An adaptive fast Gauss transform in two dimensions
This work provides a practical tool for computational physics and engineering problems requiring Gaussian convolution, though it is an incremental improvement over existing fast Gauss transform methods.
The authors present a unified fast Gauss transform in two dimensions using an adaptive quad-tree discretization, achieving efficient convolution of the heat kernel for any Gaussian variance with free-space or periodic boundary conditions.
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.