Accelerating Convergence in Simulations of Crustal Deformation with Spontaneous Rupture

Abstract:

We have extended a domain decomposition approach for modeling spontaneous (frictional) earthquake rupture in quasistatic and dynamic simulations of crustal deformation within our finite-element code, PyLith. This new approach greatly accelerates convergence in quasistatic simulations by incorporating the fault friction terms into the Jacobian for the system of equations. In the new approach the Lagrange multipliers correspond to the difference between the total fault traction and the friction traction on the fault. This replaces our original formulation [Aagaard, Knepley, Williams JGR, 118(6), 2013] in which the Lagrange multipliers correspond to the total fault traction and each iteration of the nonlinear solve required a separate solve to update the fault slip. For quasistatic simulations with a Krylov (iterative) solver, this new formulation remains compatible with our custom preconditioner for the Lagrange multiplier portion of the system of equations, which provides excellent scalability with problem size compared to conventional additive Schwarz methods. For dynamic simulations with explicit time stepping and a diagonal Jacobian for the system of equations, convergence still occurs in a single iteration.