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authorjthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>2003-07-02 12:59:12 +0000
committerjthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>2003-07-02 12:59:12 +0000
commitd7f5fbc854cf5201fa661b14e5e46de1076079bc (patch)
treed19d7d4589e9b8b28eaafa9edd5f5be6013d2561 /doc
parenta0c39be5f84c2c404f3dc28e8c461f0f3f71cb32 (diff)
change arrangement from AEIDevelopment to AEIThorns
git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1112 f88db872-0e4f-0410-b76b-b9085cfa78c5
Diffstat (limited to 'doc')
-rw-r--r--doc/documentation.tex40
1 files changed, 16 insertions, 24 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex
index 33397dc..259df19 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -156,7 +156,7 @@ H \equiv \del_i n^i + K_\ij n^i n^j - K = 0
where $n^i$ is the outward-pointing unit normal to the apparent horizon,
and $\del_i$ is the covariant derivative operator associated with the
3-metric $g_\ij$ in the slice.
-(See \cite{AEIDevelopment_AHFinderDirect_York-1989-in-Frontiers} for a
+(See \cite{AEIThorns/AHFinderDirect/York-1989-in-Frontiers} for a
derivation of equation~\eqref{AHFinderDirect/eqn-horizon}.)
Thorn~\thorn{AHFinderDirect} finds an apparent horizon by numerically
@@ -169,6 +169,10 @@ number of points on the apparent horizon, together with some auxiliary
information like the apparent horizon area and centroid position, and
the irreducable mass associated with the area.
+Besides this thorn guide, the other main sources of information on
+\thorn{AHFinderDirect} are the comments in the \verb|param.ccl| file,
+and the paper \cite{AEIThorns/AHFinderDirect/Thornburg2003:AH-finding}.
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{What \thorn{AHFinderDirect} Needs}
@@ -225,7 +229,7 @@ necessary in order for \thorn{AHFinderDirect} to work:
(literally ``ray body'', or more commonly ``star-shaped region'')
relative to some local coordinate origin (which you must specify).
A Strahlk\"{o}rper is defined by Minkowski
-(\cite[p.~108]{AEIDevelopment_AHFinderDirect_Schroeder-1986-number-theory})
+(\cite[p.~108]{AEIThorns/AHFinderDirect/Schroeder-1986-number-theory})
as
\begin{quote}
a region in $n$-dimensional Euclidean space containing the
@@ -1072,7 +1076,7 @@ in Kerr-Schild coordinates,
$m_\text{irreducible}/m_\text{ADM} = 0.949$, $0.894$, and $0.723$
for spin parameters $a \equiv J/m^2 = 0.6$, $0.8$, and $0.999$, respectively.
It would be better to (also) use the ``isolated horizons'' formalism of
-\cite{AEIDevelopment_AHFinderDirect_Dreyer-etal-2002-isolated-horizons};
+\cite{AEIThorns/AHFinderDirect/Dreyer-etal-2002-isolated-horizons};
at some point this thorn may be enhanced to do this.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -1152,7 +1156,7 @@ AHFinderDirect::initial_guess__coord_sphere__radius[1] = 2.0
\thorn{AHFinderDirect} uses the apparent horizon (henceforth \defn{horizon})
finding algorithm of
-\cite{AEIDevelopment_AHFinderDirect_Thornburg-1996-apparent-horizon-finding},
+\cite{AEIThorns/AHFinderDirect/Thornburg-1996-apparent-horizon-finding},
modified slightly to work with $g_\ij$ and $K_\ij$ on a Cartesian ($xyz$)
grid:
@@ -1173,22 +1177,8 @@ Computationally, this algorithm has 3 main parts:
\begin{itemize}
\item Computation of the ``horizon function'' $H(h)$ given a trial
surface defined by a trial horizon shape function $h$. This is
- done by interpolating%%%
-\footnote{%%%
- It's this interpolation that causes the multiprocessor
- slowdown with the present implementation -- each
- processor asks for the same set of interpolation
- points, so for $N$ processors the interpolator
- has to do $N$ times as much work. Unfortunately,
- the (global) interpolator must be called synchronously
- on all processors, so fixing this inefficiency
- requires a nontrivial interprocessor synchronization
- at each iteration of the Newton iteration (to ensure
- that all processors make the same number of Newton
- iterations).%%%
- }%%%
-{} the Cactus geometry fields $g_\ij$ and $K_\ij$
- (and optionally $\psi$) from the 3-D $xyz$ grid to the
+ done by interpolating the Cactus geometry fields $g_\ij$ and
+ $K_\ij$ (and optionally $\psi$) from the 3-D $xyz$ grid to the
(2-D set of) trial-horizon-surface grid points (also computing
$\partial_k g_\ij$ in the interpolation process), then doing
all further computations with angular grid functions defined
@@ -1196,7 +1186,7 @@ Computationally, this algorithm has 3 main parts:
\item Computation of the Jacobian matrix $\Jac[H(h)]$ of $H(h)$. This
thorn incorporates the \defn{symbolic differentiation} technique
described in
-\cite{AEIDevelopment_AHFinderDirect_Thornburg-1996-apparent-horizon-finding},
+\cite{AEIThorns/AHFinderDirect/Thornburg-1996-apparent-horizon-finding},
so this computation is quite fast. The Jacobian is a highly
sparse matrix; \thorn{AHFinderDirect} has code to store it
as either a dense matrix (for debugging purposes), or a sparse
@@ -1292,17 +1282,19 @@ interested in some other related thorns:
\begin{description}
\item[\thorn{EHFinder}] (in the \arrangement{AEIDevelopment} arrangement)
was written by Peter Diener, and finds the {\em event\/} horizon(s)
- in a numerically computed spacetime.
+ in a numerically computed spacetime. It's described in detail in
+ the paper~\cite{AEIThorns/AHFinderDirect/Diener03a}.
\item[\thorn{AHFinder}] (in the \arrangement{CactusEinstein} arrangement)
was written by Miguel Alcubierre, and includes two different
algorithms for finding apparent horizons, a minimization method
and a ``fast flow'' method based on
-\cite{AEIDevelopment_AHFinderDirect_Gundlach-1998-apparent-horizon-finding}.
+\cite{AEIThorns/AHFinderDirect/Gundlach-1998-apparent-horizon-finding}.
Unfortunately, both methods are very slow in practice.
\item[\thorn{TGRapparentHorizon2D}] (in the \arrangement{TAT} arrangement)
was written by Erik Schnetter, and is another apparent horizon
finder. It uses methods very similar to this thorn, and (like
- this thorn) is very fast and accurate.
+ this thorn) is very fast and accurate. It's described in detail
+ in the paper~\cite{AEIThorns/AHFinderDirect/Schnetter02a}.
\end{description}
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