Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Summation by parts, projections, and stability. II
Mathematics of Computation
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
Journal of Computational Physics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Journal of Scientific Computing
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Stable Difference Approximations for the Elastic Wave Equation in Second Order Formulation
SIAM Journal on Numerical Analysis
High-order local absorbing conditions for the wave equation: Extensions and improvements
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics in complex geometries with multiple faults. The bulk material is an isotropic elastic solid cut by pre-existing fault interfaces that accommodate relative motion of the material on the two sides. The fields across the interfaces are related through friction laws which depend on the sliding velocity, tractions acting on the interface, and state variables which evolve according to ordinary differential equations involving local fields.The method is based on summation-by-parts finite difference operators with irregular geometries handled through coordinate transforms and multi-block meshes. Boundary conditions as well as block interface conditions (whether frictional or otherwise) are enforced weakly through the simultaneous approximation term method, resulting in a provably stable discretization.The theoretical accuracy and stability results are confirmed with the method of manufactured solutions. The practical benefits of the new methodology are illustrated in a simulation of a subduction zone megathrust earthquake, a challenging application problem involving complex free-surface topography, nonplanar faults, and varying material properties.