Classical Mechanical Hard-Core Particles Simulated in a Rigid Enclosure using Multi-GPU Systems D.P.Playne and K.A. Hawick Computer Science, Institute for Information and Mathematical Sciences, Massey University, North Shore 102-904, Auckland, New Zealand email: { d.p.playne, k.a.hawick }@massey.ac.nz Tel: +64 9 414 0800 Fax: +64 9 441 8181 March 2012 ABSTRACT Hard-core interacting particle methods are of increasing importance for simulations and game applications as well as a tool supporting animations. We develop a high accu- racy numerical integration technique for managing hard- core colliding particles of various physical properties such as differing interaction species and hard-core radii us- ing multiple Graphical Processing Unit (m-GPU) com- puting techniques. We report on the performance trade- offs between communications and computations for vari- ous model parameters and for a range of individual GPU models and multiple-GPU combinations. We explore uses of the GPU Direct communications mechanisms between multiple GPUs accelerating the same CPU host and show that m-GPU multi-level parallelism is a powerful approach for complex N-Body simulations that will deploy well on commodity systems. KEY WORDS m-GPU; GPUDirect; N-Body; hard-core collisions; poly- disperse radii; multi-species. 1 Introduction Models based upon classical N-Body particle systems [2] are commonly used at various levels of approximation in game simulations [5,11,12] but still play an important role in understanding physical phenomena such as diffusion, phase mixing and separation [4], and other behaviours that arise from specific geometric distributions. Considerable work has been reported in the literature on uses of molecular dynamics whereby approximate poten- tial models are used to simulate atomic and molecular systems [14, 30, 36]. A recent review by Larsson and co-workers [26] points out that there is still considerable scope for improved algorithms and for hybrid solutions to the molecular dynamics N-Body applications problem. Another N-Body application area of significance is in sim- Figure 1: Three-dimensional particle system with rigid walls. ulating astrophysical phenomena including: general rela- tivity systems [44]; cosmological simulations [37]; simu- lations related to dark matter theories [25]; and other mod- ifications to Newtonian gravity [39]. A body of recent im- portant work is progressing in this field where simulation provides an important means of exploring the implications of various theories of dark matter. It is therefore of continuing importance to understand the computational performance for N-Body particle system simulations and indeed such simulations have found use as benchmark kernels for high-performance computing sys- tems [8, 19, 20, 23, 29, 33, 38]. In the limit of a large number of particles and a thermody- namically equilibrated system a simple benchmark rating such as number of particle updates per second suffices, but in practice, many gaming situations in which particle mod- els are employed the system is quite definitely not in equi- librium. Much present research into understanding growth and transient behaviour in physical, chemical and biolog-