Simulating earthquake rupture on realistic fault geometries is a difficult proposition for two main reasons: Faults, the physical surfaces on which earthquakes rupture, are geometrically complex on multiple scales; any discretization must handle multiple intersecting surfaces of discontinuity embedded within the computational domain. And these surfaces are often kilometers underground, and therefore not observable directly; simulations must understand and quantify solution variability as a function of varying geometry.

Most common finite element methods for earthquake rupture require meshes which coincide with the entire fault network – all discontinuities must lie on element edges. This is extremely limiting, as automatically and robustly generating such meshes for both accurate simulation and complicated geometries is an unsolved problem. Repeatedly generating such meshes while varying geometry is, at this point, intractable.

However, extended finite element methods provide a way to build discontinuities not into the mesh but into the approximation space. Fault geometry can therefore be varied (almost) independently of computation mesh. Here we demonstrate the potential of such methods for simulating long-time, repeated earthquake rupture on complicated fault networks.