A Hybrid Fast Multipole Method for Cosmological N-body Simulations

TL;DR

This paper introduces a hybrid algorithm combining a modified Fast Multipole Method with Particle Mesh techniques to efficiently simulate large-scale cosmological N-body systems, improving computational speed and accuracy.

Contribution

It presents a novel hybrid approach that modifies the FMM with a Gaussian factor and integrates it with PM for better large-scale cosmological simulations.

Findings

Reduces computation compared to original FMM

Maintains high accuracy with new multipole acceptance criteria

Demonstrates effective parallel implementation

Abstract

We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity, incorporating with 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 criteria for the hybrid method is introduced to solve potential precision loss induced by the truncation. Such procedures reduce the mount of computation than an original FMM and decouple the global communication. A simplified version of code is introduced to verify the hybrid algorithm, accuracy and parallel implementation.