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

Fuente: arXiv
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Main Authors: Liang, Jiuyang, Xu, Zhenli, Zhou, Qi
Format: Preprint
Published: 2023
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author Liang, Jiuyang
Xu, Zhenli
Zhou, Qi
author_facet Liang, Jiuyang
Xu, Zhenli
Zhou, Qi
contents 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 $\mathcal{O}(b^{-M})$ for the energy and $\mathcal{O}(b^{-3M})$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2305_05369
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Error estimate of the u-series method for molecular dynamics simulations
Liang, Jiuyang
Xu, Zhenli
Zhou, Qi
Numerical Analysis
41A25, 82M37, 68W40, 42A38
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 $\mathcal{O}(b^{-M})$ for the energy and $\mathcal{O}(b^{-3M})$ 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.
title Error estimate of the u-series method for molecular dynamics simulations
topic Numerical Analysis
41A25, 82M37, 68W40, 42A38
url https://arxiv.org/abs/2305.05369