\frame{ \frametitle{WaveToy Thorn: Wave Equation}
 For a given source function $S(x,y,z,t)$ find a scalar wave
 field $\varphi(x,y,z,t)$ inside the domain $\mathcal{D}$
 with a boundary condition:
 \begin{columns}[t]
    \column{.3\textwidth}
      \begin{figure}[!htp]
      \begin{center}
      \begin{tikzpicture}[rotate=5,scale=1.2]
        \filldraw[fill=green!60!white, draw=green!50!black, thick] 
             (-1,-1) rectangle (1,1);
        \draw (0,0) node {{\large $\mathcal{D}$}};
        \draw (1.4,0.2) node {$\partial\mathcal{D}$};
        \draw[->,thick,color=red] (1.1,0.2) -- (1,0.2);
      \end{tikzpicture}
      \end{center}
      \end{figure}
      
    \column{.6\textwidth}
      \begin{itemize}
      \item inside $\mathcal{D}$:
            \begin{equation*}
            \frac{\partial^2\varphi}{\partial t^2} = c^2\Delta\varphi + S
            \end{equation*}
      \item on the boundary  $\partial\mathcal{D}$:
            \begin{equation*}
            \varphi|_{\partial\mathcal{D}} = \varphi(t=0)
            \end{equation*}
      \end{itemize}
 \end{columns}   
}

\frame{ \frametitle{WaveToy Thorn: Discretization}
 Discretization: \\
 approximating continuous function $\varphi(x,t)$ 
 with a grid function $\varphi^{(n)}_{i}$:
 \begin{columns}[t]
    \column{.2\textwidth}
      \begin{figure}[!htp]
      \begin{center}
      \begin{tikzpicture}[scale=1.1]
        \draw (-1,0) -- (1,0);
        \draw (0,-1) -- (0,1);
        \scope[fill=green!50!blue, draw=black]
          \filldraw (0,0) circle (0.07cm);
          \filldraw (1,0) circle (0.07cm);
          \filldraw (0,1) circle (0.07cm);
          \filldraw (-1,0) circle (0.07cm);
          \filldraw (0,-1) circle (0.07cm);
        \endscope
        \scope[xshift=0.45cm,yshift=0.25cm]
          \draw (0,0) node {{\tiny $\varphi^{(n)}_{i}$}};
          \draw (1,0) node {{\tiny $\varphi^{(n)}_{i+1}$}};
          \draw (0,1) node {{\tiny $\varphi^{(n+1)}_{i}$}};
          \draw (-1,0) node {{\tiny $\varphi^{(n)}_{i-1}$}};
          \draw (0,-1) node {{\tiny $\varphi^{(n-1)}_{i}$}};
        \endscope
      \end{tikzpicture}
      \end{center}
      \end{figure}

    \column{.8\textwidth}
      \begin{eqnarray*}
      \\
      &\frac{\partial^2\varphi}{\partial t^2} = 
        c^2 (\partial_x^2\varphi) + S \\
      &\Downarrow (c\equiv1)\\
      &\frac{\varphi^{(n+1)}_{i} - 2\varphi^{(n)}_{i}+\varphi^{(n-1)}_{i}}
           {2\Delta t^2} =
      \frac{\varphi^{(n)}_{i+1} - 2\varphi^{(n)}_{i}+\varphi^{(n)}_{i-1}}
           {2\Delta x^2} + S^{(n)}_{i}
      \end{eqnarray*}
 \end{columns}   
}

\frame{ \frametitle{WaveToy Thorn}
 Thorn structure:

