A novel multiple-walk parallel algorithm for the Barnes–Hut treecode on GPUs – towards cost effective, high performance N-body simulation

Abstract

Recently, general-purpose computation on graphics processing units (GPGPU) has become an increasingly popular field of study as graphics processing units (GPUs) continue to be proposed as high performance and relatively low cost implementation platforms for scientific computing applications. Among these applications figure astrophysical N-body simulations, which form one of the most challenging problems in computational science. However, in most reported studies, a simple O(N 2 ) algorithm was used for GPGPUs, and the resulting performances were not observed to be better than those of conventional CPUs that were based on more optimized O(N log N) algorithms such as the tree algorithm or the particle-particle particle-mesh algorithm. Because of the difficulty in getting efficient implementations of such algorithms on GPUs, a GPU cluster had no practical advantage over general-purpose PC clusters for N-body simulations. In this paper, we report a new method for efficient parallel implementation of the tree algorithm on GPUs. Our novel tree code allows the realization of an N-body simulation on a GPU cluster at a much higher performance than that on general PC clusters. We practically performed a cosmological simulation with 562 million particles on a GPU cluster using 128 NVIDIA GeForce 8800GTS GPUs at an overall cost of 168 172 $. We obtained a sustained performance of 20.1 Tflops, which when normalized against a general-purpose CPU implementation leads to a performance of 8.50 Tflops. The achieved cost/performance was hence a mere $19.8 /Gflops which shows the high competitiveness of GPGPUs.

A sparse octree gravitational N-body code that runs entirely on the GPU processor

“…Therefore a method was developed to create lists of interacting particles on the host and then let the GRAPE solve the gravitational interactions [12,13]. Recently this method has successfully been applied to GPUs [14,15,16]. With the GPU being able to efficiently calculate the force interactions, other parts like the tree-construction and tree-traverse become the bottleneck of the application.…”

Directionally unsplit hydrodynamic schemes with hybrid MPI/OpenMP/GPU parallelization in AMR

“…Moreover, nowadays the developments of GPU applications have moved beyond the single GPU stage, and both performance and parallel efficiency of the applications must be optimized. In astrophysical simulations, considerable performance speed-ups in multi-GPU systems have been demonstrated in a broad range of applications, for example, the direct N -body simulations (e.g., Schive et al 2008;Gaburov et al 2009;Spurzem et al 2011), Barnes-Hut tree algorithm (Hamada et al 2009), and reionization simulations (Aubert & Teyssier 2010). grid patches with an oct-tree data structure, and the relaxing total variation diminishing scheme (RTVD; Jin & Xin 1995) with directional splitting is adopted in the hydrodynamic solver.…”

The Size Scale of Star Clusters

“…During the past decade, the clock rates of Central Processing Units have been practically stagnant, while GPUs provide a proven alternative for high-performance computing (Barsdell et al 2010), particularly for N-body codes (Hamada et al 2009). The models are run at the Center for Astrophysics and Supercomputing of Swinburne University.…”