2-周期Stokes势的快速谱精确求和
Fast and spectrally accurate summation of 2-periodic Stokes potentials
摘要：
我们得到了一个Ewald分解的平面周期性的Stokeslet和一个新的PME型O（N log N）的方法快速评估所产生的总和。分解是自然的2 P对应的经典的3 P分解由桥本，并给出了在文献中没有找到的明确的形式。截断误差估计，以帮助选择参数。快速，PME型，方法似乎是第一个快速计算平面周期性的Stokeslet埃瓦尔德和的方法，并具有三个有吸引力的特性：它是光谱准确的;它使用的内存最小的网格埃瓦尔德方法可以使用;并提供清晰的数值误差和如何选择参数。分析和数值结果支持这一点。我们将探讨所提出的方法的实用性，并调查将其应用到2-周期边界积分斯托克斯问题所涉及的计算问题。
英文摘要：
We derive a Ewald decomposition for the Stokeslet in planar periodicity and a novel PME-type O(N log N) method for the fast evaluation of the resulting sums. The decomposition is the natural 2P counterpart to the classical 3P decomposition by Hasimoto, and is given in an explicit form not found in the literature. Truncation error estimates are provided to aid in selecting parameters. The fast, PME-type, method appears to be the first fast method for computing Stokeslet Ewald sums in planar periodicity, and has three attractive properties: it is spectrally accurate; it uses the minimal amount of memory that a gridded Ewald method can use; and provides clarity regarding numerical errors and how to choose parameters. Analytical and numerical results are give to support this. We explore the practicalities of the proposed method, and survey the computational issues involved in applying it to 2-periodic boundary integral Stokes problems.
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