Fast Ewald summation for free-space Stokes potentials

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• 作者：Ludvig af Klinteberg ; Davoud Saffar Shamshirgar…
• 刊名：Research in the Mathematical Sciences
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：4
• 期：1
• 全文大小：1047KB
• 刊物类别：Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis;
• 刊物主题：Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis;
• 出版者：Springer International Publishing
• ISSN：2197-9847
• 卷排序：4

文摘

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 \(O(N \log N)\) 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.