论文信息 - The very fast multipole method

The very fast multipole method

The fast multipole method (FMM) has become an important alternative to traditional methods such as the Ewald method for computing the long‐range interactions necessary to simulate charged or dipolar systems. In this paper, we present an improvement of this method, which we shall call the very fast multipole method (VFMM). The VFMM is shown to be a factor of about 1.2 faster than the FMM for two‐dimensional systems and a factor about 2–3 times faster for three‐dimensional systems without losing any accuracy for the worst case error.

[1] L. Greengard. The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[2] K. Schmidt,et al. Implementing the fast multipole method in three dimensions , 1991 .

[3] W. Goddard,et al. Atomic level simulations on a million particles: The cell multipole method for Coulomb and London nonbond interactions , 1992 .

[4] T. Darden,et al. Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[5] J. W. Causey,et al. Accelerated molecular dynamics simulation with the parallel fast multipole algorithm , 1992 .

[6] J. Perram,et al. Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems , 1992 .

[7] H. G. Petersen,et al. An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles , 1988 .

[8] Leslie Greengard,et al. A fast algorithm for particle simulations , 1987 .

[9] W. Goddard,et al. The reduced cell multipole method for Coulomb interactions in periodic systems with million-atom unit cells , 1992 .

[10] J. Perram,et al. Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.