The motivation of this project is to develop an efficient parallelized simulation of large multi-particle systems, which can be used directly to problems like the sphere equidistribution[] and N-body problem with fairly uniform spatial distribution

The motivation of this project is to develop an efficient parallelized simulation of dynamics of large multi-particle systems on a parallel CPU/GPU high performance computing architecture. The work includes three parts: parallelization of the fast multipole method (FMM), multi-scale time stepping integrators and mapping the computation of nearby particles forces to GPUs. Possible applications of the target software include, but not limited to, efficient simulation of classic N-body problems with fairly uniform distribution and finding minimum Coulomb potential in the modern sphere equidistribution [6]. The report is organized as follows: section 2 gives a short introduction to the scientific background; section 3 presents the basic ideas and theories of the FMM related to the parallelization and GPU enhancement; section 4 is about the strategy and details of parallelization; section 5 shows the implementations of the multi-scale time stepping Beeman integrators; section 6 introduces the implementation of GPU computation of neighboring particles interplays; section 7 is the validation and verification of the code, followed by the conclusions and future work in section 8.