(112a) Monte Carlo On Gpus; A Proof of Detailed Balance

Graphics processing units (GPUs) offer inexpensive supercomputing capabilities for problems that can be parallelized.  However, Monte Carlo (MC) methods are difficult to parallelize efficiently without violating detailed balance [1]. As a result, MC simulations of material systems have not enjoyed the tremendous speedups on GPUs that are transforming molecular dynamics software.  In this work we present an algorithm for performing MC simulations on GPUs.  We prove this approach obeys detailed balance and implement it for a system of hard disks.  Simulations of up to 4.3 million disks are performed on a single GPU and we validate our calculated equation of state by comparing with previous work [2].  The GPU implementation achieves a speedup of 73.5x compared to a single-core serial implementation and 9.4x compared to an 8-core parallel implementation.  Up to 411 sweeps per second are achieved for a system of one million hard disks.

[1] Tal Levy, Guy Cohen, and Eran Rabanai. Simulating lattice spin models on graphics processing units. Journal of Chemical Theory and Computation, 6(11):3293—3301, 2010.

[2] Etienne P. Bernard, and Wener Krauth. Two step melting in two dimensions: First-Order liquid-hexatic transition, Physical Review Letters, 107(15), 2011.