change so that only processor #0 writes data files

(other processors still do all the computations, but writes are supressed)


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@922 f88db872-0e4f-0410-b76b-b9085cfa78c5

1 files changed, 36 insertions, 11 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
index d6d8a20..e03538e 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -270,10 +270,20 @@ here's what works and what doesn't:
 	are only provided by the thorns \thorn{PUGHInterp} and
 	\thorn{LocalInterp} respectively, so you need to have
 	these thorns compiled into your configuration and activated.
-\item	Even though it uses the new global interpolation API,
-	at present \thorn{AHFinderDirect} doesn't work properly
-	for multi-processor Cactus runs.
-	I hope to properly support multi-processor operation soon.
+\item	\thorn{AHFinderDirect} works in multi-processor Cactus runs,
+	but at present it's quite inefficient for large numbers of
+	processors.  (It exhibits ``anti-scaling'' with the number
+	of processors: the run time gets {\em larger\/} as the number
+	of processors increases.)%%%
+\footnote{%%%
+	 The run time on $N$ processors should be roughly
+	 $\alpha + \beta N$ for some (positive!) constants
+	 $\alpha$ and $\beta$.  I estimate the value of $N$
+	 for which the run time is twice the single-processor
+	 value, to be on the order of 10 to 20 for the current
+	 implementation.%%%
+	 }%%%
+{}	I hope to fix this inefficiency soon.
 \end{itemize}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -885,12 +895,26 @@ 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 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 solely on $S^2$ (\ie{} at the horizon-surface grid points).
+	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
+	(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
+	solely on $S^2$ (\ie{} at the horizon-surface grid points).
 \item	Computation of the Jacobian matrix $\Jac[H(h)]$ of $H(h)$.  This
 	thorn incorporates the \defn{symbolic differentiation} technique
 	described in
@@ -998,7 +1022,8 @@ interested in some other related thorns:
 \section{Acknowledgments}
 
 I thank Ian Hawke, Peter Diener, and Erik Schnetter for many valuable
-conversations, and the whole Cactus crew for a great infrastructure!
+conversations, to Thomas Radke for his work on the new interpolators,
+and the whole Cactus crew for a great infrastructure!
 I thank the Alexander von Humboldt foundation and the AEI visitors'
 and postdoctoral fellowships programs for financial support.