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A new version of the fast multipole method for screened Coulomb interactions in three dimensions. (English) Zbl 1143.78372
Summary: 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 \(189p^{4}\) 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 \(40p^{2}+6p^{3}\) operations per box.

78M99 Basic methods for problems in optics and electromagnetic theory
65B10 Numerical summation of series
65N99 Numerical methods for partial differential equations, boundary value problems
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