@article{932d32309cc84925a919a83cee49de65,
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.",
keywords = "Adaptive mesh refinement, Fast Gauss transform, Heat equation",
author = "Jun Wang and Leslie Greengard",
note = "Funding Information: ∗Submitted to the journal{\textquoteright}s Methods and Algorithms for Scientific Computing section December 5, 2017; accepted for publication (in revised form) February 20, 2018; published electronically May 3, 2018. http://www.siam.org/journals/sisc/40-3/M115986.html Funding: The second author{\textquoteright}s work was supported in part by the Applied Mathematical Sciences Program of the U.S. Department of Energy under contract DEFGO288ER25053 and by the RiskEcon Lab for Decision Metrics, Courant Institute. †Courant Institute of Mathematical Sciences, New York University, New York, NY 10012. Current address: Flatiron Institute, Simons Foundation, New York, NY 10010 (junwang@flatironinstitute. org). ‡Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, and Flatiron Institute, Simons Foundation, New York, NY 10010 (greengard@cims.nyu.edu). Publisher Copyright: {\textcopyright} 2018 SIAM.",
year = "2018",
doi = "10.1137/17M1159865",
language = "English (US)",
volume = "40",
pages = "A1274--A1300",
journal = "SIAM Journal of Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}