  We review the recent researches of numerical simulations on faulting, which
are interpreted in this paper as the evolution of the state of the fault plane
and the evolution of fault structure. The theme includes the fault constitutive
(friction) law, the properties of the gauge particles, the initial phase of the
rupture, the dynamic rupture process, the interaction of the fault segments,
the fault zone dynamics, and so on. Many numerical methods have been developed:
boundary integral equation methods (BIEM), finite difference methods (FDM),
finite or spectral element methods (FEM, SEM) as well as distinct element
methods (DEM), discrete element methods (again DEM) or lattice solid models
(LSM). The fault dynamics should be solved as a complex non-linear system,
which shows multiple hierarchical structures on its property and behavior. The
researches have progressively advanced since the 1990's both numerically and
physically thanks to high performance computing environments. The interaction
at small scales is modeled to provide a large scale property of the fault. The
dynamic rupture has been actively studied especially for the effect on the
fault geometry evolution or due to the existed fault structure. The
(quasi-)static and the initial processes of the fault movement have been also
explored in a seismic cycle. The effect of fluid or heat has been also taken
into account in the mechanics. All these efforts help us to understand the
phenomena and the unified understanding (simulation) over different
spacio-temporal scales is more and more expected.
