An iterative PPPM method for simulating Coulombic systems on distributed memory parallel computers

We describe results obtained from a new implementation of Hockney's Particle-Particle Particle-Mesh (PPPM) method for evaluation of Coulomb energies and forces in simulations of charged particles. Rather than taking the usual approach, solving Poisson's equation by means of a Fourier transformation, we use an iterative Poisson solver. In a molecular dynamics (MD) simulation the solution from the previous time-step provides a good starting point for the next solution. This reduces the number of iterations per time-step to acceptable values. The iterative scheme has a complexity O(N), and, in contrast with the Fourier transform based approach, it is easily implemented on a parallel architecture with a minimum of communication overhead. We examine the origin of the errors in the algorithm and find that reasonable accuracies in the Coulomb interaction can best be attained by making the charge density profile as smooth as possible. This involves spreading the particle charges over a large number of grid points. Assigning these charges then becomes the most time consuming part of the algorithm. We show how we can then gain a considerable saving in computing time by employing a diffusion equation as a charge spreading mechanism. The effect of employing the algorithm with an accuracy less than that typically tolerated in an Ewald summation is studied by computing, from an MD simulation of silica, quantities that are sensitive to the long range part of the Coulomb interaction. These results are compared to full Ewald sum reference simulations and found to be within the statistical error.