论文标题
与库仑相互作用的粒子系统的随机批次ewald方法
A random batch Ewald method for particle systems with Coulomb interactions
论文作者
论文摘要
我们开发了一种随机批次ewald（RBE）方法，用于具有远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 Systems的每个步骤中都达到了$ o（n）$复杂性。 RBE方法基于库仑内核的Ewald拆分，其带有随机的“迷你批次”类型技术，以加快分裂远程部分的傅立叶系列的总和。通过利用傅立叶系数的快速衰减特性，采用了重要性采样来减少诱导的力差异。随机近似是没有偏见的。有界力场的分析给出了该方法的一些理论支持。与Debye-Hückel理论和古典Ewald总结相比，提出了对带电系统的两个典型问题的模拟，以说明RBE方法的准确性和效率，表明该方法具有易于通过线性缩放来实现的吸引力，并且对许多实际应用有望实现。
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 the $N$-body systems. The RBE method is based on the Ewald splitting for the Coulomb kernel with a random "mini-batch" 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 and the classical Ewald summation, demonstrating that the proposed method has the attractiveness of being easy to implement with the linear scaling and is promising for many practical applications.
