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authorjthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>2002-10-17 22:27:44 +0000
committerjthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>2002-10-17 22:27:44 +0000
commitf6d399914423ae47efcad3beb3c9ca6e2e96488f (patch)
tree4d1cad667a9c5e580c2de2b543ac2f9f17bee546 /doc
parent992b4ad347b6a9e861dc81bf651b64bef60325b3 (diff)
expand documentation to describe the multipatch system,
and add a figure illustrating this git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@847 f88db872-0e4f-0410-b76b-b9085cfa78c5
Diffstat (limited to 'doc')
-rw-r--r--doc/3patch.gnuplot52
-rw-r--r--doc/3patch.par50
-rw-r--r--doc/AEIDevelopment_AHFinderDirect_3patch.eps1723
-rw-r--r--doc/documentation.tex79
-rw-r--r--doc/makefile28
5 files changed, 1920 insertions, 12 deletions
diff --git a/doc/3patch.gnuplot b/doc/3patch.gnuplot
new file mode 100644
index 0000000..dc7ec05
--- /dev/null
+++ b/doc/3patch.gnuplot
@@ -0,0 +1,52 @@
+# gnuplot command file to produce postscript file for 3patch figure
+
+set term postscript eps color solid
+set size 1.5, 2.25
+set output 'AEIDevelopment_AHFinderDirect_3patch.eps'
+
+unset key
+set view 60, 111
+set border 0
+
+unset xtics
+unset ytics
+unset ztics
+
+splot '-' w lines -1, \
+ '-' w lines -1, \
+ '-' w lines -1, \
+ '<../src/misc/select.patch +z <3patch.h.t0.ah1.gp' \
+ using 4:5:6 w lines 1, \
+ '<../src/misc/select.patch +x <3patch.h.t0.ah1.gp' \
+ using 4:5:6 w lines 2, \
+ '<../src/misc/select.patch +y <3patch.h.t0.ah1.gp' \
+ using 4:5:6 w lines 3, \
+ "<../src/misc/select.patch +z <3patch.h.t0.ah1.gp \
+ | gawk '($4 == 0) && ($5 >= 0.0)' -" \
+ using 4:5:6 w lines -1, \
+ "<../src/misc/select.patch +z <3patch.h.t0.ah1.gp \
+ | gawk '($4 >= 0) && ($5 == 0.0)' -" \
+ using 4:5:6 w lines -1, \
+ "<../src/misc/select.patch +x <3patch.h.t0.ah1.gp \
+ | gawk '($5 == 0) && ($6 >= 0.0)' -" \
+ using 4:5:6 w lines -1, \
+ "<../src/misc/select.patch +x <3patch.h.t0.ah1.gp \
+ | gawk '($5 >= 0) && ($6 == 0.0)' -" \
+ using 4:5:6 w lines -1, \
+ "<../src/misc/select.patch +y <3patch.h.t0.ah1.gp \
+ | gawk '($4 == 0) && ($6 >= 0.0)' -" \
+ using 4:5:6 w lines -1, \
+ "<../src/misc/select.patch +y <3patch.h.t0.ah1.gp \
+ | gawk '($4 >= 0) && ($6 == 0.0)' -" \
+ using 4:5:6 w lines -1
+0.0 0.0 0.0
+1.3 0.0 0.0
+eof
+0.0 0.0 0.0
+0.0 1.3 0.0
+eof
+0.0 0.0 0.0
+0.0 0.0 1.3
+eof
+
+set output
diff --git a/doc/3patch.par b/doc/3patch.par
new file mode 100644
index 0000000..7905a3e
--- /dev/null
+++ b/doc/3patch.par
@@ -0,0 +1,50 @@
+# par file to write out data used to produce 3patch figure
+
+ActiveThorns = "CartGrid3D LocalInterp PUGH ADMBase ADMCoupling StaticConformal CoordGauge Exact AHFinderDirect"
+
+# PUGH
+Driver::ghost_size = 0
+Driver::global_nx = 31
+Driver::global_ny = 31
+Driver::global_nz = 31
+
+# CartGrid3D
+Grid::domain = "full"
+Grid::type = "byspacing"
+Grid::dxyz = 0.1
+Grid::xyzmin = -3.0
+Grid::xyzmax = 3.0
+
+# initial data only
+cactus::cctk_itlast = 0
+
+# ADMBase
+ADMBase::initial_lapse = "exact"
+ADMBase::initial_shift = "exact"
+ADMBase::initial_data = "exact"
+ADMBase::lapse_evolution_method = "static"
+ADMBase::shift_evolution_method = "static"
+ADMBase::metric_type = "physical"
+
+# Exact
+Exact::exact_model = "Schwarzschild/EF"
+Exact::Schwarzschild_EF__mass = 1.0
+
+AHFinderDirect::find_AHs_at_poststep = "false" # initial data only