 \begin{columns}[t]
    \column{.4\textwidth}
    \begin{exampleblock}{interface.ccl}
      \begin{itemize}
      \item grid function {\color{blue}phi[3]}:
      \end{itemize}
      \begin{figure}[!htp]
      \begin{center}
      \begin{tikzpicture}
        \scope[fill=white!90!green, draw=black]
          \filldraw (-1.5,-1) -- (0.5,-1) -- (1.5,-0.2) -- (-0.5,-0.2) -- cycle; 
          \filldraw (-1.5,-0.4) -- (0.5,-0.4) -- (1.5,0.4) -- (-0.5,0.4) -- cycle; 
          \filldraw (-1.5,0.2) -- (0.5,0.2) -- (1.5,1) -- (-0.5,1) -- cycle; 
        \endscope
        \scope[fill=green!50!blue, draw=black, dashed, very thin]
          \draw (-0.6,0) -- (0.6,0);
          \draw (0,-0.6) -- (0,0.6);
          \draw (-0.35,-0.3) -- (0.35,0.3);
          \filldraw (0,0) circle (0.07cm);
          \filldraw (0.6,0) circle (0.07cm);
          \filldraw (0,0.6) circle (0.07cm);
          \filldraw (-0.6,0) circle (0.07cm);
          \filldraw (0,-0.6) circle (0.07cm);
          \filldraw (-0.35,-0.3) circle (0.07cm);
          \filldraw (0.35,0.3)   circle (0.07cm);
        \endscope
        \scope[left=2pt,yshift=0.2cm]
          \draw (-1.5,-1)   node {\color{blue}phi\_p\_p};
          \draw (-1.5,-0.4) node {\color{blue}phi\_p};
          \draw (-1.5, 0.2) node {\color{blue}phi};
        \endscope
        \scope[xshift=0.6cm,yshift=0.2cm]
          \draw (-1.5,-1)   node {{\tiny $\varphi^{(n-2)}$}};
          \draw (-1.5,-0.4) node {{\tiny $\varphi^{(n-1)}$}};
          \draw (-1.5, 0.2) node {{\tiny $\varphi^{(n)}$}};
        \endscope
      %\includegraphics[height=0.3\textheight]{time_levels}
      \end{tikzpicture}
      \end{center}
      \end{figure}
      \begin{itemize}
      \item {\small Boundary\_SelectVarForBC}
      \end{itemize}
    \end{exampleblock}

    \column{.4\textwidth}
    \begin{exampleblock}{param.ccl}
      \begin{itemize}
      \item Parameters of initial Gaussian pulse: 
            amplitude {\color{brown}$A$}, 
            radius {\color{brown}$R$}, 
            width {\color{brown}$\sigma$}
      \end{itemize}
    \end{exampleblock}

    \begin{exampleblock}{schedule.ccl}
      \begin{itemize}
      \item WaveToy\_InitialData
      \item WaveToy\_Evolution
      \item WaveToy\_Boundaries
      \end{itemize}
    \end{exampleblock}
 \end{columns}   
}

% \frame{ \frametitle{WaveToy Thorn}
%  \begin{itemize}
%  \item Choose initial values $\Phi_{i,j,k,0}$;
%  \item Loop:
%    \begin{itemize}
%    \item Calculate field at current time based on discretized wave equation
%    \item On boundary points, where derivatives may not be present, apply chosen
%          boundary conditions
%    \end{itemize} 
%  \end{itemize} 
% }

\frame{ \frametitle{WaveToy Thorn: Algorithm Illustration}
 \begin{columns}[t]
 \column{.7\textwidth}
   \begin{figure}[!htp]
   \begin{center}
     \begin{tikzpicture}
       
       %\draw[->] (0,0) -- (1,1);
       % Step 1: axes and grid
       \draw[->,very thin] (-.6,-.4) -- (6,-.4);
       \draw[->,very thin] (-.4,-.6) -- (-.4,3);
       \draw[left=2pt] (-.4,2.5)   node {$t$};
       \draw[above=2pt] (5.8,-0.4) node {$x$};

       \uncover<1>{
         \draw[xstep=.6cm,ystep=.4cm,gray,dashed]
              (0,0) grid(5.4cm,2.6cm);
       }%

       % Step 2: splitting between two processors
       \uncover<2->{
         \draw (0,2.8) -- (.6,3.2) -- (2.4,3.2) -- (3,2.8);
         \draw[above=1pt] (1.4,3.2) node {\emph{PROC1}};
  
         \draw[xshift=2.4cm] (0,2.8) -- (.6,3.2) -- (2.4,3.2) -- (3,2.8);
         \draw[above=1pt] (3.8,3.2) node {\emph{PROC2}};
       }%
       \uncover<2-4>{
         \draw[xstep=.6cm,ystep=.4cm,gray,dashed] 
              (0,0)   grid (3.0cm,2.6cm);
         \draw[xstep=.6cm,ystep=.4cm,gray,dashed,xshift=0.05cm,yshift=0.05cm] 
              (2.4,0) grid (5.4cm,2.6cm);
       }%

