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Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

机译：B样条插值的多级求和用于分子动力学模拟中的成对相互作用

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摘要

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short. (C) 2016 AIP Publishing LLC.
机译：用于在分子动力学模拟中计算静电相互作用的多级求和方法构造了成对相互作用核及其梯度的近似值，可以用与原子数成线性比例的成本进行评估。该方法将内核平滑地分为范围增加和可变性降低的部分内核的总和，其中较远距离的部分从粗糙度增加的网格中插值。多级求和尤其适用于动态和最小化，因为它可以产生连续的梯度。本文探讨了B样条的使用，以提高多级求和方法（针对非周期性边界）的准确性，而无需进行除预处理步骤（其成本也会线性缩放）以外的其他计算。有效地获得准确结果涉及技术难题，这是通过新颖的预处理算法克服的。数值实验表明，所得到的方法在准确性上有实质性的提高，并且其性能与快速多极方法的实施总体上具有竞争力，并且对于分子动力学的汉密尔顿公式而言明显更好。改进足以将多级求和建立为在分子动力学模拟中计算成对相互作用的重要竞争者。特别是，该方法似乎在两种情况下具有独特的分子动力学能力：非周期性边界条件和大规模并行计算，而粒子网Ewald方法中采用的快速傅立叶变换则不足。 （C）2016 AIP出版有限责任公司。

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