+AHFinderDirect::method = "horizon function" # just evaluate H(h) function
+AHFinderDirect::output_ghost_zones_for_h = "true"
+AHFinderDirect::h_base_file_name = "3patch.h"
+
+AHFinderDirect::patch_system_type = "+xyz octant"
+AHFinderDirect::delta_drho_dsigma = 4.5
+
+AHFinderDirect::N_horizons = 1
+AHFinderDirect::origin_x[1] = 0.0
+AHFinderDirect::origin_y[1] = 0.0
+AHFinderDirect::origin_z[1] = 0.0
+
+AHFinderDirect::initial_guess_method = "coordinate sphere"
+AHFinderDirect::initial_guess__coord_sphere__x_center[1] = 0.0
+AHFinderDirect::initial_guess__coord_sphere__y_center[1] = 0.0
+AHFinderDirect::initial_guess__coord_sphere__z_center[1] = 0.0
+AHFinderDirect::initial_guess__coord_sphere__radius[1] = 1.0
diff --git a/doc/AEIDevelopment_AHFinderDirect_3patch.eps b/doc/AEIDevelopment_AHFinderDirect_3patch.eps
new file mode 100644
index 0000000..be02964
--- /dev/null
+++ b/doc/AEIDevelopment_AHFinderDirect_3patch.eps
@@ -0,0 +1,1723 @@
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+%%Trailer
+%%DocumentFonts: Helvetica
diff --git a/doc/documentation.tex b/doc/documentation.tex
index c2a888f..68fcbe2 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -201,11 +201,6 @@ equations for $h$ at the angular grid points, and solve this system
of equations by a global Newton's method (or a variant with improved
convergence).
-I use a multiple grid patch system to cover $S^2$ without coordinate
-singularities. In general there are 6~patches, one each covering a
-neighborhood of the $\pm z$, $\pm x$, and $\pm y$ axes, but if the slice
-has suitable symmetries, this may be reduced to 5, 4, or 3~patches.
-
Computationally, this algorithm has 3 main parts:
\begin{itemize}
\item Computation of the ``horizon function'' $H(h)$ given a trial
@@ -233,6 +228,70 @@ Computationally, this algorithm has 3 main parts:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{The Multipatch System}
+
+Perhaps the most unusual feature of \thorn{AHFinderDirect} is the
+``multipatch'' system used to cover $S^2$ without coordinate singularities.
+In general there are 6~patches, one each covering a neighborhood of
+the $\pm z$, $\pm x$, and $\pm y$ axes, but this may be reduced in
+the presence of suitable symmetries. For example,
+figure~\ref{AEIDevelopment_AHFinderDirect_fig-3patch}
+on page~\pageref{AEIDevelopment_AHFinderDirect_fig-3patch} shows a system
+of 3~patches covering the $+xyz$~octant of $S^2$. This would be
+suitable for finding an apparent horizon with mirror symmetry about
+the (local) $z=0$~plane, and either 90~degree periodic rotation symmetry
+about the (local) $z$~axis, or mirror symmetry about each of the (local)
+$x$~and $y$~axes.
+
+\begin{figure}[htbp]
+\begin{center}
+\includegraphics{AEIDevelopment_AHFinderDirect_3patch.eps}
+\end{center}
+\caption[Illustration of the Multipatch System]
+ {
+ This figure shows a multipatch system covering the
+ $(+,+,+)$~octant of the unit sphere~$S^2$ with 3~patches.
+ The angular resolution is 5~degrees. Notice that the
+ patches overlap by several ``ghost zone'' grid points.
+ }
+\label{AEIDevelopment_AHFinderDirect_fig-3patch}
+\end{figure}
+
+To allow easy angular finite differencing within the patch system,
+each patch is extended beyond its nominal extent by a ``ghost zone''%%%
+\footnote{%%%
+ Note that this terminology differs somewhat
+ from that used by Cactus in general; Cactus
+ would call these ``patch zones'' or ``symmetry
+ zones''.
