An adaptive fast gauss transform in two dimensions

Jun Wang; Leslie Greengard

doi:10.1137/17M1159865

An adaptive fast gauss transform in two dimensions

Jun Wang, Leslie Greengard

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	A1274-A1300
Journal	SIAM Journal on Scientific Computing
Volume	40
Issue number	3
DOIs	https://doi.org/10.1137/17M1159865
State	Published - 2018

Keywords

Adaptive mesh refinement
Fast Gauss transform
Heat equation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1137/17M1159865

Cite this

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AB - 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.

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KW - Heat equation

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An adaptive fast gauss transform in two dimensions

Abstract

Keywords

ASJC Scopus subject areas

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