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首页> 外文期刊>Journal of Computational Physics >Spectral accuracy in fast Ewald-based methods for particle simulations
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Spectral accuracy in fast Ewald-based methods for particle simulations

机译：基于Ewald的快速粒子模拟方法的光谱精度

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摘要

A spectrally accurate fast method for electrostatic calculations under periodic boundary conditions is presented. We follow the established framework of FFT-based Ewald summation, but obtain a method with an important decoupling of errors: it is shown, for the proposed method, that the error due to frequency domain truncation can be separated from the approximation error added by the fast method. This has the significance that the truncation of the underlying Ewald sum prescribes the size of the grid used in the FFT-based fast method, which clearly is the minimal grid. Both errors are of exponential-squared order, and the latter can be controlled independently of the grid size. We compare numerically to the established SPME method by Essmann et al. and see that the memory required can be reduced by orders of magnitude. We also benchmark efficiency (i.e. error as a function of computing time) against the SPME method, which indicates that our method is competitive. Analytical error estimates are proven and used to select parameters with a great degree of reliability and ease.
机译：提出了一种光谱精确的快速方法，用于在周期性边界条件下进行静电计算。我们遵循已建立的基于FFT的Ewald求和框架，但是获得了一种具有重要的误差解耦的方法：对于所提出的方法，表明可以将频域截断引起的误差与由加法器添加的近似误差分开。快速的方法。这具有重要的意义，即基础Ewald和的截断规定了基于FFT的快速方法中使用的网格的大小，这显然是最小网格。两种误差均为指数平方级，并且可以独立于网格大小来控制后者。我们在数值上与Essmann等人建立的SPME方法进行比较。并且看到所需的内存可以减少几个数量级。我们还针对SPME方法对效率进行了基准测试（即误差作为计算时间的函数），这表明我们的方法具有竞争力。分析误差估计值已得到验证，可用于高度可靠和轻松地选择参数。

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