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

✍ Scribed by Bo Zhang; Jingfang Huang; Nikos P. Pitsianis; Xiaobai Sun

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 983 KB
• Volume: 230
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2011.03.049

✦ Synopsis

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-tomultipole, 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.