Doing numerical cosmology with the Cactus code

The article presents some aspects concerning the construction of a new thorn for the Cactus code, a complete 3-dimensional machinery for numerical relativity. This thorn is completely dedicated to numerical simulations in cosmology, that means it can provide evolutions of different cosmological models, mainly based on Friedman-Robertson-Walker metric. Some numerical results are presented, testing the convergence, stability and the applicability of the code.Comment: 18 pages, 8 figures, Late

COFFEE -- An MPI-parallelized Python package for the numerical evolution of differential equations

COFFEE (ConFormal Field Equation Evolver) is a Python package primarily developed to numerically evolve systems of partial differential equations over time using the method of lines. It includes a variety of time integrators and finite differencing stencils with the summation-by-parts property, as well as pseudo-spectral functionality for angular derivatives of spin-weighted functions. Some additional capabilities include being MPI-parallelisable on a variety of different geometries, HDF data output and post processing scripts to visualize data, and an actions class that allows users to create code for analysis after each timestep.Comment: 12 pages, 1 figure, accepted to be published in Software

Maple+GrTensorII libraries for cosmology

The article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmologyComment: LaTeX LLNCS style, 8 pages, accepted for SYNASC 2004 - 6th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, September 26-30 200

Design of an expanding cosmological background for the moving punctures approach to numerical relativity

Gravitational waves astronomy is a new field ushered in by the first detection of a par of merging black holes. Numerical relativity is the only tool capable of solving Einstein’s equations for the the dynamics and resulting gravitational waves of that binary black hole system. In this project we will first learn how to use the numerical relativity code at Georgia Tech for black hole systems, then enhance the code with well understood improvements with the goal of improving the waveforms used in the detection. If time permits, we will use these improved waveforms in LIGO/Virgo data analysis.Outgoin

Finding apparent horizons and other two-surfaces of constant expansion

Apparent horizons are structures of spacelike hypersurfaces that can be determined locally in time. Closed surfaces of constant expansion (CE surfaces) are a generalisation of apparent horizons. I present an efficient method for locating CE surfaces. This method uses an explicit representation of the surface, allowing for arbitrary resolutions and, in principle, shapes. The CE surface equation is then solved as a nonlinear elliptic equation. It is reasonable to assume that CE surfaces foliate a spacelike hypersurface outside of some interior region, thus defining an invariant (but still slicing-dependent) radial coordinate. This can be used to determine gauge modes and to compare time evolutions with different gauge conditions. CE surfaces also provide an efficient way to find new apparent horizons as they appear e.g. in binary black hole simulations.Comment: 21 pages, 8 figures; two references adde

Numerical Relativity As A Tool For Computational Astrophysics

The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by an extremely complex set of coupled, nonlinear, hyperbolic-elliptic partial differential equations. The largest parallel supercomputers are finally approaching the speed and memory required to solve the complete set of Einstein's equations for the first time since they were written over 80 years ago, allowing one to attempt full 3D simulations of such exciting events as colliding black holes and neutron stars. In this paper we review the computational effort in this direction, and discuss a new 3D multi-purpose parallel code called ``Cactus'' for general relativistic astrophysics. Directions for further work are indicated where appropriate.Comment: Review for JCA

Towards a wave-extraction method for numerical relativity: IV. Testing the quasi-Kinnersley method in the Bondi-Sachs framework

We present a numerical study of the evolution of a non-linearly disturbed black hole described by the Bondi--Sachs metric, for which the outgoing gravitational waves can readily be found using the news function. We compare the gravitational wave output obtained with the use of the news function in the Bondi--Sachs framework, with that obtained from the Weyl scalars, where the latter are evaluated in a quasi-Kinnersley tetrad. The latter method has the advantage of being applicable to any formulation of Einstein's equations---including the ADM formulation and its various descendants---in addition to being robust. Using the non-linearly disturbed Bondi--Sachs black hole as a test-bed, we show that the two approaches give wave-extraction results which are in very good agreement. When wave extraction through the Weyl scalars is done in a non quasi-Kinnersley tetrad, the results are markedly different from those obtained using the news function.Comment: 12 pages, 11 figure