ABSTRACT
Particle-Particle-Particle-Mesh (P3M) algorithms are a class of hybrid algorithms developed by the authors (Hockney et al., 1973; Eastwood and Hockney, 1974; Eastwood, 1975, Eastwood, 1976b ; Eastwood et al. 1980). These algorithms enable correlated systems with long-range (for example, coulombic) forces to be simulated for much larger ensembles of particles than was hitherto possible. The essence of the method is to express the interparticle force as the sum of two component parts ; the short-range part f sr, which is nonzero only for particle separations less than some cutoff radius re , and the smoothly varying part R, which has a transform which is approximately band-limited (that is to say, is approximately nonzero for only a limited range of k). The total short-range force on a particle F sr is computed by direct particle-particle (PP) pair force summation and the smoothly varying part is approximated by the particle-mesh (PM) force calculation. Although we restrict discussions in this chapter to long-range forces which are purely coulombic, the results we obtain may be generalized to arbitrary force laws by replacing charge by another suitable measure of the strengths of force centers and by replacing the coulombic reference force R by the appropriate alternative.
