Multipole Ewald sums for the fast multipole method

Kevin Schmidt, Michael A. Lee

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


A generalized Ewald summation for electric multipoles in periodic arrays is presented in the form needed for multipole transformations used in the fast multipole method. In the fast multipole method the time-consuming Ewald sums are thus eliminated in favor of a simple matrix transformation with almost no computational cost. The derivation also applies to traditional electrostatic potential calculations in periodic charged systems. A summary computational prescription is provided.

Original languageEnglish (US)
Pages (from-to)411-424
Number of pages14
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 1997


  • Ewald sum
  • Fast multipole method
  • N-body problem

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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