+ }%%%
+{} (2~grid points wide in
+figure~\ref{AEIDevelopment_AHFinderDirect_fig-3patch}). Angular grid
+function values in the ghost zone can be obtained by interpatch
+interpolation%%%
+\footnote{%%%
+ Due to the way the patch coordinates are defined,
+ adjacent patches always share a common ``perpendicular''
+ angular coordinate, so only 1-D interpolation
+ is needed here.
+ }%%%
+{} or by applying symmetry operations. Once this is done, then angular
+finite differencing within the nominal extent of each patch can proceed
+normally, ignoring the patch boundaries. \thorn{AHFinderDirect} can
+be configured at compile time to use either 2nd~order or 4th~order
+angular finite differencing (3~point or 5~point angular molecules);
+the default is 4th~order (5~point). See \verb|src/include/config.h|
+if you want to change this.
+
+By default \thorn{AHFinderDirect} will automagically choose a patch
+system type for each apparent horizon searched for, based on the local
+coordinate origin and the symmetries implicit in the Cactus grid type.
+This generally works well, but if desired you can instead manually
+specify the patch system type, the angular resolution, the width of
+the ghost zones, etc. See the \verb|param.ccl| file for details.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
\section{Using \thorn{AHFinderDirect}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -664,7 +723,7 @@ parameters controlling if and how these should be written to data files:
apparent horizon number
\item the second \verb|%s| is the
file name extension, which defaults to
- \verb|gnuplot| (see the \verb|param.ccl|
+ \verb|"gp"| (see the \verb|param.ccl|
file if you want to change this)
\end{itemize}
\item Comment lines begin with \verb|#|.
@@ -711,9 +770,9 @@ parameters controlling if and how these should be written to data files:
described above.
\end{description}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Accuracy and Diagnostics}
+\section{Accuracy and Diagnostics}
The apparent horizon positions are typically computed very accurately;
tests on Kerr spacetimes give typical errors of $10^{-4}m$ to $10^{-5}m$.
@@ -754,8 +813,8 @@ tests. The \verb|Kerr-tiny.par| parameter file is close to a minimal
# to the black hole, to make this a non-trivial test for the apparent
# horizon finder.
#
-# This parameter is "tiny" in the sense that it sets only a small number
-# of AHFinderDirect parameters.
+# This parameter file is "tiny" in the sense that it sets only a
+# small number of AHFinderDirect parameters.
# next two lines is actually one long line
# (Cactus doesn't seem to grok \-newline continuation here :( :( )
diff --git a/doc/makefile b/doc/makefile
index 4592087..ab8680c 100644
--- a/doc/makefile
+++ b/doc/makefile
@@ -1,12 +1,18 @@
# Makefile for documentation
-# $Header: /usr/local/svn/cvs-repositories/numrelcvs/AEIThorns/AHFinderDirect/doc/makefile,v 1.2 2002-09-16 18:08:06 jthorn Exp $
+# $Header: /usr/local/svn/cvs-repositories/numrelcvs/AEIThorns/AHFinderDirect/doc/makefile,v 1.3 2002-10-17 22:27:44 jthorn Exp $
#
-# Targets:
+# ***** main targets *****
# default latex & dvips everything
# bib bibtex everything
# clean remove all machine-generated files
#
+# ***** targets for rebuilding figures in the thorn guide *****
+# 3patch-cactus run Cactus to generate the data file for the
+# 3patch figure
+# 3patch-gnuplot run gnuplot to generate the postscript file
+# for the 3patch figure
+#
#
# Note this Makefile always re-TeXs things, even if the .tex files
@@ -17,6 +23,10 @@
###############################################################################
+#
+# ***** main targets *****
+#
+
.PHONY : default
default : ps
@@ -35,3 +45,17 @@ bib :
.PHONY : clean
clean :
-rm *.dvi *.ps *.aux *.bbl *.log *.blg
+
+###############################################################################
+
+#
+# ***** targets for rebuilding figures in the thorn guide *****
+#
+
+.PHONY : 3patch-cactus
+3patch-cactus :
+ cactus_test-ahfinderdirect 3patch.par 2>&1 | tee 3patch.log
+
+.PHONY : 3patch-gnuplot
+3patch-gnuplot :
+ gnuplot 3patch.gnuplot
generated by cgit v1.2.3 (git 2.39.1) at 2024-07-12 21:32:21 +0000