TY - JOUR

T1 - A new version of the fast multipole method for screened Coulomb interactions in three dimensions

AU - Greengard, Leslie F.

AU - Huang, Jingfang

N1 - Funding Information:
1This work was supported in part by the Applied Mathematical Sciences Program of the U.S. Department of Energy DEFGO288ER25053. 2Fax: (919) 962-9345. E-mail: huang@amath.unc.edu. The work of this author was supported by the Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract DE-FGO288ER25053.

PY - 2002/8/10

Y1 - 2002/8/10

N2 - 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 189 p4 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.

AB - 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 189 p4 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.

KW - Fast multipole method

KW - Screened Coulomb interaction

KW - Translation operators

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U2 - 10.1006/jcph.2002.7110

DO - 10.1006/jcph.2002.7110

M3 - Article

AN - SCOPUS:0037055750

SN - 0021-9991

VL - 180

SP - 642

EP - 658

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -