A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions |
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| Authors: | Leslie F. Greengard Jingfang Huang |
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| Affiliation: | a Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York, 10012;b Department of Mathematics, University of North Carolina at Chapel Hill, CB 3250 Phillips Hall, Chapel Hill, North Carolina, 27599 |
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| Abstract: | We present a new version of the fast multipole method (FMM) for screened Coulomb interactions in three dimensions. Existing schemes can compute such interactions in O(N) time, where N denotes the number of particles. The constant implicit in the O(N) notation, however, is dominated by the expense of translating far-field spherical harmonic expansions to local ones. For each box in the FMM data structure, this requires 189p4 operations per box, where p is the order of the expansions used. The new formulation relies on an expansion in evanescent plane waves, with which the amount of work can be reduced to 40p2+6p3 operations per box. |
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| Keywords: | Abbreviations: translation operatorsAbbreviations: fast multipole methodAbbreviations: screened Coulomb interaction |
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