Accelerating fast multipole methods for the Helmholtz equation at low frequencies

Leslie Greengard, Jingfang Huang, Vladimir Rokhlin, Stephen Wandzura

Research output: Contribution to journalArticle

Abstract

The analytic foundations for a new version of the fast multipole method (FMM) for the scalar Helmholtz equation in the low-frequency regime are presented. The computational cost of existing FMM implementations, is dominated by the expense of translating far-field partial wave expansions to local ones, requiring 189p4 or 189p3 operations per box, where harmonics up to order p2 have been retained. By developing a new expansion in plane waves, these translation operators can be diagonalized. The approach combines evanescent and propagating plane waves to reduce the computational cost of FMM implementation.

Original languageEnglish (US)
Pages (from-to)32-38
Number of pages7
JournalIEEE computational science & engineering
Volume5
Issue number3
DOIs
StatePublished - Jul 1998

ASJC Scopus subject areas

  • Engineering(all)

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