Massively Parallel Molecular Dynamics Simulations for Many-Body Potentials
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dimensional configuration, which is beginning to approach length scales of microelectronics features or grain sizes in metals. However, this number would need to be scaled up by a factor = 1014 to approach one mole of matter. An equally severe restriction is that MD simulations operate with time steps on the order of femtoseconds, so that a simulation of one second elapsed time would necessitate the execution of = 1015 time steps. Thus a microscopic simulation of fatigue in a turbine blade, to pick just one example, is out of the question with current hardware and algorithms. Of course, one may not need this amount of detail to be able to accurately model the phenomenon and predict its properties. Continuum models, treated analytically or, more commonly, by the finite element method and other numerical approximations, have been very valuable in this regard. Schemes linking the microscopic (quantum mechanical) models and the continuum limit, will become increasingly important in the future. Simulations on the scale just described have only become possible through the advent of parallel computers. MD simulations are, at least in principle, well suited for parallel computation, since they involve the concurrent application of the same operation to different data elements, i.e. all particle force calculations and updates are performed simultaneously. Nevertheless the actual parallelization of an MD code for a given type of interaction potential and a given target machine is not a trivial task. Attention must be paid to such important issues as load balancing and avoiding the communication bottleneck. The appropriate strategy will be problem and machine dependent. For a given type of parallel computer, the optimal algorithm may even depend on the size of the system being studied. Several papers have discussed these topics in a variety of settings [2-5]. In the present work we analyze MD algorithms for Single-Instruction Multiple-Data (SIMD) computers with square mesh connectivity. We focus on short-ranged two- and three-body 125 Mat. Res. Soc. Symp. Proc. Vol. 408 © 1996 Materials Research Society
potentials and numbers of particles (N) that are of the same order of magnitude as the number of processors (P). This covers a generic class of problems, including some biomolecules, polymers, and clusters. As a specific example, we study large Si-clusters in which the atoms are taken to interact through a Stillinger-Weber potential [6]. We have also employed the same programs in a study of fullerene tubes [7] in which the atoms are taken to interact through a Tersoff-Brenner potential [8]. Here we present timing results and algorithmic details, deferring a discussion of the physical findings to a future paper [9]. We are specifically excluding long-range potentials from the discussion. These pose their own problems since an exact calculation of all the forces scales as O(N 2 ) which is prohibitive for all but the smallest systems. Various approximate methods, with a gentler time complexity, have been proposed and have been
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