SIAM Review, Volume 66, Issue 2, Page 287-315, May 2024.
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 grid point, despite being fully adaptive.

中文翻译：

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离散和连续源自适应快速高斯变换的新版本

SIAM Review，第 66 卷，第 2 期，第 287-315 页，2024 年 5 月。
我们提出了适用于离散和连续源的新版本快速高斯变换 (FGT)。完全避免了经典的埃尔米特展开，仅利用高斯核的平面波表示和新的分层合并方案。对于在自适应张量积网格上采样的连续源分布，我们利用高斯核的可分离结构来加速计算。对于离散源，该方案依靠非均匀快速傅里叶变换（NUFFT）来构建近场平面波表示。该方案已针对自由空间或周期性边界条件实施。在许多情况下，尽管是完全自适应的，但每个网格点工作的速度与传统 FFT 相当或更好。