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 …

Equations arising in general relativity are usually too complicated to be solved analytically
and one must rely on numerical methods to solve sets of coupled partial differential …

This book introduces the modern field of 3+ 1 numerical relativity. The book has been written
in a way as to be as self-contained as possible, and only assumes a basic knowledge of …

A new representation of the Einstein evolution equations is presented that is first order,
linearly degenerate and symmetric hyperbolic. This new system uses the generalized …

Numerical simulations of 15 orbits of an equal-mass binary black-hole system are
presented. Gravitational waveforms from these simulations, covering more than 30 cycles …

We provide a detailed analysis of several aspects of the turduckening technique for evolving
black holes. At the analytical level we study the constraint propagation for a family of …

The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass
nonspinning binary black hole system are presented. Gravitational waveforms from these …

A general-covariant extension of Einstein's field equations is considered with a view to
numerical relativity applications. The basic variables are taken to be the metric tensor and …

We review the dramatic progress in the simulations of compact objects and compact-object
binaries that has taken place in the first two decades of the twenty-first century. This includes …

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 …