Error estimate of the u-series method for molecular dynamics simulations

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED
Jiuyang Liang , Zhenli Xu , Qi Zhou
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引用次数: 0

Abstract

This paper provides an error estimate for the u-series method of the Coulomb interaction in molecular dynamics simulations. We show that the number of truncated Gaussians M in the u-series and the base of interpolation nodes b in the bilateral serial approximation are two key parameters for the algorithm accuracy, and that the errors converge as O(bM) for the energy and O(b3M) for the force. Error bounds due to numerical quadrature and cutoff in both the electrostatic energy and forces are obtained. Closed-form formulae are also provided, which are useful in the parameter setup for simulations under a given accuracy. The results are verified by analyzing the errors of two practical systems.
分子动力学模拟u系列方法的误差估计
本文给出了分子动力学模拟中库仑相互作用的u系列方法的误差估计。我们证明了u序列中截断的高斯数M和双边序列逼近中插值节点的基数b是算法精度的两个关键参数,并且误差收敛为能量的O(b−M)和力的O(b−3M)。得到了静电能量和静电力的数值正交和截止误差限。本文还提供了封闭形式的公式,用于在给定精度下的仿真参数设置。通过对两个实际系统的误差分析,验证了上述结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis 物理-物理:数学物理
CiteScore
5.40
自引率
4.00%
发文量
67
审稿时长
22.9 weeks
期刊介绍: Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.
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