       % Step 3: memory "allocations" 
       \uncover<3>{
         \draw[color=blue] (1.5,-0.6) node {\tiny x, phi, phi\_p, phi\_p\_p};
         \draw[color=blue] (4.2,-0.6) node {\tiny x, phi, phi\_p, phi\_p\_p};
       }%

       % Step 4: CoordBase / CartGrid3D
       \uncover<4->{
          \foreach \x in {0.0,0.6,1.2,1.8,2.4,3.0,3.6,4.2,4.8,5.4}
            \draw (\x cm,-0.4cm) node[anchor=south] {{\tiny $\x$}};
          \draw[very thick,color=brown,xstep=0.6cm,ystep=1cm,yshift=-0.4cm] 
            (0cm,-1pt) grid (3.0cm,1pt);
          \draw[color=blue] (1.5,-0.6) node {\small x};

          \draw[very thick,color=brown,xstep=0.6cm,ystep=1cm,xshift=2.45cm,yshift=-0.35cm] 
            (0cm,-1pt) grid (3.0cm,1pt);
          \draw[color=blue] (4.2,-0.6) node {\small x};
       }
       \uncover<4-5>{
         \draw[color=blue] (1.5,-1.0) node {\tiny phi, phi\_p, phi\_p\_p};
         \draw[color=blue] (4.2,-1.0) node {\tiny phi, phi\_p, phi\_p\_p};
       }%

       % Step 5: Time
       \uncover<5->{
         \draw[xstep=.6cm,ystep=.4cm,gray,dashed] 
              (0,0)   grid (3.0cm,2.6cm);
         \draw[xstep=.6cm,ystep=.4cm,gray,dashed,xshift=0.05cm,yshift=0.05cm] 
              (2.4,0) grid (5.4cm,2.6cm);
       }%
       \uncover<5>{
         \scope[color=red,thick,fill=white]
           \draw (-0.5,0.4) -- (0.0,0.4);
           \draw (-0.5,0.8) -- (0.0,0.8);
           \draw[->] (-0.1,1.2) -- (-0.1,0.8);
           \draw[<-] (-0.1,0.4) -- (-0.1,0.0);
         \endscope
         \draw (0,0.6) node[anchor=west,fill=white] {$\Delta t = \lambda\Delta x_{\min}$};
       }

       % Step 6: Initial data routines
       \uncover<6->{
         \scope[very thick,color=green,xstep=0.6cm,ystep=1cm]
          \draw[xshift=0cm,yshift=0cm]       (0cm,-1pt) grid (3.0cm,1pt);
          \draw[xshift=2.45cm,yshift=0.05cm] (0cm,-1pt) grid (3.0cm,1pt);         
          \draw[xshift=0cm,yshift=0.4cm]     (0cm,-1pt) grid (3.0cm,1pt);
          \draw[xshift=2.45cm,yshift=0.45cm] (0cm,-1pt) grid (3.0cm,1pt);         
          \draw[xshift=0cm,yshift=0.8cm,color=black]     (0cm,-1pt) grid (3.0cm,1pt);
          \draw[xshift=2.45cm,yshift=0.85cm,color=black] (0cm,-1pt) grid (3.0cm,1pt);         
         \endscope
       }%
       \uncover<6>{
         \scope[color=blue]
           \draw (-0.5,0.0) node[anchor=east] {\small phi\_p};
           \draw (-0.5,0.4) node[anchor=east] {\small phi};
           \draw (-0.5,0.8) node[anchor=east] {\small phi\_p\_p};
         \endscope
       }

       % Step 7: Layers rotation
       \uncover<7>{
         %\draw[thick,color=red,->] (-0.5,-0.1) arc (-25:25:1.1cm);
         \draw[thick,color=red,->] (-1.8, 0.8) arc (155:205:1.1cm);
       }
       \uncover<7-11>{
         \scope[color=blue]
           \draw (-0.5,0.0) node[anchor=east] {\small phi\_p\_p};
           \draw (-0.5,0.4) node[anchor=east] {\small phi\_p};
           \draw (-0.5,0.8) node[anchor=east] {\small phi};
         \endscope
       }

