default is now order=2 for geometry interpolation;

desribe this and the tradeoffs for this vs order=3


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1179 f88db872-0e4f-0410-b76b-b9085cfa78c5

1 files changed, 16 insertions, 15 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
index 87a307a..ca62035 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -1121,28 +1121,29 @@ each time that apparent horizon is found:
      \end{tabular}
      ]
 \mbox{}\\
-	These parameters control the (3-D) \\defn{geometry interpolation}
+	These parameters control the (3-D) \defn{geometry interpolation}
 	of the spacetime geometry ($g_{ij}$ and $K_{ij}$, or their
 	\thorn{StaticConformal} equivalents) to the apparent horizon
-	position.  The defaults are set to use a cubic Hermite
-	interpolator.  This works well, but because of the interpolator
-	molecule size you must use $\verb|driver::ghost_size| \ge 3$.
-	If you want to use a smaller value of \verb|driver::ghost_size|
-	you need to use a geometry interpolator with a smaller molecule
-	size.  In particular, to use $\verb|driver::ghost_size| = 2$
-	you should use
+	position.  The defaults are set to use a quadratic Hermite
+	interpolator.  This works fairly well, but because of the interpolator
+	molecule size you must use $\verb|driver::ghost_size| \ge 2$.
+
+	If you want to get very high accuracy from \thorn{AHFinderDirect},
+	then you should use a cubic Hermite geometry interpolator, by
+	setting
 	\begin{verbatim}
 	AHFinderDirect::geometry_interpolator_pars = \
- "order=2 \
+ "order=3 \
   boundary_off_centering_tolerance={1.0e-10 1.0e-10 1.0e-10 1.0e-10 1.0e-10 1.0e-10} \
   boundary_extrapolation_tolerance={0.0 0.0 0.0 0.0 0.0 0.0}"
 	\end{verbatim}
-	\thorn{AHFinderDirect} should still work well with these
-	parameters; it will run about 2~to 3~times faster, but the
-	lower geometry-interpolation order will degrade the accuracy
-	by (very roughly) a factor of~10 (which isn't a problem in practice).
-	The sample parameter file \verb|par/misner-ghost2-mask-noshrink.par|
-	shows an example of using these parameters.
+	Assuming perfectly accurate geometry variables in the 3-D Cactus grid,
+	this will make \thorn{AHFinderDirect} (very) roughly an order
+	of magnitude more accurate.  However, the larger molecule size
+	will make it about a factor of 2--3~slower, and will also require
+	that you set $\verb|driver::ghost_size| \ge 3$.
+	The sample parameter file \verb|par/Kerr-order3.par|
+	shows an example of this.
 
 \item[\code{N\_zones\_per\_right\_angle[}$n$\code{]}]
 \mbox{}\\