A new finite-difference method for earthquake cycles accelerated by GPU and multigrid method

SUMMARY Earthquake cycle modelling is critical to help us understand the underlying physical mechanisms of earthquake processes. However, it is a very challenging scientific problem because of the variety of spatial and temporal scales involved in fault friction behaviour. Scholars have researched this problem based on different numerical methods, but there is still an urgent need to develop more rigorous and robust numerical methods. We construct a new finite-difference operator to approximate the variable-coefficient second derivatives by combining the central-difference method with the equivalent medium parametrization method. Using the method of manufactured solutions, we perform rigorous convergence tests, and the results show that the new finite-difference operator achieves second-order convergence. We use this new method in 2-D earthquake cycle simulation and the geometric multigrid method as an iterative solver to accelerate the computation while optimizing the code on a graphics processing unit (GPU) platform to improve computational efficiency further. We simulate the earthquake sequences on a vertical fault in homogeneous and heterogeneous basin models using our method and SCycle, respectively. The comparison of results shows good agreement. Our method can be utilized to study the long-term slip histories of large-scale faults in complicated mediums, as demonstrated by these results.