A Fourier-series-based kernel-independent fast multipole method

作者：Zhang, Bo^*; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai

来源：Journal of Computational Physics, 2011, 230(15): 5807-5821.

DOI：10.1016/j.jcp.2011.03.049

• Fast multipole method
• Green's function
• Compressive approximation
• Fourier series

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.

• 出版日期2011-7-1