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

  • Authors:

  • Bo Zhang;Jingfang Huang;Nikos P. Pitsianis;Xiaobai Sun

  • Affiliations:

  • Department of Computer Science, Duke University, Durham, NC 27708, USA;Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Phillips Hall, Chapel Hill, NC 27599, USA;Department of Computer Science, Duke University, Durham, NC 27708, USA and Department of Electrical and Computer Engineering, Aristotle University, Thessaloniki 54124, Greece;Department of Computer Science, Duke University, Durham, NC 27708, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

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.