A hybrid Fast Multipole Method for cosmological N-body simulations

We investigate a hybrid numerical algorithm aimed at large-scale cosmological N-body simulation for on-going and future high precision sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity, incorporating a Particle Mesh (PM) method for long-range potential, which is applied to deal with extremely large particle number. In this work, we present a specific strategy to modify a conventional FMM by a Gaussian shaped factor and provide quantitative expressions for the interaction kernels between multipole expansions. Moreover, a proper Multipole Acceptance Criterion for the hybrid method is introduced to solve potential precision loss induced by the truncation. Such procedures reduce the amount of computation compared to an original FMM and decouple the global communication. A simplified version of code is introduced to verify the hybrid algorithm, accuracy and parallel implementation.