  We present a new version of the fast Gauss transform (FGT) for discrete and
continuous sources. Classical Hermite expansions are avoided entirely, making
use only of the plane-wave representation of the Gaussian kernel and a new
hierarchical merging scheme. For continuous source distributions sampled on
adaptive tensor-product grids, we exploit the separable structure of the
Gaussian kernel to accelerate the computation. For discrete sources, the scheme
relies on the nonuniform fast Fourier transform (NUFFT) to construct near field
plane wave representations. The scheme has been implemented for either
free-space or periodic boundary conditions. In many regimes, the speed is
comparable to or better than that of the conventional FFT in work per
gridpoint, despite being fully adaptive.
