blob: 963647f2c44ef5715bd2118de49ccc658db75268 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
|
% /*@@
% @file documentation.tex
% @date 20 May 2002
% @author Gabrielle Allen
% @desc
% IDConstraintViolate
% @enddesc
% @version $Header$
% @@*/
\documentclass{article}
\usepackage{../../../../doc/latex/cactus}
\begin{document}
\title{Creating Constraint Violating Initial Data}
\author{Gabrielle Allen}
\date{$Date$}
\maketitle
% Do not delete next line
% START CACTUS THORNGUIDE
\begin{abstract}
The \texttt{IDConstraintViolate} thorn creates initial data
which purposefully violates the constraint equations for testing purposes.
\end{abstract}
\section{Gaussian}
Choosing the {\tt ADMBase} parameter {\tt initial\_data} to have the
value {\tt Constraint violating gaussian} creates initial data with the
form
\begin{eqnarray*}
g_{xx} = g_{yy} = g_{zz} &=& 1 + A \exp \left(\frac{-(r-r_0)^2}{\sigma^2}\right)
\\
g_{xy} = g_{xz} = g_{yz} &=& 0
\\
K_{ij} &=& 0
\end{eqnarray*}
where the size and shape of the Gaussian is specified by parameters, $A$={\tt amplitude}, $r_0$={\tt radius} and $\sigma$={\tt sigma}.
% Do not delete next line
% END CACTUS THORNGUIDE
\end{document}
|
