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This paper concerns mainly with parallel and distributed implementations of molecular dynamics simulations of the Lennard-Jones potential model. The reported research work studies and experiments different algorithms and parallelization techniques for shared memory and message passing architectures, and the programs are executed on single-core processors, multi-core processors, GPU, and GPU cluster. The solution based on efficient versions of the neighbor list algorithm and space division technique is further discussed. The obtained speedups for multi-core processor, GPU, and GPU cluster, relative to the single-core processor implementation of the program, are analyzed, and the advantages of the algorithms are highlighted.