Joan Masso

The cactus framework and toolkit: design and applications

We describe Cactus, a framework for building a variety of computing applications in science and engineering, including astrophysics, relativity and chemical engineering.We first motivate by example the need for such frameworks to support multi-platform, high performance applications across diverse communities. We then describe the design of the latest release of Cactus (Version 4.0) a complete rewrite of earlier versions, which enables highly modular, multi-language, parallel applications to be developed by single researchers and large collaborations alike. Making extensive use of abstractions, we detail how we are able to provide the latest advances in computational science, such as interchangeable parallel data distribution and high performance IO layers, while hiding most details of the underlying computational libraries from the application developer. We survey how Cactus 4.0 is being used by various application communities, and describe how it will also enable these applications to run on the computational Grids of the near future.

New formalism for numerical relativity.

We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal slicing, making it potentially very useful for numerical relativity. This development permits the application to the Einstein equations of advanced numerical methods developed to solve the fluid dynamic equations, {\em without} overly restricting the time slicing, for the first time. The full set of characteristic fields and speeds is explicitly given.

Solving Einstein's equations on supercomputers

In 1916, Albert Einstein published his famous general theory of relativity, which contains the rules of gravity and provides the basis for modern theories of astrophysics and cosmology. For many years, physicists, astrophysicists and mathematicians have striven to develop techniques for unlocking the secrets contained in Einsteins theory of gravity; more recently, computational science research groups have added their expertise to the endeavor. Because the underlying scientific project provides such a demanding and rich system for computational science, techniques developed to solve Einsteins equations will apply immediately to a large family of scientific and engineering problems. The authors have developed a collaborative computational framework that allows remote monitoring and visualization of simulations, at the center of which lies a community code called Cactus. Many researchers in the general scientific computing community have already adopted Cactus, as have numerical relativists and astrophysicists. In June 1999, an international team of researchers at various sites ran some of the largest such simulations in numerical relativity yet undertaken, using a 256-processor SGI Origin 2000 supercomputer at the National Center for Supercomputing Applications (NCSA). Other globally distributed scientific teams are running visual simulations of Einsteins equations on the gravitational effects of colliding black holes.

First order hyperbolic formalism for numerical relativity

The causal structure of Einstein’s evolution equations is considered. We show that in general they can be written as a first-order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution equations, which can lead to numerical inaccuracies, can be eliminated by using the Hamiltonian constraint. Furthermore, we show that the entire system is hyperbolic when the time coordinate is chosen in an invariant algebraic way, and for any fixed choice of the shift. This is achieved by using the momentum constraints in such a way that no additional space or time derivatives of the equations need to be computed. The slicings that allow hyperbolicity in this formulation belong to a large class, including harmonic, maximal, and many others that have been commonly used in numerical relativity. We provide details of some of the advanced numerical methods that this formulation of the equations allows, and we also discuss certain advantages that a hyperbolic formulation provides when treating boundary conditions. @S0556-2821~97!05616-6# PACS number~s!: 04.25.Dm

Boosted three-dimensional black-hole evolutions with singularity excision

Binary black-hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three-dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on single black-hole evolutions and the first successful demonstration of a black hole moving freely through a three-dimensional computational grid via a Cauchy evolution: a hole moving near 6M at 0.1c during a total evolution of duration near 60M. [S0031-9007(98)05652-X]

GRAVITATIONAL WAVE EXTRACTION AND OUTER BOUNDARY CONDITIONS BY PERTURBATIVE MATCHING

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three-dimensional numerical relativity code.

Stable Characteristic Evolution of Generic Three-Dimensional Single-Black-Hole Spacetimes

We report new results which establish that the accurate 3dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a selection of distorted, moving and spinning single black holes, with evolution times up to 60,000M. 04.25.Dm,04.30.Db

Dynamics of Apparent and Event Horizons.

The dynamics of apparent and event horizons of various black hole spacetimes, including those containing distorted, rotating and colliding black holes, are studied. We have developed a powerful and efficient new method for locating the event horizon, making possible the study of both types of horizons in numerical relativity. We show that both the event and apparent horizons, in all dynamical black hole spacetimes studied, oscillate with the quasinormal frequency.

Event horizons in numerical relativity: Methods and tests

This is the first paper in a series on event horizons in numerical relativity. In this paper we present methods for obtaining the location of an event horizon in a numerically generated spacetime. The location of an event horizon is determined based on two key ideas: (1) integrating backward in time, and (2) integrating the whole horizon surface. The accuracy and efficiency of the methods are examined with various sample spacetimes, including both analytic (Schwarzschild and Kerr) and numerically generated black holes. The numerically evolved spacetimes contain highly distorted black holes, rotating black holes, and colliding black holes. In all cases studied, our methods can find event horizons to within a very small fraction of a grid zone.

Test-beds and applications for apparent horizon finders in numerical relativity

We present a series of test-beds for numerical codes designed to find apparent horizons. We compare three apparent horizon finders that use different numerical methods: one of them in axisymmetry and two which are fully three dimensional. We concentrate first on a toy model that has a simple horizon structure, and then go on to study single and multiple black hole datasets. We use our finders to look for apparent horizons in Brill wave initial data where we discover that some results published previously are not correct. For pure wave and multiple black hole spacetimes, we apply our finders to survey parameter space.