Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …

Many evolution problems in physics are described by partial differential equations on an
infinite domain; therefore, one is interested in the solutions to such problems for a given …

High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …

Time dependent problems frequently pose challenges in areas of science and engineering
dealing with numerical analysis, scientific computation, mathematical models, and most …

We simulate earthquake cycles with rate-and-state fault friction and off-fault power-law
viscoelasticity for the classic 2D antiplane shear problem of a vertical, strike-slip plate …

Many applications rely on solving time-dependent partial differential equations (PDEs) that
include second derivatives. Summation-by-parts (SBP) operators are crucial for developing …

We present an efficient numerical method for earthquake cycle simulations that employs a
finite difference discretization of the off‐fault material to accommodate spatially variable …

We use high order finite difference methods to solve the wave equation in the second order
form. The spatial discretization is performed by finite difference operators satisfying a …

The Whillans Ice Plain (WIP), Antarctica, experiences twice daily tidally modulated stick‐slip
cycles. Slip events last about 30 min, have sliding velocities as high as∼ 0.5 mm/s (15 …

We consider fourth order accurate compact schemes, in both space and time, for the second
order wave equation with a variable speed of sound. We demonstrate that usually this is …