This work presents novel discrete event-based simulation algorithms based on the Quantized State System (QSS) numerical methods. QSS provides attractive features for particle transportation processes, in particular a very efficient handling of discontinuities in the simulation of continuous systems. We focus on High Energy Physics (HEP) particle tracking applications that typically rely on discrete time-based methods, and study the advantages of adopting a discrete event-based numerical approach that resolves efficiently the crossing of geometry boundaries by a traveling particle. For this purpose we follow two complementary strategies. First, a new co-simulation technique connects the Geant4 simulation toolkit with a standalone QSS solver. Second, a new native QSS numerical stepper is embedded into Geant4. We compare both approaches against the latest Geant4 default steppers in different HEP setups, including a complex real scenario (the CMS particle detector at CERN). Our techniques achieve relevant simulation speedups in a wide range of scenarios, particularly when the intensity of discrete-event handling dominates performance in the solving of the continuous laws of particle motion.
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