diff --git a/report.tex b/report.tex index 48de47e..98bfcbd 100644 --- a/report.tex +++ b/report.tex @@ -296,6 +296,7 @@ \end{frame} \begin{frame}{Searching for a first order Z4c}{First order Z4c?} + \subsection{First order Z4c?} \begin{figure} \centering \begin{tikzpicture}[ @@ -342,7 +343,27 @@ \end{tikzpicture} \caption{Commenly used systems, and first order reductions.} \end{figure} - + \end{frame} + + \begin{frame}{Searching for a first order Z4c}{Why not existing first order formulations} + \begin{itemize} + \item GH + \begin{itemize} + \item Not compatible with moving puncture mothod + \end{itemize} + \item FOCCZ4 + \begin{itemize} + \item No constraint damping for new constraints introduced during the reduction + \end{itemize} + \item FOZ4 + \begin{itemize} + \item It's almost a copy of FOCCZ4. No constraint damping for new constraints introduced during the reduction + \end{itemize} + \item FOBSSN + \begin{itemize} + \item Probably works; not well tested in the community; WIP in \texttt{nmesh} + \end{itemize} + \end{itemize} \end{frame} \begin{frame}{Searching for a first order Z4c}{Hyperbolicity of first order systems} @@ -457,28 +478,6 @@ and thus the system is still strongly hyperbolic, and well-posed in the $L^2$ sense. \end{frame} - \begin{frame}{Existing first order formulations} - \subsection{Existing first order formulations} - \begin{itemize} - \item GH - \begin{itemize} - \item Not compatible with moving puncture mothod - \end{itemize} - \item FOCCZ4 - \begin{itemize} - \item No constraint damping - \end{itemize} - \item FOZ4 - \begin{itemize} - \item No constraint damping - \end{itemize} - \item FOBSSN - \begin{itemize} - \item Probably works; not well tested in the community; WIP in \texttt{nmesh} - \end{itemize} - \end{itemize} - \end{frame} - \begin{frame}{References} \printbibliography \end{frame}