Galerkin boundary integral equation method for spontaneous rupture propagation problems

We develop a Galerkin finite element boundary integral equation method (GaBIEM) for spontaneous rupture propagation problems for a planar fault embedded in a homogeneous full 2D space. A simple 2D anti plane rupture propagation problem, with a slip-weakening friction law, is simulated by the GaBIEM. This method allows one to separate explicitly the kernel into singular static and time-dependent parts, and a nonsingular dynamic component. The simulated results throw light into the performance of the GaBIEM and highlight differences with respect to that of the traditional, collocation, boundary integral equation method (BIEM). The rate of convergence of the GaBIEM, as measured from a root mean square (RMS) analysis of the difference of approximate solutions corresponding to increasingly finer element sizes is of a higher order than that of the BIEM. There is no restriction on the CFL stability number since an implicit, unconditionally stable method is used for the time integration. The error of the approximation increases with the time step, as expected, and it can remain below that of the BIEM.