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Diffstat (limited to 'doc/documentation.tex')
| -rw-r--r-- | doc/documentation.tex | 22 |
1 files changed, 4 insertions, 18 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex index 3d74028..edf9b49 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -212,24 +212,10 @@ necessary in order for \thorn{AHFinderDirect} to work: singularity in the geometry somewhere near the apparent horizon, then you need to have a high enough Cactus 3-D grid resolution that the geometry interpolation doesn't ``see'' - the singularity. For example, the initial data parameters - \begin{verbatim} - ADMBase::initial_data = "misner_bh" - IDAnalyticBH::mu = 2.0 - ADMBase::initial_lapse = "Cadez" - \end{verbatim} - specify Misner data with $\mu=2$, using the \v{C}ade\v{z} - slicing. This geometry has a singularity at $z = \pm 1$ - on the $z$~axis. With \verb|grid::dxyz = 0.040| or smaller, - \thorn{AHFinderDirect} has no problems finding the apparent - horizons (which have centroid $z = \pm 1.03077$ and radia - roughtly 0.28), but with \verb|grid::dxyz = 0.050| or larger, - \thorn{AHFinderDirect} fails to find the horizon after finding - \verb|NaN| and infinity values in the interpolated geometry - close to the pole. Another failure mode which - \thorn{AHFinderDirect} may report in such a situation - (where the Cactus 3-D grid resolution is too low) is that - the interpolated $g_{ij}$ fails to be positive definite. + the singularity. (If \thorn{AHFinderDirect} ``sees'' the + singularity, it may ``just'' fail to find the horizon, + and/or it may report that the interpolated $g_{ij}$ fails + to be positive definite or even contains NaNs.) \item At the moment \thorn{AHFinderDirect} and the Cactus interpolators don't know how to avoid an excised region, so if the apparent horizon (or any trial horizon surface as the algorithm is iterating |