Domain decomposition method for dynamic faulting under slip-dependent friction

The anti-plane shearing problem on a system of finite faults under a slip-dependent friction in a linear elastic domain is considered. Using a Newmark method for the time discretization of the problem, we have obtained an elliptic variational inequality at each time step. An upper bound for the time step size, which is not a CFL condition, is deduced from the solution uniqueness criterion using the first eigenvalue of the tangent problem. Finite element form of the variational inequality is solved by a Schwarz method assuming that the inner nodes of the domain lie in one subdomain and the nodes on the fault lie in other subdomains. Two decompositions of the domain are analyzed, one made up of two subdomains and another one with three subdomains. Numerical experiments are performed to illustrate convergence for a single time step (convergence of the Schwarz algorithm, influence of the mesh size, influence of the time step), convergence in time (instability capturing, energy dissipation, optimal time step) and an application to a relevant physical problem (interacting parallel fault segments).