Kernel aggregated fast multipole method
Kernel aggregated fast multipole method
复制标题
核聚合快速多极子方法
DOI：
10.1007/s10444-021-09896-1
复制
发表时间：
2020
影响因子：
1.7
通讯作者：
R. Blackwell
中科院分区：
文献类型：
--
作者：
Wen Yan;R. Blackwell
斯托克斯流问题的许多不同的模拟方法都涉及到一个共同的计算强度很大的任务——对O（N2）对点的核函数求和。一种流行的技术是核独立快速多极方法（KIFMM），它为所有点构建一个空间自适应八叉树，并在每个八叉树框周围放置少量等效多极点和局部等效点，并使用这些等效点以O(N)代价完成核和。在这些等价点之间可以使用更简单的核，以提高KIFMM的效率。在这里，我们对这一思想进行了进一步的扩展和应用，以实现各种核的有效求和和灵活的边界条件。由于该方法在八叉树遍历的不同阶段使用不同的核函数，因此我们将其称为核聚合快速多极子方法（KAFMM）。我们已经将我们的方法实现为基于高性能库PVFMM的开源软件库STKFMM，支持拉普拉斯核、Stokeslet、正则化Stokeslet、Rotne-Prager-Yamakawa （RPY）张量、Stokes双层算子和牵引算子。所有核均支持开放边界条件和周期边界条件，Stokeslet张量和RPY张量均支持无滑移壁边界条件。该包被设计为即用型，并且可以很容易地扩展到其他内核。
Many different simulation methods for Stokes flow problems involve a common computationally intense task—the summation of a kernel function over O(N2) 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.
DOI：
10.1016/j.jcp.2020.109524
发表时间：
2019-09
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Wen Yan;Eduardo Corona;D. Malhotra;S. Veerapaneni;M. Shelley
通讯作者：
Wen Yan;Eduardo Corona;D. Malhotra;S. Veerapaneni;M. Shelley