SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page B937-B960, January 2021.
We develop a random batch Ewald (RBE) method for molecular dynamics simulations of particle systems with long-range Coulomb interactions, which achieves an $O(N)$ complexity in each step of simulating $N$-body systems. The RBE method is based on the Ewald splitting for the Coulomb kernel with a random “minibatch” type technique introduced to speed up the summation of the Fourier series for the long-range part of the splitting. Importance sampling is employed to reduce the induced force variance by taking advantage of the fast decay property of the Fourier coefficients. The stochastic approximation is unbiased with controlled variance. Analysis for bounded force fields gives some theoretic support of the method. Simulations of two typical problems of charged systems are presented to illustrate the accuracy and efficiency of the RBE method in comparison to the results from the Debye--Hückel theory, the classical Ewald summation, and the particle-particle particle-mesh method, demonstrating that the proposed method has the attractiveness of being easy to implement with the linear scaling and is promising for many practical applications.

中文翻译：

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具有库仑相互作用的粒子系统的随机批量 Ewald 方法

SIAM 科学计算杂志，第 43 卷，第 4 期，第 B937-B960 页，2021 年 1 月。
我们开发了一种随机批量 Ewald (RBE) 方法，用于具有长程库仑相互作用的粒子系统的分子动力学模拟，该方法在模拟 $N$-body 系统的每个步骤中实现 $O(N)$ 复杂度。RBE 方法基于库仑核的 Ewald 分裂，引入了随机“小批量”类型的技术，以加速分裂的远程部分的傅立叶级数的求和。通过利用傅立叶系数的快速衰减特性，采用重要性采样来减少诱导力的变化。随机近似是无偏的，具有受控方差。对有界力场的分析为该方法提供了一些理论支持。