An Adaptive Fast Gauss Transform in Two Dimensions

Jun Wang Yau Mathematical Sciences Center, Tsinghua University Leslie Greengard Courant Institute, New York University

Numerical Analysis and Scientific Computing mathscidoc:2205.25001

Journal of Computational Physics, 40, (3), 2018.5
A variety of problems in computational physics and engineering require the convolu- tion 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.
fast Gauss transform, heat equation, adaptive mesh refinement
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@inproceedings{jun2018an,
  title={An Adaptive Fast Gauss Transform in Two Dimensions},
  author={Jun Wang, and Leslie Greengard},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517121328825473184},
  booktitle={Journal of Computational Physics},
  volume={40},
  number={3},
  year={2018},
}
Jun Wang, and Leslie Greengard. An Adaptive Fast Gauss Transform in Two Dimensions. 2018. Vol. 40. In Journal of Computational Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517121328825473184.
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