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We present a 3D hybrid method which combines the Finite Element Method (FEM)and the Spectral Boundary Integral method (SBIM) to model nonlinear problems inunbounded domains. The flexibility of FEM is used to model the complex,heterogeneous, and nonlinear part -- such as the dynamic rupture along a faultwith near fault plasticity -- and the high accuracy and computationalefficiency of SBIM is used to simulate the exterior half spaces perfectlytruncating all incident waves. The exact truncation allows us to greatly reducethe domain of spatial discretization compared to a traditional FEM approach,leading to considerable savings in computational cost and memory requirements.The coupling of FEM and SBIM is achieved by the exchange of traction anddisplacement boundary conditions at the computationally defined boundary. Themethod is suited to implementation on massively parallel computers. We validatethe developed method by means of a benchmark problem. Three more complexexamples with a low velocity fault zone, low velocity off-fault inclusion, andinteraction of multiple faults, respectively, demonstrate the capability of thehybrid scheme in solving problems of very large sizes. Finally, we discusspotential applications of the hybrid method for problems in geophysics andengineering.

A three-dimensional hybrid finite element -- spectral boundary integral method for modeling earthquakes in complex unbounded domains