Parallelization of Particle-Particle, Particle-Mesh Method within N-Body Simulation

Abstract

N-Body problem has become an intricate part of the computational sciences, and there has been rise to many methods to solve and approximate the problem. The solution potentially requires on the order of calculations each time step, therefore efficient performance of these N-Body algorithms is very significant (5). This work describes the parallelization and optimization of the Particle-Particle, Particle-Mesh (P3M) algorithm within GalaxSeeHPC, an open-source N-Body Simulation code. Upon successful profiling, MPI (Message Passing Interface) routines were implemented into the population of the density grid in the P3M method in GalaxSeeHPC. Each problem size recorded different results, and for a problem set dealing with 10,000 celestial bodies, speedups up to 10x were achieved. However, in accordance to Amdahl's Law, maximum speedups for the code should have been closer to 16x. In order to achieve maximum optimization, additional research is needed and parallelization of the Fourier Transform routines could prove to be rewarding. In conclusion, the GalaxSeeHPC Simulation was successfully parallelized and obtained very respectable results, while further optimization remains possible.