A new version of the fast multipole method for screened Coulomb interactions in three dimensions

  • Authors:

  • Leslie F. Greengard;Jingfang Huang

  • Affiliations:

  • Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York;Department of Mathematics, University of North Carolina at Chapel Hill, CB 3250 Phillips Hall, Chapel Hill, North Carolina

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

We present a new version of the fast multipole method (FMM) for screened Coulomb interactions in three dimensions. Existing schemes can compute such interactions in O(N) time, where N denotes the number of particles. The constant implicit in the O(N) notation, however, is dominated by the expense of translating far-field spherical harmonic expansions to local ones. For each box in the FMM data structure, this requires 189p4 operations per box, where p is the order of the expansions used, The new formulation relies on an expansion in evanescent plane waves, with which the amount of work can be reduced to 40p2 + 6p3 operations per box.