  We present a 3D hybrid method which combines the Finite Element Method (FEM)
and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in
unbounded domains. The flexibility of FEM is used to model the complex,
heterogeneous, and nonlinear part -- such as the dynamic rupture along a fault
with near fault plasticity -- and the high accuracy and computational
efficiency of SBIM is used to simulate the exterior half spaces perfectly
truncating all incident waves. The exact truncation allows us to greatly reduce
the 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 and
displacement boundary conditions at the computationally defined boundary. The
method is suited to implementation on massively parallel computers. We validate
the developed method by means of a benchmark problem. Three more complex
examples with a low velocity fault zone, low velocity off-fault inclusion, and
interaction of multiple faults, respectively, demonstrate the capability of the
hybrid scheme in solving problems of very large sizes. Finally, we discuss
potential applications of the hybrid method for problems in geophysics and
engineering.
