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 …

The Lax–Wendroff theorem stipulates that a discretely conservative operator is necessary to
accurately capture discontinuities. The discrete operator, however, need not be derived from …

Finite difference operators approximating second derivatives with variable coefficients and
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …

This work presents an entropy stable discontinuous Galerkin (DG) spectral element
approximation for systems of non-linear conservation laws with general geometric (h) and …

Computational fluid dynamics can be used to gain deeper insight into compressible flow
physics, but current limitations in numerical methods, computing hardware, data analysis …

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 …

A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-
domain (FDTD) subgridding method is proposed to model geometrically fine structures in …