[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 286)

[ian.hinder at aei.mpg.de]

User: hinder
Date: 2012/03/12 10:57 AM

Modified:
 /
  ET.tex

Log:
 ET.tex: Rework discussion of NRAR error criteria according to referee comments

File Changes:

Directory: /
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File [modified]: ET.tex
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--- ET.tex	2012-03-12 15:56:23 UTC (rev 285)
+++ ET.tex	2012-03-12 15:57:39 UTC (rev 286)
@@ -2728,18 +2728,22 @@
 %seems to be the one corresponding to an $8$-th order accurate finite 
 %difference approximation.
 We also indicate on both plots the time at which the gravitational
-wave frequency reaches $\omega=0.2/\mathrm{M}$. We follow a community standard, agreed 
-to over the course of the NRAR\cite{NRAR:web} collaboration, that constrains
-the numerical resolution so that the accumulated phase error is not
-larger than $0.05$ radians at a gravitational wave frequency of
-$\omega=0.2/\mathrm{M}$. From the plot, we assert that the phase error between the 
-higher and high resolutions and the one between high and medium-high
-resolutions satisfies this criterion, while the phase error between 
-the medium-high and medium resolutions barely satisfies the criterion; and the
-one between medium and low resolutions does not. We conclude then
-that the three highest resolution runs do have sufficient resolution
-to extract waveforms for use in the construction of analytic waveform 
-templates. 
+wave frequency reaches $\omega=0.2/\mathrm{M}$.  This reference time
+has been suggested, for example in the NRAR\cite{NRAR:web}
+collaboration, as a useful point at which errors can be compared
+between codes.  The suggestion is that the accumulated phase error
+should not be larger than $0.05$ radians at this reference time, and
+that this is roughly the scale of accuracy which might be useful for
+comparisons with analytic approximation methods. From the plot, we
+assert that the phase difference between the higher and high
+resolutions and the one between high and medium-high resolutions
+satisfies this criterion, while the phase difference between the
+medium-high and medium resolutions barely satisfies the criterion; and
+the one between medium and low resolutions does not. We conclude then
+that the three highest resolution runs do have the suggested accuracy.
+While the waveform shown here is too short for comparison with
+analytic methods, we illustrate here that these sorts of comparisons
+can be made using the toolkit.
 
 \begin{figure}
         \includegraphics[width=0.45\textwidth]{tracks}