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Yingjie Wang
2026-04-09 23:55:41 -04:00
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% \node[draw=none, above=1mm of gh, font=\scriptsize] {full first order}; % \node[draw=none, above=1mm of gh, font=\scriptsize] {full first order};
\end{tikzpicture} \end{tikzpicture}
\caption{evolution systems} \caption{Evolution systems. Second order systems are in blue, and first order systems are in red. Solid arrows represent direct modifications, while dashed arrows represent relation. Dotted bidirectional arrows represent equivalence between systems.}
\end{figure} \end{figure}
\begin{itemize}
\item Z4 and GH are said to be equivalent. They damps the momentum constraint and the Hamiltonian constraint respectively. They evolve the physical metric, and thus not compatible with the moving puncture method.
\item The rests are using the conformal metric, and thus compatible with the moving puncture method.
\begin{itemize}
\item Z4c and CCZ4 are modifications of Z4, introducing the conformal metric from BSSN to Z4, and damping both the momentum and Hamiltonian constraints.
\item Z4c is simpler than CCZ4. Moreover, it controls the constraints very well in many tests in the community.
\end{itemize}
\end{itemize}
\end{frame} \end{frame}
\begin{frame}{Searching for a first order Z4c}{Hyperbolicity of first order systems} \begin{frame}{Searching for a first order Z4c}{Hyperbolicity of first order systems}