ENUF方法--基于非均匀快速傅立叶变换的Ewald求和：实现、简化及应用
The ENUF Method -- Ewald Summation based on Non-Uniform Fast Fourier Transform: Implementation, Parallelization, and Application
摘要：
模型系统的计算机模拟被广泛用于探索物理学、化学、生物学、材料科学和工程学等领域的惊人现象。带电粒子间的长程静电相互作用是决定模型系统结构和状态的重要因素。如何有效地计算部分或全周期边界条件下模型系统中的静电相互作用一直是一个具有挑战性的课题。在过去的几十年里，已经提出了各种各样的计算方案，其中Ewald求和方法是最可靠的路线，以准确地处理模型系统中的静电相互作用。此外，已经做了大量的努力来提高基于Ewald求和的方法的计算效率。代表性的例子是基于截断，反应场，多极，多重网格和粒子网格计划的方法。我们勾画了ENUF方法，Ewald求和方法的缩写基于非均匀快速傅立叶变换技术，并已实现了这种方法在基于粒子的模拟包计算静电能量和力在微观和介观水平。对聚电解质、树枝状聚合物-膜复合物和离子流体的构象性质的广泛计算研究表明，ENUF方法及其衍生物将能量和动量保持到浮点精度，并表现出具有最佳物理参数的$\mathcal{O}(N\log N)$的计算复杂性。这些ENUF为基础的方法是有吸引力的替代品，在分子模拟中，需要高精度和高效率的模拟方法，以加速在扩展的时空尺度上的静电相互作用的计算。
英文摘要：
Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between charged particles constitute a prominent factor in determining structures and states of model systems. How to efficiently calculate electrostatic interactions in model systems subjected to partial or full periodic boundary conditions has been a grand challenging task. In the past decades, a large variety of computational schemes have been proposed, among which the Ewald summation method is the most reliable route to accurately deal with electrostatic interactions in model systems. In addition, extensive effort has been done to improve computational efficiency of the Ewald summation based methods. Representative examples are approaches based on cutoffs, reaction fields, multi-poles, multi-grids, and particle-mesh schemes. We sketched an ENUF method, an abbreviation for the Ewald summation method based on Non-Uniform fast Fourier transform technique, and have implemented this method in particle-based simulation packages to calculate electrostatic energies and forces at micro- and mesoscopic levels. Extensive computational studies of conformational properties of polyelectrolytes, dendrimer-membrane complexes, and ionic fluids demonstrated that the ENUF method and its derivatives conserve both energy and momentum to floating point accuracy, and exhibit a computational complexity of $\mathcal{O}(N\log N)$ with optimal physical parameters. These ENUF based methods are attractive alternatives in molecular simulations where high accuracy and efficiency of simulation methods are needed to accelerate calculations of electrostatic interactions at extended spatiotemporal scales.
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