Particle-particle particle-mesh methods are often used in molecular dynamics codes to approximate the effects of long-range forces between atoms where it would not be feasible to compute all pair-wise interactions. While short-range interactions are computed in a pair-wise fashion, the forces produced by long-range interactions are obtained by mapping particle charge to a grid, solving Poisson's equation in the frequency domain for the electrical potential, and then mapping the local potential back to the particles. Using the popular molecular dynamics code LAMMPS, we present vectorization and new implementations of the two mapping algorithms. We also discuss how using larger stencil sizes when mapping charges and forces better takes advantage of the Xeon Phi architecture, both by making use of its large vector registers and because a larger stencil allows a coarser grid to be used. This shifts work from the poorly-scaling FFTs used to solve Poisson's equation and to the newly-accelerated and highly parallel mapping functions. The acceleration of the PPPM method as a whole also affects the optimal input parameters in a similar fashion; using a smaller cutoff to shift work from the pair-wise short-range computation to the long-range PPPM computation saves time even while using a finer charge grid to preserve accuracy.
