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

Jing-Rebecca Li 1, 2 Leslie Greengard 2
1 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
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.
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Submitted on : Friday, January 25, 2013 - 2:04:32 PM
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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, Elsevier, 2007, 226 (2), pp.1891--1901. ⟨10.1016/⟩. ⟨hal-00781132⟩



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