standardize terminology: $\Theta$ = expansion of trial surface

(a long time ago I used $H$, and I missed a few places when I switched)


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1408 f88db872-0e4f-0410-b76b-b9085cfa78c5

1 files changed, 9 insertions, 9 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
index 9bace6c..5c6551f 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -153,7 +153,7 @@ There may be several such surfaces, some nested inside others; an
 In terms of the usual $3+1$ variables, an apparent horizon satisfies
 the equation
 \begin{equation}
-H \equiv \del_i n^i + K_\ij n^i n^j - K = 0
+\Theta \equiv \del_i n^i + K_\ij n^i n^j - K = 0
 					\label{AHFinderDirect/eqn-horizon}
 \end{equation}
 where $n^i$ is the outward-pointing unit normal to the apparent horizon,
@@ -446,8 +446,8 @@ section~\ref{AHFinderDirect/sect-examples} should make this clear.
 	\item[\code{"algorithm highlights"}]
 	\mbox{}\\
 		Also print a single line for each Newton iteration giving
-		the 2-norm and $\infty$-norm of the $H(h)$ function defined
-		by equation~\eqref{AHFinderDirect/eqn-horizon}.
+		the 2-norm and $\infty$-norm of the $\Theta(h)$ function
+		defined by equation~\eqref{AHFinderDirect/eqn-horizon}.
 		This is the default.
 	\item[\code{"algorithm details"}]
 	\mbox{}\\
@@ -1639,7 +1639,7 @@ improved convergence).
 
 Computationally, this algorithm has 3 main parts:
 \begin{itemize}
-\item	Computation of the ``horizon function'' $H(h)$ given a trial
+\item	Computation of the ``horizon function'' $\Theta(h)$ 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
@@ -1647,8 +1647,8 @@ Computationally, this algorithm has 3 main parts:
 	$\partial_k g_\ij$ 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
+\item	Computation of the Jacobian matrix $\Jac[\Theta(h)]$ of $\Theta(h)$.
+	This thorn incorporates the \defn{symbolic differentiation} technique
 	described in
 \cite{AEIThorns/AHFinderDirect/Thornburg-1996-apparent-horizon-finding},
 	so this computation is quite fast.  The Jacobian is a highly
@@ -1656,9 +1656,9 @@ Computationally, this algorithm has 3 main parts:
 	as either a dense matrix (for debugging purposes), or a sparse
 	matrix (the default).  Which option is used is determined by
 	a compile-time configuration in \verb|src/include/config.h|.
-\item	Solving the nonlinear equations $H(h) = 0$ by a global Newton's
-	method or a variant.  How this is done depends on how the Jacobian
-	is stored.  At present,
+\item	Solving the nonlinear equations $\Theta(h) = 0$ by a global
+	Newton's method or a variant.  How this is done depends on how
+	the Jacobian is stored.  At present,
 	\begin{itemize}
 	\item	If \thorn{AHFinderDirect} is configured to store the
 		Jacobian as a dense matrix, then LAPACK is used to solve