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

doi:10.1016/j.jcp.2005.12.001

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

Mathematics

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

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 language	English (US)
Pages (from-to)	300-325
Number of pages	26
Journal	Journal of Computational Physics
Volume	216
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2005.12.001
State	Published - Jul 20 2006

Keywords

Fast multipole method
Helmholtz equation
Scattering problems

ASJC Scopus subject areas

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

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10.1016/j.jcp.2005.12.001

Cite this

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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.",

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AU - Cheng, Hongwei

AU - Crutchfield, William Y.

AU - Gimbutas, Zydrunas

AU - Greengard, Leslie F.

AU - Ethridge, J. Frank

AU - Huang, Jingfang

AU - Rokhlin, Vladimir

AU - Yarvin, Norman

AU - Zhao, Junsheng

PY - 2006/7/20

Y1 - 2006/7/20

N2 - 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.

AB - 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.

KW - Fast multipole method

KW - Helmholtz equation

KW - Scattering problems

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

Abstract

Keywords

ASJC Scopus subject areas

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