rocquencour, 78153 Le Chesnay Cedex, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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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.