A Nitsche-extended finite element method for earthquake rupture on complex fault systems

Abstract The extended finite element method (XFEM) provides a natural way to incorporate strong and weak discontinuities into discretizations. It alleviates the need to mesh discontinuities, allowing simulation meshes to be nearly independent of discontinuity geometry. Currently, both quasistatic deformation and dynamic earthquake rupture simulations under standard FEM are limited to simplified fault networks, as generating meshes that both conform with the faults and have appropriate properties for accurate simulation is a difficult problem. In addition, fault geometry is not well known; robustness of solution to fault geometry must be determined. Remeshing with varying geometry would make such tests computationally unfeasible. The XFEM makes a natural choice for discretization in these crustal deformation simulations on complex fault systems. Here, we develop a method based upon the XFEM using Nitsche’s method to apply boundary conditions, enabling the solution of static deformation and dynamic earthquake models. We compare several approaches to calculating and applying frictional tractions. Finally, we demonstrate the method with two problems: an earthquake community dynamic code verification benchmark and a quasistatic problem on a fault system model of southern California.

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