An adaptive fast gauss transform in two dimensions

Research output: Contribution to journalArticle

Abstract

A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified fast Gauss transform for this purpose in two dimensions, making use of an adaptive quad-tree discretization on a unit square which is assumed to contain all sources. Our implementation permits either free-space or periodic boundary conditions to be imposed, and is efficient for any choice of variance in the Gaussian.

Original languageEnglish (US)
Pages (from-to)A1274-A1300
JournalSIAM Journal on Scientific Computing
Volume40
Issue number3
DOIs
StatePublished - 2018

Keywords

  • Adaptive mesh refinement
  • Fast Gauss transform
  • Heat equation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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