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Discrete dislocation dynamics (DDD) simulations are being increasingly employed to investigate metal plasticity at the mesoscale. However, in spite of its ability to access beyond the length and time limits of atomistic methods, the DDD model is still limited by its high computational cost, with ranges of achievable strains too low and strain rates too high by several orders of magnitude compared with typical experimental conditions. By combining the efficiency of the recently developed subcycling time-integrator with the highly parallel architecture of graphics processing unit (GPU) devices, we developed a DDD model that provides significant acceleration compared to existing implementations. Our GPU-accelerated implementation enables large-scale DDD simulations that can reach relevant levels of strain using a moderate amount of computational resources.