Electrostatic interactions involving point multipoles are being increasingly implemented to achieve higher accuracy in molecular simulations. A major drawback of multipolar electrostatics is the increased computational cost. Here we develop and compare two Cartesian tree algorithms which employ Taylor approximations and hierarchical clustering to speed up the evaluation of point multipole interactions. We present results from applying the algorithms to compute the free space Coulomb potential and forces of different sets of interacting point multipoles with different densities. The methods achieve high accuracy and speedup of more than an order of magnitude over direct sum calculations and scale well in parallel.

中文翻译：

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快速评估点多极静电相互作用的无网格层次聚类方法

涉及点多极的静电相互作用正越来越多地实现，以在分子模拟中实现更高的精度。多极静电的主要缺点是计算成本增加。在这里，我们开发和比较两种采用泰勒近似和层次聚类的笛卡尔树算法，以加快点多极相互作用的评估。我们介绍了通过应用算法来计算自由空间库仑电势和具有不同密度的不同点的多组相互作用点的力的结果。该方法在直接总和计算上可实现较高的精度和超过一个数量级的加速，并且可以很好地并行扩展。