Thomas B Thompson, Brendan J Meade

Boundary element methods have become a foundational tool in earthquake science for the modeling of earthquake cycle kinematics. Despite their wide use and convenience typical rectangular and triangular constant slip dislocation methods produce stress singularities at the edges of every element rendering these models physically unrealistic. As we demonstrate, in an earthquake cycle simulation where the stress influences the fault slip through a friction relationship, these un-physical stress singularities manifest in severe numerical artifacts which limit their applicability to the calculation of on fault stresses and dynamic earthquake cycle modeling. To solve this problem, we develop a singularity free Galerkin boundary element method using continuous linear displacement and slip basis functions. We use Gaussian and Sauter-Schwab quadrature combined with a Stokes theorem based regularization approach in lieu of analytical formulae. In order to solve the large dense linear systems that emerge from boundary element methods, we use a fast multipole method to accurately approximate far-field element interactions. Combining these theoretical approaches with an optimized parallel implementation and GPU acceleration, we are able to solve one million element problems in seconds on a desktop computer.