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Title: An Adaptive Fast Gauss Transform in Two Dimensions

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.

Authors:
 [1];  [1]
  1. New York Univ. (NYU), New York, NY (United States)
Publication Date:
Research Org.:
New York Univ. (NYU), NY (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1511004
Grant/Contract Number:  
FG02-88ER25053
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 40; Journal Issue: 3; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; fast Gauss transform; heat equation; adaptive mesh refinement

Citation Formats

Wang, Jun, and Greengard, Leslie. An Adaptive Fast Gauss Transform in Two Dimensions. United States: N. p., 2018. Web. doi:10.1137/17m1159865.
Wang, Jun, & Greengard, Leslie. An Adaptive Fast Gauss Transform in Two Dimensions. United States. https://doi.org/10.1137/17m1159865
Wang, Jun, and Greengard, Leslie. Thu . "An Adaptive Fast Gauss Transform in Two Dimensions". United States. https://doi.org/10.1137/17m1159865. https://www.osti.gov/servlets/purl/1511004.
@article{osti_1511004,
title = {An Adaptive Fast Gauss Transform in Two Dimensions},
author = {Wang, Jun and Greengard, Leslie},
abstractNote = {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.},
doi = {10.1137/17m1159865},
journal = {SIAM Journal on Scientific Computing},
number = 3,
volume = 40,
place = {United States},
year = {2018},
month = {5}
}

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Works referencing / citing this record:

Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensions
journal, October 2018