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 …

I review the development of numerical evolution codes for general relativity based upon the
characteristic initial-value problem. Progress in characteristic evolution is traced from the …

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 …

We present a new formulation of the Einstein equations based on a conformal and traceless
decomposition of the covariant form of the Z4 system. This formulation combines the …

We present ENIGMA, a time domain, inspiral-merger-ringdown waveform model that
describes nonspinning binary black holes systems that evolve on moderately eccentric …

Numerical relativity simulations of compact binaries with the Z4c and Baumgarte-Shapiro-
Shibata-Nakamura-Oohara-Kojima (BSSNOK) formulations are compared. The Z4c …

A generalized framework is presented that extends the classical theory of finite-difference
summation-by-parts (SBP) operators to include a wide range of operators, where the main …

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves
nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid …

We study a higher derivative extension to General Relativity and present a fully nonlinear/
nonperturbative treatment to construct initial data and study its dynamical behavior 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 …