A wideband fast multipole method for the Helmholtz equation in three dimensions

Hongwei Cheng, William Y. Crutchfield, Zydrunas Gimbutas, Leslie F. Greengard, J. Frank Ethridge, Jingfang Huang, Vladimir Rokhlin, Norman Yarvin, Junsheng Zhao

Research output: Contribution to journalArticlepeer-review


We describe a wideband version of the Fast Multipole Method for the Helmholtz equation in three dimensions. It unifies previously existing versions of the FMM for high and low frequencies into an algorithm which is accurate and efficient for any frequency, having a CPU time of O(N) if low-frequency computations dominate, or O(N log N) if high-frequency computations dominate. The performance of the algorithm is illustrated with numerical examples.

Original languageEnglish (US)
Pages (from-to)300-325
Number of pages26
JournalJournal of Computational Physics
Issue number1
StatePublished - Jul 20 2006


  • Fast multipole method
  • Helmholtz equation
  • Scattering problems

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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