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

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

Research output: Contribution to journalArticle

Abstract

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
Volume216
Issue number1
DOIs
StatePublished - Jul 20 2006

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Helmholtz equation
Helmholtz equations
multipoles
low frequencies
broadband
Program processors

Keywords

  • Fast multipole method
  • Helmholtz equation
  • Scattering problems

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Cheng, H., Crutchfield, W. Y., Gimbutas, Z., Greengard, L., Ethridge, J. F., Huang, J., ... Zhao, J. (2006). A wideband fast multipole method for the Helmholtz equation in three dimensions. Journal of Computational Physics, 216(1), 300-325. https://doi.org/10.1016/j.jcp.2005.12.001

A wideband fast multipole method for the Helmholtz equation in three dimensions. / Cheng, Hongwei; Crutchfield, William Y.; Gimbutas, Zydrunas; Greengard, Leslie; Ethridge, J. Frank; Huang, Jingfang; Rokhlin, Vladimir; Yarvin, Norman; Zhao, Junsheng.

In: Journal of Computational Physics, Vol. 216, No. 1, 20.07.2006, p. 300-325.

Research output: Contribution to journalArticle

Cheng, H, Crutchfield, WY, Gimbutas, Z, Greengard, L, Ethridge, JF, Huang, J, Rokhlin, V, Yarvin, N & Zhao, J 2006, 'A wideband fast multipole method for the Helmholtz equation in three dimensions', Journal of Computational Physics, vol. 216, no. 1, pp. 300-325. https://doi.org/10.1016/j.jcp.2005.12.001
Cheng, Hongwei ; Crutchfield, William Y. ; Gimbutas, Zydrunas ; Greengard, Leslie ; Ethridge, J. Frank ; Huang, Jingfang ; Rokhlin, Vladimir ; Yarvin, Norman ; Zhao, Junsheng. / A wideband fast multipole method for the Helmholtz equation in three dimensions. In: Journal of Computational Physics. 2006 ; Vol. 216, No. 1. pp. 300-325.
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