Prefetch parallelization and optimization of Monte Carlo in the grand canonical, isothermal-isobaric, and Gibbs ensemble

Parallelization of Monte Carlo (MC) is required to observe the same growth as molecular dynamics because computer processor clock speeds have plateaued while the number of cores has increased. Although prefetch parallelization can speed up an Monte Carlo molecular simulation by a factor of 3 using four parallel threads for simultaneous single-particle displacements in the canonical ensemble, other ensembles require multiple trial types that impact efficiency when threads wait for the other threads with more time-consuming trials, such as volume changes or particle insertions and deletions in the isothermal-isobaric, grand canonical, and Gibbs ensemble. Load balancing increases efficiency by attempting the same trial in each thread of a parallel batch but violates detailed balance if done incorrectly. By computing standard deviations as a function of processor time, efficiency is systematically investigated over a variety of ensembles, load balancing algorithms, and trial attempt and acceptance probabilities for dense liquids of Lennard-Jones and an extended simple point charge model of water, to reveal numerous efficiency gains, including in serial simulations. Parallel efficiency in these ensembles approached the theoretical maximum by reducing overhead costs with improved algorithms and data structures released in the open-source Monte Carlo software called FEASST.