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

Authors:
Hongwei Cheng;William Y. Crutchfield;Zydrunas Gimbutas;Leslie F. Greengard;J. Frank Ethridge;Jingfang Huang;Vladimir Rokhlin;Norman Yarvin;Junsheng Zhao
Affiliations:
Plain Sight Systems, Hamden, CT;Plain Sight Systems, Hamden, CT;Plain Sight Systems, Hamden, CT;Courant Institute of Mathematical Sciences, New York University, New York, NY;Plain Sight Systems, Hamden, CT;Department of Mathematics, University of North Carolina, Chapel Hill, NC;Department of Computer Science, Yale University, New Haven, CT;Plain Sight Systems, Hamden, CT;Plain Sight Systems, Hamden, CT
Venue:
Journal of Computational Physics
Year:
2006

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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 logN) if high-frequency computations dominate. The performance of the algorithm is illustrated with numerical examples.