Fast Ewald summation for free-space Stokes potentials
Fast Ewald summation for free-space Stokes potentials
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自由空间斯托克斯势的快速埃瓦尔德求和
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
A. Tornberg
中科院分区：
文献类型：
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作者：
Ludvig af Klinteberg;D. S. Shamshirgar;A. Tornberg
我们提出了一种快速评估自由空间斯托克斯势的光谱精确方法，即，涉及大量自由空间绿色函数的求和。我们认为涉及stokeslets，stressles和rotlets出现在边界积分方法和潜在的方法求解斯托克斯方程的总和。该方法结合了用于周期性问题的谱埃瓦尔德方法的框架（Lindbo和Tornberg in J Comput Phys 229（23）：8994-9010，2010）。doi：10.1016/j.jcp.2010.08.026），以及在均匀网格上使用快速傅立叶变换（FFT）求解自由空间谐波和双谐波方程的非常新的方法（Vico等人，J Comput Phys 323：191-203，2016）。doi：10.1016/j.jcp.2016.07.028）。卷积与截断高斯函数被用来放置点源的网格。通过不依赖于这些源的标量网格量的预先计算，具有高斯的网格的过采样量可以保持在因子2，这是FFT的非周期卷积的最小值。由此产生的算法有一个计算复杂度为$$O（N \log N）$$O（NlogN）的N个源和目标的问题。与快速多极子方法的比较表明，新方法的性能是竞争力。
We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, stresslets and rotlets that appear in boundary integral methods and potential methods for solving Stokes equations. The method combines the framework of the Spectral Ewald method for periodic problems (Lindbo and Tornberg in J Comput Phys 229(23):8994–9010, 2010. doi:10.1016/j.jcp.2010.08.026), with a very recent approach to solving the free-space harmonic and biharmonic equations using fast Fourier transforms (FFTs) on a uniform grid (Vico et al. in J Comput Phys 323:191–203, 2016. doi:10.1016/j.jcp.2016.07.028). Convolution with a truncated Gaussian function is used to place point sources on a grid. With precomputation of a scalar grid quantity that does not depend on these sources, the amount of oversampling of the grids with Gaussians can be kept at a factor of two, the minimum for aperiodic convolutions by FFTs. The resulting algorithm has a computational complexity of $$O(N \log N)$$O(NlogN) for problems with N sources and targets. Comparison is made with a fast multipole method to show that the performance of the new method is competitive.