  An improved version of a recently developed stochastic cluster dynamics (SCD)
method {[}Marian, J. and Bulatov, V. V., {\it J. Nucl. Mater.} \textbf{415}
(2014) 84-95{]} is introduced as an alternative to rate theory (RT) methods for
solving coupled ordinary differential equation (ODE) systems for irradiation
damage simulations. SCD circumvents by design the curse of dimensionality of
the variable space that renders traditional ODE-based RT approaches inefficient
when handling complex defect population comprised of multiple (more than two)
defect species. Several improvements introduced here enable efficient and
accurate simulations of irradiated materials up to realistic (high) damage
doses characteristic of next-generation nuclear systems. The first improvement
is a procedure for efficiently updating the defect reaction-network and event
selection in the context of a dynamically expanding reaction-network. Next is a
novel implementation of the $\tau$-leaping method that speeds up SCD
simulations by advancing the state of the reaction network in large time
increments when appropriate. Lastly, a volume rescaling procedure is introduced
to control the computational complexity of the expanding reaction-network
through occasional reductions of the defect population while maintaining
accurate statistics. The enhanced SCD method is then applied to model defect
cluster accumulation in iron thin films subjected to triple ion-beam
($\text{Fe}^{3+}$, $\text{He}^{+}$ and $ $$\text{H\ensuremath{{}^{+}}}$$ $)
irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo
simulations are prohibitively expensive.
