Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary, electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular dynamics simulations which are major tools for problems at the nano-/micro- scale. Various algorithms aim to speed up the pairwise Coulomb interactions to a linear scaling but the poor scalability limits the size of simulated systems. Here, we conduct an efficient molecular dynamics algorithm with the random batch Ewald method on all-atom systems where the complete Fourier components in the Coulomb interaction are replaced by randomly selected mini batches. By simulating the N-body systems up to 100 million particles using 10 thousand CPU cores, we show that this algorithm furnishes O(N) complexity, almost perfect scalability and an order of magnitude faster computational speed when compared to the existing state-of-the-art algorithms. Further examinations of our algorithm on distinct systems, including pure water, micro-phase-separated electrolyte and protein solution demonstrate that the spatiotemporal information on all time and length scales investigated and thermodynamic quantities derived from our algorithm are in perfect agreement with those obtained from the existing algorithms. Therefore, our algorithm provides a breakthrough solution on scalability of computing the Coulomb interaction. It is particularly useful and cost-effective to simulate ultra-large systems, which was either impossible or very costing to conduct using existing algorithms, thus would benefit the broad community of sciences.

中文翻译：

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超可扩展分子动力学算法

库仑相互作用遵循反平方力定律，量化两个静止的带电粒子之间的力。库仑相互作用的长程性质对分子动力学模拟提出了重大挑战，而分子动力学模拟是解决纳米/微米尺度问题的主要工具。各种算法旨在将成对库仑相互作用加速到线性缩放，但较差的可扩展性限制了模拟系统的大小。在这里，我们在全原子系统上使用随机批次 Ewald 方法进行有效的分子动力学算法，其中库仑相互作用中的完整傅立叶分量被随机选择的小批次替换。通过使用 1 万个 CPU 内核模拟多达 1 亿个粒子的 N 体系​​统，我们表明该算法提供 O(N) 复杂度，与现有的最先进算法相比，几乎完美的可扩展性和更快的计算速度。在不同系统（包括纯水、微相分离电解质和蛋白质溶液）上对我们的算法的进一步检查表明，所研究的所有时间和长度尺度上的时空信息以及从我们的算法中得出的热力学量与从现有算法。因此，我们的算法为计算库仑相互作用的可扩展性提供了突破性的解决方案。模拟超大型系统特别有用且具有成本效益，而使用现有算法进行这种操作是不可能的或成本非常高的，因此将使广泛的科学界受益。