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Full-Text Articles in Physics
Implementation Of Standard Testbeds For Numerical Relativity, Maria Babiuc-Hamilton, Sascha Husa, Daniela Alic, Ian Hinder, Christiane Lechner, Erik Schnetter, Yosef Zlochower, Nils Dorband, Jeffrey Winicour, D. Pollney, B´Ela Szilagyi
Implementation Of Standard Testbeds For Numerical Relativity, Maria Babiuc-Hamilton, Sascha Husa, Daniela Alic, Ian Hinder, Christiane Lechner, Erik Schnetter, Yosef Zlochower, Nils Dorband, Jeffrey Winicour, D. Pollney, B´Ela Szilagyi
Maria Babiuc-Hamilton
We discuss results that have been obtained from the implementation of the initial round of testbeds for numerical relativity which was proposed in the first paper of the Apples with Apples Alliance. We present benchmark results for various codes which provide templates for analyzing the testbeds and to draw conclusions about various features of the codes. This allows us to sharpen the initial test specifications, design a new test and add theoretical insight.
Some Mathematical Problems In Numerical Relativity, Maria Babiuc-Hamilton, B´Ela Szilagyi, Jeffrey Winicour
Some Mathematical Problems In Numerical Relativity, Maria Babiuc-Hamilton, B´Ela Szilagyi, Jeffrey Winicour
Maria Babiuc-Hamilton
The main goal of numerical relativity is the long time simulation of highly nonlinear spacetimes that cannot be treated by perturbation theory. This involves analytic, computational and physical issues. At present, the major impasses to achieving global simulations of physical usefulness are of an analytic/ computational nature. We present here some examples of how analytic insight can lend useful guidance for the improvement of numerical approaches.
Binary Black Hole Waveform Extraction At Null Infinity, Maria Babiuc-Hamilton, Jeffrey Winicour, Yosef Zlochower
Binary Black Hole Waveform Extraction At Null Infinity, Maria Babiuc-Hamilton, Jeffrey Winicour, Yosef Zlochower
Maria Babiuc-Hamilton
In this paper, we present a work in progress toward an efficient and economical computational module which interfaces between Cauchy and characteristic evolution codes. Our goal is to provide a standardized waveform extraction tool for the numerical relativity community which will allow CCE to be readily applied to a generic Cauchy code. The tool provides a means of unambiguous comparison between the waveforms generated by evolution codes based upon different formulations of the Einstein equations and different numerical approximation.
Gravitational Wave Extraction Based On Cauchy–Characteristic Extraction And Characteristic Evolution, Maria Babiuc-Hamilton, Yosef Zlochower, Béla Szilágyi, Ian Hawke
Gravitational Wave Extraction Based On Cauchy–Characteristic Extraction And Characteristic Evolution, Maria Babiuc-Hamilton, Yosef Zlochower, Béla Szilágyi, Ian Hawke
Maria Babiuc-Hamilton
We implement a code to find the gravitational news at future null infinity by using data from a Cauchy code as boundary data for a characteristic code. This technique of Cauchy–characteristic extraction (CCE) allows for the unambiguous extraction of gravitational waves from numerical simulations. We first test the technique on non-radiative spacetimes: Minkowski spacetime, perturbations of Minkowski spacetime and static black hole spacetimes in various gauges. We show the convergence and limitations of the algorithm and illustrate its success in cases where other wave extraction methods fail. We further apply our techniques to a standard radiative test case for wave …
Testing Numerical Evolution With The Shifted Gauge Wave, Maria Babiuc-Hamilton, Jeffrey Winicour, B´Ela Szilágyi
Testing Numerical Evolution With The Shifted Gauge Wave, Maria Babiuc-Hamilton, Jeffrey Winicour, B´Ela Szilágyi
Maria Babiuc-Hamilton
Computational methods are essential to provide waveforms from coalescing black holes, which are expected to produce strong signals for the gravitational wave observatories being developed. Although partial simulations of the coalescence have been reported, scientifically useful waveforms have so far not been delivered. The goal of the AppleswithApples (AwA) Alliance is to design, coordinate and document standardized code tests for comparing numerical relativity codes. The first round of AwA tests has now been completed and the results are being analyzed. These initial tests are based upon the periodic boundary conditions designed to isolate performance of the main evolution code. Here …
Finite Difference Schemes For Second Order Systems Describing Black Holes, Mohammad Motamed, Maria Babiuc-Hamilton, B. Szilágyi, H-O. Kreiss, J. Winicour
Finite Difference Schemes For Second Order Systems Describing Black Holes, Mohammad Motamed, Maria Babiuc-Hamilton, B. Szilágyi, H-O. Kreiss, J. Winicour
Maria Babiuc-Hamilton
In the harmonic description of general relativity, the principal part of Einstein’s equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem.
Constraint-Preserving Sommerfeld Conditions For The Harmonic Einstein Equations, Maria Babiuc-Hamilton, H-O. Kreiss, Jeffrey Winicour
Constraint-Preserving Sommerfeld Conditions For The Harmonic Einstein Equations, Maria Babiuc-Hamilton, H-O. Kreiss, Jeffrey Winicour
Maria Babiuc-Hamilton
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of the Sommerfeld-type for such systems has recently been proposed. We implement these boundary conditions in a nonlinear 3D evolution code and test their accuracy.
Harmonic Initial-Boundary Evolution In General Relativity, Maria Babiuc-Hamilton, B´Ela Szil´Agyi, Jeffrey Winicour
Harmonic Initial-Boundary Evolution In General Relativity, Maria Babiuc-Hamilton, B´Ela Szil´Agyi, Jeffrey Winicour
Maria Babiuc-Hamilton
Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in harmonic coordinates. The resulting algorithm is implemented as a 3-dimensional numerical code which we demonstrate to provide stable, convergent Cauchy evolution in gauge wave and shifted gauge wave testbeds. Code performance is compared for Dirichlet, Neumann, and Sommerfeld boundary conditions and for boundary conditions which explicitly incorporate constraint preservation. The results are used to assess strategies for obtaining physically realistic boundary data by means of Cauchy-characteristic matching.