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 quadtree discretization on a unit square which is assumed to contain all sources. Our implementation permits either freespace or periodic boundary conditions to be imposed, and is efficient for any choice of variance in the Gaussian.
 Authors:

 New York Univ. (NYU), New York, NY (United States)
 Publication Date:
 Research Org.:
 New York Univ. (NYU), New York, NY (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1511004
 Grant/Contract Number:
 FG0288ER25053
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 40; Journal Issue: 3; Journal ID: ISSN 10648275
 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. doi:https://doi.org/10.1137/17m1159865
Wang, Jun, and Greengard, Leslie. Thu .
"An Adaptive Fast Gauss Transform in Two Dimensions". United States. doi: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 quadtree discretization on a unit square which is assumed to contain all sources. Our implementation permits either freespace 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}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Cited by: 2 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referencing / citing this record:
Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensions
journal, October 2018
 Wang, Jun; Greengard, Leslie
 Advances in Computational Mathematics, Vol. 45, Issue 2