Error estimate of the u-series method for molecular dynamics simulations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913635241033728 |
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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 |
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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 |