Accelerating fast multipole methods for the Helmholtz equation at low frequencies

Leslie Greengard; Jingfang Huang; Vladimir Rokhlin; Stephen Wandzura

doi:10.1109/99.714591

Accelerating fast multipole methods for the Helmholtz equation at low frequencies

Leslie Greengard, Jingfang Huang, Vladimir Rokhlin, Stephen Wandzura

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	32-38
Number of pages	7
Journal	IEEE computational science & engineering
Volume	5
Issue number	3
DOIs	https://doi.org/10.1109/99.714591
State	Published - 1998

ASJC Scopus subject areas

General Engineering

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10.1109/99.714591

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title = "Accelerating fast multipole methods for the Helmholtz equation at low frequencies",

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.",

author = "Leslie Greengard and Jingfang Huang and Vladimir Rokhlin and Stephen Wandzura",

note = "Funding Information: The work of Leslie Creengard and Jingfang Huang was supported in part by the Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract DE-FC0288ER25053. The work of Leslie Creengard and Vladimir Rohklin was supported in part by DARPA/ AFOSR under Contract F49620-95-C-0075. Rohklin was also supported in part by ONR under Grant NO0014 - 96-1 -01 88. Steve Wandzura's work was supported by DARPA/DSO under contract MDA972-95-C-002.",

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doi = "10.1109/99.714591",

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AU - Wandzura, Stephen

N1 - Funding Information: The work of Leslie Creengard and Jingfang Huang was supported in part by the Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract DE-FC0288ER25053. The work of Leslie Creengard and Vladimir Rohklin was supported in part by DARPA/ AFOSR under Contract F49620-95-C-0075. Rohklin was also supported in part by ONR under Grant NO0014 - 96-1 -01 88. Steve Wandzura's work was supported by DARPA/DSO under contract MDA972-95-C-002.

PY - 1998

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AB - 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.

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Accelerating fast multipole methods for the Helmholtz equation at low frequencies

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