  A massively parallel kinetic Monte Carlo (kMC) approach is proposed for
simulating ionic migration in a crystal system by introducing the atomic
fragmentation scheme (fragment kMC). The fragment kMC method achieved a
reasonable parallel efficiency with 1728 central processing unit (CPU) cores,
and the method enables the simulation of ionic diffusion in $\mu$m-scale
perovskite crystals. To demonstrate the feasibility of the proposed approach,
the fragment kMC method was applied to predict the diffusion coefficients of
hydrogen and oxygen in SrTiO$_{(3-x)}$H$_x$ and BaTiO$_{(3-x)}$H$_x$ system.
Finally, the fragment kMC method was customized for $\mu$-scale BaTiO$_3$
simulation under an applied bias voltage, and oxygen diffusion in BaTiO$_3$
model was evaluated. The respective grain sizes are sub-nanometre, and we
conclude that the proposed fragment kMC method can be applied to calculate the
extent of ionic migration in $\mu$-scale materials with fully atomistic
simulation models at a reasonable computational cost.
