The evaluation of electrostatic energy for a set of point charges in a periodic lattice is a computationally expensive part of molecular dynamics simulations (and other applications) because of the long-range nature of the Coulomb interaction. A standard approach is to decompose the Coulomb potential into a near part, typically evaluated by direct summation up to a cutoff radius, and a far part, typically evaluated in Fourier space. In practice, all decomposition approaches involve approximations-such as cutting off the near-part direct sum-but it may be possible to find new decompositions with improved trade-offs between accuracy and performance. Here, we present the u-series, a new decomposition of the Coulomb potential that is more accurate than the standard (Ewald) decomposition for a given amount of computational effort and achieves the same accuracy as the Ewald decomposition with approximately half the computational effort. These improvements, which we demonstrate numerically using a lipid membrane system, arise because the u-series is smooth on the entire real axis and exact up to the cutoff radius. Additional performance improvements over the Ewald decomposition may be possible in certain situations because the far part of the u-series is a sum of Gaussians and can thus be evaluated using algorithms that require a separable convolution kernel; we describe one such algorithm that reduces communication latency at the expense of communication bandwidth and computation, a trade-off that may be advantageous on modern massively parallel supercomputers.

中文翻译：

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u系列：用于静电计算的可分离分解，精度更高。

由于库仑相互作用的远距离特性，对周期性晶格中的一组点电荷的静电能进行评估是分子动力学模拟（和其他应用程序）在计算上昂贵的部分。一种标准方法是将库仑电势分解为一个近端部分（通常通过直接求和直到截止半径来评估）和一个远端部分（通常在傅立叶空间中评估）。在实践中，所有分解方法都涉及近似值（例如，截取近部分的直接和），但有可能找到新的分解方法，并在精度和性能之间进行权衡取舍。在这里，我们介绍U系列，对于给定的计算量，比标准（Ewald）分解更精确的库仑势的新分解，并且以大约一半的计算量实现与Ewald分解相同的精度。我们使用脂质膜系统在数值上证明了这些改进，是因为u系列在整个实轴上都是平滑的，并且精确到截止半径。在某些情况下，可以通过Ewald分解实现其他性能改进，因为u系列的大部分是高斯的总和，因此可以使用需要可分离卷积核的算法进行评估。我们描述了一种这样的算法，它以通信带宽和计算为代价来减少通信等待时间，