[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 177)

jfaber at einsteintoolkit.org jfaber at einsteintoolkit.org
Mon Nov 7 22:25:04 CST 2011


User: jfaber
Date: 2011/11/07 10:25 PM

Modified:
 /
  ET.tex

Log:
 Beginning editing the Examples section.

File Changes:

Directory: /
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File [modified]: ET.tex
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--- ET.tex	2011-11-08 03:40:35 UTC (rev 176)
+++ ET.tex	2011-11-08 04:25:03 UTC (rev 177)
@@ -2282,44 +2282,45 @@
 To demonstrate the properties of the code and its capabilities, we have used it to simulate common astrophysical configurations of interest.  Given the community-oriented direction of the project, the parameter files required to launch these simulations and a host of others are included and documented in the code releases, along with the datafiles produced by a representative set of simulation parameters to allow for code validation and confirmation of correct code performance on new platforms and architetures.  As part of the internal validation process, 
 nightly builds are checked against a set of benchmarks to ensure that consistent results are generated with the inclusion of all new commits to the code.
 
+The performance of the Toolkit for vacuum configurations is demonstrated through evolutions of single, rotating BHs and the merger of binary black hole configurations (sections~\ref{sec:1bh-example} and \ref{sec:bbh-example}, respectively).   Linear oscillations about equilibirum for an isolated NS are discussed in section~\ref{sec:tov_oscillations}, and the collapse of a NS to a BH, including dynamical formation of a horizon, in section~\ref{sec:collapse_example}.  Finally, to show a less traditional application of the code, we show its ability to perform cosmological simulations by evolving a Kasner spacetime (see section~\ref{sec:cosmology}).
 \subsection{Spinning BH\pages{2 Peter}}
+\label{sec:1bh-example}
 As a first example we perform simulations of a single distorted rotating BH. 
 We use \codename{TwoPunctures} to set up initial data for a single 
 puncture of mass $M_{\mathrm{bh}}=1$ and dimensionless spin parameter 
 $a = S_{\mathrm{bh}}/M_{\mathrm{bh}}^2 = 0.7$. Evolution of the data is 
 performed by \codename{McLachlan}, apparent horizon finding by 
-\codename{AHFinderDirect}, gravitational wave extraction by 
+\codename{AHFinderDirect}, and gravitational wave extraction by 
 \codename{WeylScal4} and \codename{Multipole}. Additional analysis of the
-horizons is done by \codename{QuasiLocalMeasures}. The runs where performed
-using fixed mesh refinement provided by \codename{Carpet} using 8 levels
+horizons is done by \codename{QuasiLocalMeasures}. The runs were performed
+with fixed mesh refinement provided by \codename{Carpet}, using 8 levels
 of refinement on a quadrant grid (symmetries provided by 
 \codename{ReflectionSymmetry} and \codename{RotatingSymmetry180}). The outer
-boundaries where placed at $R=256M$. We performed runs at 3 different
-resolutions. The low resolution was $0.024M (3.072M)$, medium was 
-$0.016M (2.048M)$ and high was $0.012M (1.536M)$ where the first number is the
-resolution on the finest grid and the second number in parenthesis is the
-resolution on the coarsest grid. The runs where performed using the tapering
-evolution scheme in \codename{Carpet} in order to avoid interpolation in
+boundaries were placed at $R=256M$. We performed runs at 3 different
+resolutions: the low resolution was $0.024M (3.072M)$, medium was 
+$0.016M (2.048M)$ and high was $0.012M (1.536M)$, where the numbers refer to the 
+resolution on the finest (coarsest) grid. The runs where performed using the tapering
+evolution scheme in \codename{Carpet} to avoid interpolation in
 time during prolongation. The initial data corresponds to a rotating BH
-perturbed by a Brill wave and as such has a non-zero
-gravitational wave content. We evolved using 4th order finite differencing from
-$T=0M$ until the BH had settled down to a stationary state at $T=120M$.
+perturbed by a Brill wave and, as such, has a non-zero
+gravitational wave content. We evolved the BH using 4th-order finite differencing from
+$T=0M$ until it had settled down to a stationary state at $T=120M$.
 
 Figure~\ref{fig:kerr_waves} shows the $\ell =2, m=0$ mode of $r\Psi_4$ 
-extracted at $R=30M$ and its convergence.
+extracted at $R=30M$, and its numerical convergence.
 \begin{figure}
  \includegraphics[width=0.33\textwidth,angle=-90]{examples/kerr/figs/waves}
  \includegraphics[width=0.33\textwidth,angle=-90]{examples/kerr/figs/waves_conv}
- \caption{The right plot shows the extracted $\ell =2, m=0$ mode of $\Psi_4$
-          as function of time from the high resolution run. The extraction was
+ \caption{The extracted $\ell =2, m=0$ mode of $\Psi_4$
+          as function of time from the high resolution run (left plot). The extraction was
           done at $R=30M$. Shown is both the real (solid red curve) and the
-          imaginary (dashed green curve) part of the waveform. The left plot
-          shows for the real part of the $\ell =2, m=0$ waveforms the
+          imaginary (dashed green curve) part of the waveform. On the right, we
+          show the
           difference between the medium and low resolution runs (solid red
-          curve), the difference between the high and medium resolution runs
-          (long dashed green curve) as well as the scaled (for 4th order
-          convergence) difference between the medium and low resolution runs
-          (short dashed blue curve).}
+          curve), between the high and medium resolution runs
+          (long dashed green curve), and the scaled difference (for 4th order
+          convergence) between the medium and low resolution runs
+          (short dashed blue curve) for the real part of the $\ell =2, m=0$ waveforms.}
  \label{fig:kerr_waves}
 \end{figure}
 In the left plot the red (solid) curve is the real part and the green (dashed)
@@ -2635,7 +2636,7 @@
 \end{figure}
 
 \subsection{Linear oscillations of TOV stars\pages{2 Frank}}
-\label{sec:tov_oscilations}
+\label{sec:tov_oscillations}
 The examples in the previous subsections did not include the evolution of
 matter within a relativistic spacetime. One interesting test of a coupled
 matter-spacetime evolution is to measure the eigenfrequencies of a stable TOV
@@ -2737,6 +2738,7 @@
 \end{figure}
 
 \subsection{Collapse\pages{2 Christian, Roland}}
+\label{sec:collapse_example}
 The previous examples dealt either with a preexisting black hole (BBH) or
 with a smooth singularity free spacetime (TOV oscillations).  The evolution
 codes in the toolkit however are
@@ -2822,7 +2824,7 @@
 factor.
 
 
-\subsection{Cosmology}
+\subsection{Cosmology}\label{sec:cosmology}
 The Einstein Toolkit is not only designed to evolve compact-object
 spacetimes, but it is also capable of solving the initial-value
 problem for spacetimes with radically different topology and global



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