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

Kernel Aggregated Fast Multipole Method: Efficient summation of Laplace and Stokes kernel functions