Many different simulation methods for Stokes flow problems involve a common computationally intense task -- the summation of a kernel function over $O(N^2)$ pairs of points. One popular technique is the Kernel Independent Fast Multipole Method (KIFMM), which constructs a spatial adaptive octree for all points and places a small number of equivalent multipole and local equivalent points around each octree box, and completes the kernel sum with $O(N)$ cost, using these equivalent points. Simpler kernels can be used between these equivalent points to improve the efficiency of KIFMM. Here we present further extensions and applications to this idea, to enable efficient summations and flexible boundary conditions for various kernels. We call our method the Kernel Aggregated Fast Multipole Method (KAFMM), because it uses different kernel functions at different stages of octree traversal. We have implemented our method as an open-source software library STKFMM based on the high performance library PVFMM, with support for Laplace kernels, the Stokeslet, regularized Stokeslet, Rotne-Prager-Yamakawa (RPY) tensor, and the Stokes double-layer and traction operators. Open and periodic boundary conditions are supported for all kernels, and the no-slip wall boundary condition is supported for the Stokeslet and RPY tensor. The package is designed to be ready-to-use as well as being readily extensible to additional kernels.

翻译：Stokes 流问题的许多不同的模拟方法涉及一个共同的计算密集的任务 -- -- 将内核函数加在一起,超过$O(N2) 2美元一对点。一种流行的技术是核心独立快速多极法(KIFMM),该方法为所有点建立一个空间适应性奥氏树,在每个木箱周围放置少量等效多极和地方等效点,并使用这些等值点的费用完成内核总和。在这些等值点之间可以使用简易内核功能来提高 KIFMM 的效率。这里,我们对这一想法提出进一步的扩展和应用,以便能够为各种内核创造高效的和灵活的边界条件。我们称之为内核综合快速多极法(KAFMM),因为它在不同阶段使用不同的内核内核功能,并且用等值来完成内核的开源软件库StKMMM(Stoker ST),这是基于高性能 PVFMMM的开放软件库的开放性软库, 支持的Lace- 内核、 常规的Ytrainal-ral-ral-ral-ral-s 和Stoil-rak-rak-s-s-s-s-s-rak-s-s-stan-s-stanlock-s-tol-s-tol-s-s-toll-stanl-s-st-st-st-r-r-r-r-st-s-s-r-r-r-r-r-r-r-s-s-s-s-s-s-s-s-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-