Parallel Algorithms for Molecular-Dynamics Simulations of Coulombic Systems
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PARALLEL ALGORITHMS FOR MOLECULAR-DYNAMICS SIMULATIONS OF COULOMBIIC SYSTEMS
WEI LI, RAJIV K. KALIA, SIMON DE LEEUW, ATICHIRO NAKANO, DONALD
GREENWELL, AND PRIYA VASHISHTA Concurrent Computing Laboratory for Material Simulations, Department of Physics & Astronomy, and Department of Computer Science, Louisiana State University, Baton Rouge, LA 70803 ABSTRACT In molecular-dynamics simulations for the long-range Coulomb interaction, a great deal of effort is devoted to reducing the computational complexity of the usual N2 operations in the direct calculation. For bulk systems, we have designed a parallel algorithm based on the domain-decomposition strategy for the Ewald summation. The performance of the algorithm is evaluated on the in-house iPSC/860 system. We find that this algorithm reduces the computational complexity to O(N). For a 64,000-particle plasma in three dimension, the execution time on an 8-node system is 27.4 sec per MD time step. The interprocessor communication is a small fraction of the total execution time. We find linear speedups and a parallel efficiency of 0.85. For comparison, parallel algorithms are also designed for the Fast Multipole Method (FMM) - a divide and conquer scheme in which the system is divided into cubic subdomains and interactions between distant charged regions are calculated with a truncated multipole expansion. The performance of the FMM on Touchstone Delta machine is discussed.
INTRODUCTION In recent years, the emergence of massively parallel computers has spurred a great deal of effort in the area of atomistic simulations. Most of the activity has revolved around the design of highly efficient concurrent algorithms to implement large-scale material simulations. Hitherto, on sequential machines these simulations were limited to system sizes of merely 102 104 particles. For most bulk systems, these system sizes are adequate. However, order of magnitude bigger systems are required in simulations involving the study of growth or fracture or novel systems comprising nanosize particles. In many materials, such as semiconductor binary oxides (Si0 2, GeO2), chalcogenides (GeSe 2 , SiSe2), Ill-V semiconductors (GaAs, InI, InSb), and fast-ion conductors (Ag 2 S, Ag 2 Se), the most dominant interaction is the Coulomb potential arising as a result of charge-transfer effects. Therefore, it is important to design efficient algorithms to implement Coulomb interaction on concurrent architectures. Simulations of Coulombic systems are either carried out with free-boundary conditions or periodic boundary conditions. In the first case, the straightforward evaluation of interaction increases as N2 , where N is the number of particles in the system. For simulations involving periodic boundary conditions, the executing time varies as N 3/2 [1,2]. Clearly, it is impractical to use the straightforward approach in large-scale Coulombic systems. Recently, several divide-and-conquer schemes have been implemented to reduce the computational complexity. These algorithms separate the Coulomb potentia
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