From 2d031812d302379fe809b35d4c834451b0dde2cb Mon Sep 17 00:00:00 2001 From: goodale Date: Thu, 25 Apr 2002 22:03:52 +0000 Subject: Initial import of new Einstein stuff. This has the new thorns, but not all are fully functional yet. When I have completed this stage I'll send an updated spec out with some questions which have arisen during this process. Please don't import anything new without checking with me first, as I want to play games on the server copying cvs files around to preserve histories on files which are only minimally touched. Tom git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinBase/StaticConformal/trunk@2 0cbbb82d-14ec-4423-a1fb-2ab18257ecaa --- doc/documentation.tex | 57 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 57 insertions(+) create mode 100644 doc/documentation.tex (limited to 'doc') diff --git a/doc/documentation.tex b/doc/documentation.tex new file mode 100644 index 0000000..519a092 --- /dev/null +++ b/doc/documentation.tex @@ -0,0 +1,57 @@ +\documentclass{article} +\begin{document} + +\title{StaticConformal} +\author{Tom Goodale et al} +\date{April 2002} +\maketitle + +\abstract{Base thorn to provide the variables for the static conformal factor} + +\section{Purpose} + +This thorn provides the variables defining a static conformal factor +which is used to transform the physical metric. If this thorn is +active and the {\bf ADMBase::metric\_type} parameter is set to +`static conformal' then the {\bf ADMBase::g...} variables are the +conformal values as opposed to the physical values. + +The transformation is + +$$ g_{ij}^{\mbox{physical}} = \psi^4 g_{ij}^{\mbox{conformal}} $$ + +The extrinsic curvature is not transformed. + +Memory is provided for the conformal factor {\bf psi}, its first +derivatives {\bf psix}, {\bf psiy}, {\bf psiz}, and its second +derivatives {\bf psixx}, {\bf psixy}, {\bf psixz}, {\bf psiyy}, {\bf +psiyz}, and {\bf psizz} depending on the setting of the {\bf +conformal\_storage} parameter. + +Thorns need to check the value of the grid scalar +{\bf conformal\_state} to determine how many levels of these variables have +actually been calculated. + +\begin{itemize} +\item[0] +No conformal factor has been calculated -- thorns may +assume the conformal factor is 1 at all points. (I.e. the metric is physical.) +\item[1] +The conformal factor has been calulated, but no derivatives. +\item[2] +The conformal factor and its first derivatives have been calculated. +\item[3] +The conformal factor and its first and second derivatives have been calculated. +\end{itemize} + +\section{Comments} + +The {\bf StaticConformal} thorn itself does not calculate any conformal +factor, but does initialise the {\bf conformal\_state} variable to 0. + +% Automatically created from the ccl files by using gmake thorndoc +\include{interface} +\include{param} +\include{schedule} + +\end{document} -- cgit v1.2.3