update: auto commit

report.tex

@@ -321,7 +321,7 @@
       \begin{cases}
         \Partial{t}{\phi} = \pi, \\
         \Partial{t}{\pi} = \tensor{\delta}{^i^j} \Partial{i} \tensor{\psi}{_j},\\
-        \Partial{t}{\tensor{\psi}{_i}} = \Partial{i} \pi - \gamma \mathcal{C}_i,
+        \Partial{t}{\tensor{\psi}{_i}} = \Partial{i} \pi - \gamma \left( \tensor{\psi}{_i} - \Partial{i} \phi \right),
       \end{cases}
     \end{equation}
     where $\gamma > 0$ is a constant. Then the evolution of the constraints becomes
@@ -331,6 +331,11 @@
     which means that the constraint violation will decay exponentially with time, and thus the system is more stable for numerical simulations.
   \end{frame}
 
+  \begin{frame}{Towards first order Z4c}{constraints during the reduction}
+    We have to check if the constraint damping term will change the hyperbolicity of the system. The new principal symbol matrix is
+    
+  \end{frame}
+
   \begin{frame}{Existing first order formulations}
     \subsection{Existing first order formulations}
     \begin{itemize}