Accelerating NBODY6 with Graphics Processing Units (1205.1222v1)

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.

• The paper accelerates NBODY6 by offloading regular gravitational force calculations to GPUs while utilizing parallel CPU instructions for irregular forces.
• It details a CUDA-based implementation that leverages massive parallelism to achieve significant speedups, including a 56x improvement for a 256k particle system.
• The study establishes a cost-effective framework for large-scale astrophysical simulations and paves the way for further GPU-based computational innovations.

Accelerating NBODY6 with Graphics Processing Units

The paper "Accelerating NBODY6 with Graphics Processing Units" by Keigo Nitadori and Sverre J. Aarseth provides an in-depth exploration of enhancing the computational efficiency of the NBODY6 code, which is utilized for direct $N$-body simulations. These simulations are integral in studying dynamical systems such as globular clusters. Historically, the major computational challenge with $N$-body codes like NBODY6 arises from the $N^2$ complexity in calculating gravitational forces among particles, which limits the scalability as the number of particles increases.

The authors introduce the utilization of Graphics Processing Units (GPUs) to perform these computations, significantly improving cost-effectiveness and computational speed. The adaptation involves using the GPU to compute the regular forces, which account for approximately 99 percent of total particle interactions. While local forces, which are computed more frequently, are calculated using the host CPU with parallel SSE/AVX instructions to further improve performance.

Key steps in the implementation include leveraging the CUDA programming language to enable high parallelism on GPUs. Nitadori and Aarseth detail the GPU implementation, which, for regular force computations, employs massively parallel force calculations to achieve substantial efficiency gains. Nonetheless, the irregular force calculations, which involve frequent updates and smaller interaction ranges, were found to be inefficiently handled on the GPUs due to overheads. Consequently, these computations are handled on the CPU, where the use of Streaming SIMD Extensions (SSE) and Advanced Vector Extensions (AVX), alongside OpenMP directives for parallel processing, brings considerable performance improvements.

The numerical results presented highlight the scalability and cost-efficiency of this approach. For example, the wall-clock times collected from different hardware configurations showed significant performance boosts, particularly when using dual GPU setups compared to a single GPU. For a 256k particle system, a performance improvement of up to 56 times over the non-GPU accelerated version of the code is demonstrated, indicating the success of the proposed methods.

In terms of implications, this paper positions GPU-based computations as a transformative approach for $N$-body simulations, opening opportunities for larger scale simulations at lower computational costs. For practical astrophysical applications, this efficiency translates to the ability to simulate more complex systems or the same systems in less time, thus accelerating research processes and discoveries.

Theoretically, the advancements also suggest that GPU-based methods can be extended and adapted to other computationally intensive areas within computational astrophysics. Future developments could involve further improvements in parallel algorithms, exploration of multi-GPU distributions, or integration with sophisticated numerical methods to handle increasingly complex interactions and scenarios, such as those involving different physical processes or inhomogeneous systems.

Ultimately, the advancement of NBODY6 via GPU acceleration represents a significant step forward in computational astrophysics, providing both a robust framework for current research and a promising foundation for future computational innovations.