## 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 (NM log N), 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.

Original language | English (US) |
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Pages (from-to) | 1891-1901 |

Number of pages | 11 |

Journal | Journal of Computational Physics |

Volume | 226 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 2007 |

## Keywords

- Free space
- Heat equation
- Integral representation
- Spectral approximation
- Unbounded domain

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics