论文标题
用于带电颗粒的蒙特卡洛模拟中静电相互作用的新算法
A new algorithm for electrostatic interactions in Monte Carlo simulations of charged particles
论文作者
论文摘要
为了最大程度地减少带电颗粒的蒙特卡洛模拟中的系统误差，必须准确有效地计算远程静电相互作用。标准方法，例如埃瓦尔德（Ewald）求和或经典快速多极方法的幼稚应用，导致每个大都市悬挂步骤的成本，该步骤与系统中粒子$ n $的某些正功率成正比增长。这种过高的成本可阻止对具有相当数量颗粒的系统进行准确的模拟。当前，通常通过截断引入无法控制的系统错误的库仑电势来模拟大型系统。在本文中，我们提出了一种新的多级方法，该方法将计算复杂性降低到$ \ MATHCAL {O}（\ log（n））$每个大都市悬挂步骤，同时保持与直接Ewald Sumpation相当的错误。我们表明，与以前的相关工作相比，我们的方法通过在每个大都市狂欢步骤的提案和接受阶段的更好平衡时间来降低总成本。通过模拟最多$ n = 10^5 $粒子的大型系统，我们证明了我们的实现与最先进的MC软件包具有竞争力，并允许模拟具有准确的静电的非常大的带电颗粒系统。
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of the classical Fast Multipole Method, result in a cost per Metropolis-Hastings step which grows in proportion to some positive power of the number of particles $N$ in the system. This prohibitively large cost prevents accurate simulations of systems with a sizeable number of particles. Currently, large systems are often simulated by truncating the Coulomb potential which introduces uncontrollable systematic errors. In this paper we present a new multilevel method which reduces the computational complexity to $\mathcal{O}(\log(N))$ per Metropolis-Hastings step, while maintaining errors which are comparable to direct Ewald summation. We show that compared to related previous work, our approach reduces the overall cost by better balancing time spent in the proposal- and acceptance- stages of each Metropolis-Hastings step. By simulating large systems with up to $N=10^5$ particles we demonstrate that our implementation is competitive with state-of-the-art MC packages and allows the simulation of very large systems of charged particles with accurate electrostatics.
