diff options
author | jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5> | 2003-07-02 12:59:12 +0000 |
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committer | jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5> | 2003-07-02 12:59:12 +0000 |
commit | d7f5fbc854cf5201fa661b14e5e46de1076079bc (patch) | |
tree | d19d7d4589e9b8b28eaafa9edd5f5be6013d2561 /doc | |
parent | a0c39be5f84c2c404f3dc28e8c461f0f3f71cb32 (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.tex | 40 |
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} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |