Lots of tidying changes, parameter names have changed but hopefully clearer now.

Few more documentation changes still to come

Constructing 3D data doesn't work, but this was also true before Einstein2 changes.


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinInitialData/IDBrillData/trunk@80 a678b1cf-93e1-4b43-a69d-d43939e66649

1 files changed, 43 insertions, 36 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
index 49731f9..a17be7a 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -3,13 +3,13 @@
 \begin{document}
 
 \title{IDBrillData}
-\author{Carsten Gundlach}
-\date{6 September 1999}
+\author{Carsten Gundlach, Gabrielle Allen}
+\date{$Date$}
 \maketitle
 
-\abstract{This thorn creates initial data for Brill wave spacetimes.
-It can create both axisymmetric data (in a 3D cartesian grid), as
-well as data with an angular dependency.}
+\abstract{This thorn creates time symmetric initial data for Brill
+wave spacetimes.  It can create both axisymmetric data (in a 3D
+cartesian grid), as well as data with an angular dependency.}
 
 \section{Purpose}
 
@@ -22,40 +22,38 @@ ds^2 = \Psi^4 \left[ e^{2q} \left( d\rho^2 + dz^2 \right)
 \label{eqn:brillmetric}
 \end{equation}
 where $q$ is a free function subject to certain regularity and
-fall-off conditions and $\Psi$ is a conformal factor to be solved for.
+fall-off conditions, $\rho=\sqrt{x^2+y^2}$ and $\Psi$ is a conformal
+factor to be solved for.
 
-The thorn considers several different forms of the function $q$
-depending on certain parameters that will be described below.
-Substituting the metric above into the Hamiltonian constraint results
-in an elliptic equation for the conformal factor $\Psi$ that can be
-solved numerically once the function $q$ has been specified. The
-initial data is also assumed to be time-symmetric, so the momentum
+Substituting this metric into the Hamiltonian constraint gives an
+elliptic equation for the conformal factor $\Psi$ which is then
+numerically solved for a given function $q$:
+\begin{equation}
+\hat{\nabla} \Psi - \frac{\Psi}{8} \hat{R} = 0
+\end{equation}
+where the conformal Ricci scalar is found to be
+\begin{eqnarray}
+\hat{R} = -2 \left(e^{-2q} (\partial^2_z q + \partial^2_\rho q) + 
+\frac{1}{\rho^2} (3 (\partial_\phi q)^2 + 2 \partial_\phi q)\right)
+\end{eqnarray}
+Assuming the initial data to be time symmetric means that the momentum
 constraints are trivially satisfied.
 
-% [[ DPR: The code does not use these two different initial_data
-% keywords, but the axisym parameter instead.  It should probably use
-% the two different initial_data values.  I have changed the doc below
-% to correspond with the current code: ]]
+The thorn considers several different forms of the function $q$
+depending on certain parameters that will be described below.
 
-The thorn is activated by choosing the CactusEinstein/ADMBase parameter
-``initial\_data'' to be:
-%in one of the following two ways:
+Brill initial data is activated by choosing the {\tt CactusEinstein/ADMBase}
+parameter {\tt initial\_data} to be {\tt brilldata}.
 
-\begin{itemize}
-  
-\item initial\_data = ``brilldata'': %Axisymmetric 
-Brill wave initial data
-%  (but calculated in a cartesian grid!).
-  
-%\item initial\_data = ``brilldata3D'': Brill wave initial data with an
-%  angular dependency.
-
-\end{itemize}
+In the case of axisymmetry, the Hamiltonian constraint can be written
+as an elliptic equation for $\Psi$ with just the flat space Laplacian,
+\begin{equation}
+\nabla_{flat} \Psi + \frac{\Psi}{4} (\partial_z^2 q + \partial_\rho^2 q) = 0
+\end{equation}
+If the initial data is chosen to be {\tt
+ADMBase::initial\_data = "brilldata2D"} then this elliptic equation
+is solved rather than the equation above.
 
-To choose axisymmetric data, set the parameter {\tt axisym} to true
-(the default).  Note that the data is computed on a cartesian grid in
-any event.  {\tt axisym = "no"} adds an angular dependence factor,
-which is detailed below.
 
 \section{Parameters for the thorn}
 
@@ -128,14 +126,23 @@ The elliptic solver is controlled by the additional parameters:
 
 \begin{itemize}
   
-\item solver (KEYWORD): Elliptic solver used to solve the
-  hamiltonian constraint [sor/petsc/bam] (default ``sor'').
+\item {\tt solver} (KEYWORD): Elliptic solver used to solve the
+  hamiltonian constraint [sor/petsc/bam] (default "sor").
   
-\item thresh (REAL): Threshold for elliptic solver (default
+\item {\tt thresh} (REAL): Threshold for elliptic solver (default
   0.00001).
 
 \end{itemize}
 
+\section{Notes}
+
+Thorn {\tt IDBrillData} understands both the {\tt physical} and {\tt
+static conformal} {\tt metric\_type}. In the case of a conformal
+metric being chosen, the conformal factor is set to $\Psi$. Currently
+the derivatives of the conformal factor are not calculated, so that
+only {\tt staticconformal::conformal\_storage = "factor"} is
+supported.
+
 % Automatically created from the ccl files 
 % Do not worry for now.