**A comparison between two massively parallel algorithms for Monte Carlo
computer simulation: An investigation in the grand canonical ensemble**

GS Heffelfinger and ME Lewitt, JOURNAL OF COMPUTATIONAL CHEMISTRY, 17, 250-265 (1996).

DOI: 10.1002/(SICI)1096-987X(19960130)17:2<250::AID-JCC11>3.0.CO;2-N

We present a comparison between two different approaches to parallelizing the grand canonical Monte Carlo simulation technique (GCMC) for classical fluids: a spatial decomposition and a time decomposition. The spatial decomposition relies on the fact that for short-ranged fluids, such as the cut and shifted Lennard-Jones potential used in this work, atoms separated by a greater distance than the reach of the potential act independently, and thus different processors can work concurrently in regions of the same system which are sufficiently far apart. The time decomposition is an exactly parallel approach which employs simultaneous (GCMC) simulations, one per processor, identical in every respect except the initial random number seed, with the thermodynamic output variables averaged across all processors. While scaling characteristics for the spatial decomposition are presented for 8-1024 processor systems, the comparison between the two decompositions is limited to the 8-128 processor range due to the warm-up time and memory imitations of the time decomposition. Using a combination of speed and statistical efficiency, the two algorithms are compared at two different state points. While the time decomposition reaches a given value of standard error in the system's potential energy more quickly than the spatial decomposition for both densities, the warm-up time demands of the time decomposition quickly become insurmountable as the system size increases. (C) 1996 by John Wiley & Sons, Inc.

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