Accelerating NBODY6 with Graphics Processing Units

TL;DR

This paper presents a GPU-accelerated version of the NBODY6 code, significantly improving the efficiency of direct N-body simulations for particle counts between 10,000 and 200,000 by optimizing force calculations and parallel processing techniques.

Contribution

The paper introduces a GPU-based implementation of NBODY6 that enhances computational speed for large N-body simulations, balancing force calculations and parallel processing.

Findings

Achieves significant speedup in force calculations using GPUs.

Efficiently handles simulations with 10^4 to 2×10^5 particles.

Maintains balance with dual GPU systems on standard PCs.

Abstract

We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct $N$-body simulations. Over the years, the $N^2$ nature of the direct force calculation has proved a barrier for extending the particle number. Following an early introduction of force polynomials and individual time-steps, the calculation cost was first reduced by the introduction of a neighbour scheme. After a decade of GRAPE computers which speeded up the force calculation further, we are now in the era of GPUs where relatively small hardware systems are highly cost-effective. A significant gain in efficiency is achieved by employing the GPU to obtain the so-called regular force which typically involves some 99 percent of the particles, while the remaining local forces are evaluated on the host. However, the latter operation is performed up to 20 times more frequently and may still account for a significant cost. This effort is reduced by parallel SSE/AVX procedures where each interaction term is calculated using mainly single precision. We also discuss further strategies connected with coordinate and velocity prediction required by the integration scheme. This leaves hard binaries and multiple close encounters which are treated by several regularization methods. The present nbody6-GPU code is well balanced for simulations in the particle range $10^4-2 \times 10^5$ for a dual GPU system attached to a standard PC.