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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.

##### MSC:
 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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