Stable, high order accurate adaptive schemes for long time, highly intermittent geophysics problems

Brittany A. Erickson, & Jan Nordström

Accepted 2014, SCEC Contribution #1943

Many geophysical phenomena are characterized by properties that evolve over a wide range of scales which introduce difficulties when attempting to model these features in one
computational method. We have developed a high-order finite difference method for the elastic wave equation that is able to efficiently handle varying temporal and spatial scales
in a single, stand-alone framework. We apply this method to earthquake cycle models characterized by extremely long interseismic periods interspersed with abrupt, short periods
of dynamic rupture. Through the use of summation-by-parts operators and weak enforcement of boundary conditions we derive a provably stable discretization. Time stepping is
achieved through the implicit θ-method which allows us to take large time steps during the intermittent period between earthquakes and adapts appropriately to fully resolve rupture.

Citation
Erickson, B. A., & Nordström, J. (2014). Stable, high order accurate adaptive schemes for long time, highly intermittent geophysics problems. Journal of Computational and Applied Mathematics, (accepted).