However, the efficiency of many parallel dynamic Monte Carlo methods is limited by steps where processors must wait for information from one another. To reduce waiting in such so-called conservative methods, a provident method is proposed. The method reduces waiting by relying on pre-computed Monte Carlo attempt information to avoid the original method's redundant communication of state information and unnecessary calculation of unused states. The method also improves on the original by distributing the workload more evenly among processors, through decomposing the computation of Monte Carlo attempt information by attempt number instead of location. Further advantages of the method over the original are the prevention of conflicts arising from simultaneous attempts and savings in random number generation.

The method's implementation is described and used to simulate the Ising model with Glauber dynamics. A saturated implementation is used where each processor simulates one Ising spin. Such an implementation simplifies determining information about Monte Carlo attempts and making such attempts. The method is validated by computing the model's normalised time auto-correlation function, and checking the result against that from the original conservative method. The method's speedup over the original is also demonstrated using dynamic Ising simulations on a HP ProLiant DL785 cluster.

Besides completing large Monte Carlo simulations more quickly, the method's provident nature allows for further potential optimization. Preknowledge of Monte Carlo attempt information grants the opportunity to gauge when and for how long each processor has to wait. With such estimates, waiting processors can be directed to help other processors in a coordinated manner, achieving an even greater speedup.

1

D.P. Landau, K. Binder, "A Guide to Monte Carlo Simulations in Statistical Physics", Cambridge University Press, Cambridge, United Kingdom, 2000.

2

M.H. Kalos, P.A. Whitlock, "Monte Carlo Methods", Wiley-VCH, Weinheim, Germany, 2008.

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