Particle-Particle Particle-Multigrid Method (P3MG)
Multigrid methods are known to solve the 3-dimensional Poisson
equation in O(N) complexity. The idea is to descritize the
system with an equi-spaced grid and to smear the partial charges of
the particles with a specified interpolation onto the grid. Dirichlet
boundary conditions are calculated by a multipole expansion scheme,
which has complexity O(N). Applying the multigrid technique
offers a solution of the the global potential surface in overall
complexity O(N). In order to calculate the interaction energy
between particles in the system, the energy surface has to be
corrected for the self contribution of each particle. This is
performed by subtracting the grid based calculated and charge weighted
Green's function at each charge location. An accurate near-field part
is calculated by subtracting the potential at a charges' location due
to nearby particles and in calculating exact particle-particle
interactions in this region.
Multigrid-based method for the calculation of long-ranged interactions, J. Comp. Appl. Math. (submitted).
A highly accurate and optimal method to calculate long range interactions, Proc. of NIC Workshop From Computational Biophysics to Systems Biology, (NIC Series Vol. 34, Jülich, 2006), p.189 (pdf).
A particle-particle particle-multigrid algorithm for long range interactions in molecular systems, Comp. Phys. Comm., 169, 343-346 (2005) (pdf).
Back to top
Contact: Godehard Sutmann
last change 11.06.2007 | Godehard Sutmann | Print