An Adaptive Fast Gauss Transform in Two Dimensions

Wang, Jun; Greengard, Leslie

doi:10.1137/17m1159865

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:

Wang, Jun ^[1]; Greengard, Leslie ^[1]

New York Univ. (NYU), New York, NY (United States)

Publication Date:: Thu May 03 00:00:00 EDT 2018

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.

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                    Wang, Jun, & Greengard, Leslie. An Adaptive Fast Gauss Transform in Two Dimensions.  United States.  https://doi.org/10.1137/17m1159865

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                    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.

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@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         = {Thu May 03 00:00:00 EDT 2018},

  month        = {Thu May 03 00:00:00 EDT 2018}

}

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https://doi.org/10.1137/17m1159865

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Cited by: 6 works

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Works referenced in this record:

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journal, January 2009

Tausch, Johannes; Weckiewicz, Alexander
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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

Wang, Jun; Greengard, Leslie
Advances in Computational Mathematics, Vol. 45, Issue 2
DOI: 10.1007/s10444-018-9641-5

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

Wang, Jun; Greengard, Leslie
arXiv
DOI: 10.48550/arxiv.1803.07668

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Title: An Adaptive Fast Gauss Transform in Two Dimensions

Abstract

Citation Formats

An adaptive fast multipole accelerated Poisson solver for complex geometries journal, September 2017

The Method of Layer Potentials for the Heat Equation in Lipschitz Cylinders journal, April 1989

An adaptive fast solver for the modified Helmholtz equation in two dimensions journal, January 2006

Application of the boundary element method to transient heat conduction journal, May 1991

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A Fast Algorithm for Particle Simulations journal, August 1997

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An efficient direct BEM numerical scheme for phase change problems using Fourier series journal, March 2002

A free-space adaptive FMM-Based PDE solver in three dimensions journal, January 2011

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The Fast Generalized Gauss Transform journal, January 2010

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A High-Order Solver for the Heat Equation in 1D domains with Moving Boundaries journal, January 2007

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A sharp error estimate for the fast Gauss transform journal, November 2006

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A sharp error estimate for the fast Gauss transform journal, November 2006

Efficient kernel density estimation using the fast gauss transform with applications to color modeling and tracking journal, November 2003

High Order Accurate Methods for the Evaluation of Layer Heat Potentials journal, January 2009

Multidimensional Fast Gauss Transforms by Chebyshev Expansions journal, January 2009

The Fast Gauss Transform journal, January 1991

A New Error Estimate of the Fast Gauss Transform journal, January 2002

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

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

An adaptive fast multipole accelerated Poisson solver for complex geometries
journal, September 2017

The Method of Layer Potentials for the Heat Equation in Lipschitz Cylinders
journal, April 1989

An adaptive fast solver for the modified Helmholtz equation in two dimensions
journal, January 2006

Application of the boundary element method to transient heat conduction
journal, May 1991

A New Fast-Multipole Accelerated Poisson Solver in Two Dimensions
journal, January 2001

The black-box fast multipole method
journal, December 2009

A Direct Adaptive Poisson Solver of Arbitrary Order Accuracy
journal, May 1996

Spectral Approximation of the Free-Space Heat Kernel
journal, July 2000

A Fast Algorithm for Particle Simulations
journal, August 1997

The Fast Gauss Transform
journal, January 1991

An efficient direct BEM numerical scheme for phase change problems using Fourier series
journal, March 2002

A free-space adaptive FMM-Based PDE solver in three dimensions
journal, January 2011

High Order Accurate Methods for the Evaluation of Layer Heat Potentials
journal, January 2009

Algorithm 967: A Distributed-Memory Fast Multipole Method for Volume Potentials
journal, September 2016

The Fast Generalized Gauss Transform
journal, January 2010

The Fast Gauss Transform with Variable Scales
journal, September 1991

Fast Adaptive Methods for the Free-Space Heat Equation
journal, January 1994

Multidimensional Fast Gauss Transforms by Chebyshev Expansions
journal, January 2009

Multivariate polynomial approximation in the hypercube
journal, June 2017

A High-Order Solver for the Heat Equation in 1D domains with Moving Boundaries
journal, January 2007

The Chebyshev fast Gauss and nonuniform fast Fourier transforms and their application to the evaluation of distributed heat potentials
journal, August 2008

A sharp error estimate for the fast Gauss transform
journal, November 2006

A kernel-independent adaptive fast multipole algorithm in two and three dimensions
journal, May 2004

A sharp error estimate for the fast Gauss transform
journal, November 2006

Efficient kernel density estimation using the fast gauss transform with applications to color modeling and tracking
journal, November 2003

High Order Accurate Methods for the Evaluation of Layer Heat Potentials
journal, January 2009

Multidimensional Fast Gauss Transforms by Chebyshev Expansions
journal, January 2009

The Fast Gauss Transform
journal, January 1991

A New Error Estimate of the Fast Gauss Transform
journal, January 2002

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

Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensions
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