A Fourier-series-based kernel-independent fast multipole method
A Fourier-series-based kernel-independent fast multipole method
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DOI：
10.1016/j.jcp.2011.03.049
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发表时间：
2011-07
期刊：
影响因子：
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通讯作者：
Bo Zhang-;Jingfang Huang;N. Pitsianis;Xiaobai Sun
中科院分区：
文献类型：
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作者：
Bo Zhang-;Jingfang Huang;N. Pitsianis;Xiaobai Sun
本文提出了一种新的与核无关的快速多极子方法（FMM），称为FKI-FMM，用于研究两粒子相互作用。FKI-FMM使用数值技术，以截断傅立叶级数的形式在多尺度相互作用区域上创建给定核函数的足够精确和压缩的表示。它还提供了经济运营商的多极到多极，多极到本地，本地到本地的翻译是典型的和必要的FMM算法。特别是多极到局部的平移算子，很容易对角化，在算术运算中不占主导地位。FKI-FMM提供了一个替代和竞争的选择，在其他内核独立的FMM算法，为FMM的有效应用，特别是对于应用程序的内核函数包括多物理和多尺度组件，如那些出现在最近的研究生物系统。我们提出的复杂性分析和实验结果证明FKI-FMM的准确性和效率的性能。
We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency.