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 …

Numerical relativity is the most promising tool for theoretically modeling the inspiral and
coalescence of neutron star and black hole binaries, which, in turn, are among the most …

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 …

Numerical relativity has faced the problem that standard 3+ 1 simulations of black hole
spacetimes without singularity excision and with singularity avoiding lapse and vanishing …

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 …

We present techniques for successfully performing numerical relativity simulations of binary
black holes with fourth-order accuracy. Our simulations are based on a new coding …

We study the critical O (3) model using the numerical conformal bootstrap. In particular, we
use a recently developed cutting-surface algorithm to efficiently map out the allowed space …

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 …

We investigate the effects of anisotropic perturbations in three-dimensional O (N)-symmetric
vector models. In order to assess their relevance for the critical behavior, we determine the …

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 …