documentation for spherically symmetric solutions

git-svn-id: http://svn.cactuscode.org/arrangements/CactusWave/IDScalarWave/trunk@48 f5a6acaf-da7d-456b-b0a8-35edbc60b392

1 files changed, 96 insertions, 0 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
new file mode 100644
index 0000000..fb51495
--- /dev/null
+++ b/doc/documentation.tex
@@ -0,0 +1,96 @@
+\documentclass{article}
+
+\parskip = 2 pt
+\oddsidemargin = 0 cm
+\textwidth = 16 cm
+\topmargin = -1 cm
+\textheight = 24 cm
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% MANPAGE like description setting for options, use as 
+% \begin{Lentry} \item[text] text  \end{Lentry}
+
+\usepackage{ifthen,calc}
+
+\newcommand{\entrylabel}[1]{\mbox{\textsf{#1}}\hfil}
+\newenvironment{entry}
+  {\begin{list}{}
+    {\renewcommand{\makelabel}{\entrylabel}
+      \setlength{\labelwidth}{90pt}
+      \setlength{\leftmargin}{\labelwidth+\labelsep}
+    }
+  }
+  {\end{list}}
+
+\newlength{\Mylen}
+\newcommand{\Lentrylabel}[1]{%
+  \settowidth{\Mylen}{\textsf{#1}}%
+  \ifthenelse{\lengthtest{\Mylen > \labelwidth}}%
+    {\parbox[b]{\labelwidth} %  term > labelwidth
+      {\makebox[0pt][l]{\textsf{#1}}\\}} %
+    {\textsf{#1}} %
+
+  \hfil\relax}
+\newenvironment{Lentry}
+  {\renewcommand{\entrylabel}{\Lentrylabel}
+   \begin{entry}}
+  {\end{entry}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{document}
+
+\title{IDScalarWave}
+\author{Gabrielle Allen, Horst Beyer}
+\date{2001}
+\maketitle
+
+\abstract{Initial Data for the 3D Scalar Wave Equation}
+
+\section{Purpose}
+
+This thorn provides different initial data for the 3D scalar wave
+equation. 
+
+\section{Spherically Symmetric Solutions}
+
+The general spherically symmetric solution can be written
+\begin{equation}
+\Psi(r,t) = \frac{1}{r}\left(f(r+t)+g(r-t)\right)
+\end{equation}
+where the functions $f$ and $g$ can be freely chosen. 
+
+Making the additional requirement of time symmetry at $t=0$, forces
+\begin{equation}
+f(r)=g(r)
+\end{equation}
+Thus if the solution at t=0 is given by $\phi(r)$, the general solution
+will be
+\begin{equation}
+\Psi(r,t) = \frac{1}{2r}\left( (r+t)\phi(r+t)+(r-t)\phi(r-t) \right)
+\end{equation}
+
+\section{Gaussian}
+
+The gaussian solution is {\it spherically symmetric} about the 
+origin of the Cartesian coordinate system, and is {\it time symmetric}.
+The initial profile is
+\begin{equation}
+\phi(r) = A \exp (- (r-r_0)^2/\sigma)
+\end{equation}
+and is set with the parameters
+\begin{itemize}
+
+\item {\tt amplitude} = $A$
+
+\item {\tt radius} = $r_0$
+
+\item {\tt sigma} = $\sigma$
+
+\end{itemize}
+
+% Automatically created from the ccl files by using gmake thorndoc
+\include{interface}
+\include{param}
+\include{schedule}
+
+\end{document}