  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.
