The fast multipole method for gridless particle simulation

John Ambrosiano, Leslie Greengard, Vladimir Rokhlin

Research output: Contribution to journalArticlepeer-review


The numerical solution to N-body problems in gravitation or electrostatics has traditionally been obtained via particle-in-cell methods (PIC) since direct evaluation of all pairwise interparticle forces, requiring O(N2) operations, is too expensive. Recently, hierarchical solvers, which use tree data structures and lumped-force approximations, have made gridless simulations feasible in O(N log N) operations. In this paper, we explore the use of the fast multipole method (FMM) - a highly accurate order O(N) algorithm - in particle simulations. We briefly describe the FMM and its relation to other methods. Technical considerations of gridless simulations such as discrete particle fluctuations, sampling errors and boundary conditions are discussed and compared with PIC methodology. Examples of electrostatic simulations in plasma physics are presented.

Original languageEnglish (US)
Pages (from-to)117-125
Number of pages9
JournalComputer Physics Communications
Issue number1
StatePublished - Jan 1988

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy


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