The growth of simulations of particle systems has been aided by advances in computer speed and algorithms. The adoption of algorithms to solve N-body simulation problems has been less rapid due to the fact that such scaling was only competitive for relatively large N. Our work seeks to find algorithmic modifications and practical implementations for intermediate values of N in typical use for molecular simulations. This article reviews fast multipole techniques for calculation of electrostatic interactions in molecular systems. The basic mathematics behind fast summations applied to long ranged forces is presented along with advanced techniques for accelerating the solution, including our most recent developments. The computational efficiency of the new methods facilitates both simulations of large systems as well as longer and therefore more realistic simulations of smaller systems.

中文翻译：

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粒子动力学的快速多极方法

粒子系统模拟的发展得益于计算机速度和算法的进步。由于这种缩放仅对相对较大的 N 具有竞争力，因此采用算法来解决 N 体模拟问题的速度并不快。模拟。本文回顾了用于计算分子系统中静电相互作用的快速多极技术。介绍了应用于远程力的快速求和背后的基本数学，以及用于加速解决方案的先进技术，包括我们的最新发展。