A scalable parallel algorithm for dynamic range-limited n-tuple computation in many-body molecular dynamics simulation

Recent advancements in reactive molecular dynamics (MD) simulations based on many-body interatomic potentials necessitate efficient dynamic n-tuple computation, where a set of atomic n-tuples within a given spatial range is constructed at every time step. Here, we develop a computation-pattern algebraic framework to mathematically formulate general n-tuple computation. Based on translation/reflection-invariant properties of computation patterns within this framework, we design a shift-collapse (SC) algorithm for cell-based parallel MD. Theoretical analysis quantifies the compact n-tuple search space and small communication cost of SC-MD for arbitrary n, which are reduced to those in best pair-computation approaches (e.g. eighth-shell method) for n = 2. Benchmark tests show that SC-MD outperforms our production MD code at the finest grain, with 9.7-and 5.1-fold speedups on Intel-Xeon and BlueGene/Q clusters. SC-MD also exhibits excellent strong scalability.