Parallelization of the Fast Multipole Method for Molecular Dynamics Simulations on Multicore Computers

Abstract

We have parallelized the fast multipole method (FMM) on multicore computers using OpenMP programming model. The FMM is the one of the fastest approximate force calculation algorithms for molecular dynamics simulations. Its computational complexity is linear. Parallelization of FMM on multicore computers using OpenMP has been reported since the multicore processors become increasingly popular. However the number of those FMM implementations is not large. The main reason is that those FMM implementations have moderate or low parallel efficiency for high expansion orders due to sophisticated formulae of the FMM. In addition, parallel efficiency of those implementations for high expansion orders rapidly drops to 40% or lower as the number of threads increases to 8 or higher. Our FMM implementation on multicore computers using a combination approach as well as a newly developed formula and a computational procedure (A2P) solved the above issues. Test results of our FMM implementation on a multicore computer show that our parallel efficiency with 8 threads is at least 70% for moderate and high expansion orders p = 4,5,6,7. Moreover, the parallel efficiency for moderate and high expansion orders gradually drops from 96% to 70% as the number of threads increases.