# 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:

- 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:
- [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. doi:10.1137/17m1159865.
```

```
Wang, Jun, and Greengard, Leslie. Thu .
"An Adaptive Fast Gauss Transform in Two Dimensions". United States. doi: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}

}

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.