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Analytic bond-order potentials (BOPs) allow to obtain a highly accurate description of interatomic interactions at a reasonable computational cost. However, for simulations with very large systems, the high memory demands require the use of a parallel implementation, which at the same time also optimizes the use of computational resources. The calculations of analytic BOPs are performed for a restricted volume around every atom and therefore have shown to be well suited for a message passing interface (MPI)-based parallelization based on a domain decomposition scheme, in which one process manages one big domain using the entire memory of a compute node. On the basis of this approach, the present work focuses on the analysis and enhancement of its performance on shared memory by using OpenMP threads on each MPI process, in order to use many cores per node to speed up computations and minimize memory bottlenecks. Different algorithms are described and their corresponding performance results are presented, showing significant performance gains for highly parallel systems with hybrid MPI/OpenMP simulations up to several thousands of threads.