Swarm-NG: A CUDA library for Parallel n-body Integrations with focus on simulations of planetary systems

Abstract

We present Swarm-NG, a C++ library for the efficient direct integration of many n-body systems using a Graphics Processing Unit (GPU), such as NVIDIA’s Tesla T10 and M2070 GPUs. While previous studies have demonstrated the benefit of GPUs for n-body simulations with thousands to millions of bodies, Swarm-NG focuses on many few-body systems, e.g., thousands of systems with 3…15 bodies each, as is typical for the study of planetary systems. Swarm-NG parallelizes the simulation, including both the numerical integration of the equations of motion and the evaluation of forces using NVIDIA’s “Compute Unified Device Architecture” (CUDA) on the GPU. Swarm-NG includes optimized implementations of 4th order time-symmetrized Hermite integration and mixed variable symplectic integration, as well as several sample codes for other algorithms to illustrate how non-CUDA-savvy users may themselves introduce customized integrators into the Swarm-NG framework. To optimize performance, we analyze the effect of GPU-specific parameters on performance under double precision. For an ensemble of 131072 planetary systems, each containing three bodies, the NVIDIATesla M2070 GPU outperforms a 6-core Intel Xeon X5675 CPU by a factor of ∼2.75. Thus, we conclude that modern GPUs offer an attractive alternative to a cluster of CPUs for the integration of an ensemble of many few-body systems.Applications of Swarm-NG include studying the late stages of planet formation, testing the stability of planetary systems and evaluating the goodness-of-fit between many planetary system models and observations of extrasolar planet host stars (e.g., radial velocity, astrometry, transit timing). While Swarm-NG focuses on the parallel integration of many planetary systems, the underlying integrators could be applied to a wide variety of problems that require repeatedly integrating a set of ordinary differential equations many times using different initial conditions and/or parameter values.