       % Step 8: Evaluation of RHS
       \uncover<8>{
         \scope[draw=red,thick,fill=green]
           \draw (0.0,0.4) -- (1.2,0.4);
           \draw[->] (0.6,0.0) -- (0.6,0.7);
           \filldraw (0.6,0.8) circle (0.1cm);
           \filldraw (0.6,0.0) circle (0.1cm);
           \filldraw (0.0,0.4) circle (0.1cm);
           \filldraw (0.6,0.4) circle (0.1cm);
           \filldraw (1.2,0.4) circle (0.1cm);

           % second processor:
           \scope[xshift=0.05cm,yshift=0.05cm]
             \fill (3.0,0.8) circle (0.05cm);
             \fill (3.6,0.8) circle (0.05cm);
             \scope[xshift=3.6cm]
               \draw (0.0,0.4) -- (1.2,0.4);
               \draw[->] (0.6,0.0) -- (0.6,0.7);
               \filldraw (0.6,0.8) circle (0.1cm);
               \filldraw (0.6,0.0) circle (0.1cm);
               \filldraw (0.0,0.4) circle (0.1cm);
               \filldraw (0.6,0.4) circle (0.1cm);
               \filldraw (1.2,0.4) circle (0.1cm);
             \endscope
           \endscope
         \endscope
       }%

       % Step 9: Ghost zones
       \uncover<9>{
         \scope[very thick,color=green,xstep=0.6cm,ystep=1cm]
          \draw[xshift=0.6cm,yshift=0.8cm]       (0cm,-1pt) grid (1.8cm,1pt);
          \draw[xshift=3.05cm,yshift=0.85cm] (0cm,-1pt) grid (1.8cm,1pt);         
          \draw[->,color=red] (2.4,0.7) -- (2.4,0.9);
          \draw[->,color=red] (3.05,0.9) -- (3.05,0.7);
         \endscope
       }%
       
       % Step 10: Boundary conditions
       \uncover<10>{
         \scope[very thick,color=green,xstep=0.6cm,ystep=1cm]
          \draw[xshift=0.6cm,yshift=0.8cm]       (0cm,-1pt) grid (2.4cm,1pt);
          \draw[xshift=2.45cm,yshift=0.85cm] (0cm,-1pt) grid (2.4cm,1pt);         
          \draw[->,color=red] (0.0,0.4) -- (0.0,0.8);
          \draw[->,color=red] (5.45,0.45) -- (5.45,0.85);
         \endscope
       }%

       % Step 11: Output data
       \uncover<11->{
         \scope[very thick,color=green,xstep=0.6cm,ystep=1cm]
          \draw[xshift=0cm,yshift=0.8cm]     (0cm,-1pt) grid (3.0cm,1pt);
          \draw[xshift=2.45cm,yshift=0.85cm] (0cm,-1pt) grid (3.0cm,1pt);         
         \endscope
       }

       % Step 11: Advance to the next time level
       \uncover<12>{
         \scope[very thick,color=green,xstep=0.6cm,ystep=1cm]
          \draw[xshift=0cm,yshift=1.2cm,color=black]     (0cm,-1pt) grid (3.0cm,1pt);
          \draw[xshift=2.45cm,yshift=1.25cm,color=black] (0cm,-1pt) grid (3.0cm,1pt);         
          \draw[xshift=0cm,yshift=0.8cm]     (0cm,-1pt) grid (3.0cm,1pt);
          \draw[xshift=2.45cm,yshift=0.85cm] (0cm,-1pt) grid (3.0cm,1pt);         
         \endscope
         \scope[color=blue]
           \draw (-0.5,0.4) node[anchor=east] {\small phi\_p};
           \draw (-0.5,0.8) node[anchor=east] {\small phi};
           \draw (-0.5,1.2) node[anchor=east] {\small phi\_p\_p};
         \endscope
       }

     \end{tikzpicture}
   \end{center}
   \end{figure}


 \column{.3\textwidth}
   \begin{figure}[!htp]
   \begin{center}
   \vspace{-1cm}
   \begin{tikzpicture}
      \draw (0,7) node
      [anchor=north,right,text width=3cm,rounded corners,fill=green!20,draw=blue!50!black] %,inner sep=1ex]
      (begin)
      {\begin{footnotesize}
       \begin{itemize}
       \item[]<alert@1-2> \hspace{-0.5cm} Grid structure
       \item[]<alert@3>   \hspace{-0.5cm} GF allocation
       \end{itemize}
       \end{footnotesize}};

      \draw (0,5.3) node 
      [anchor=north,right,text width=3cm,rounded corners,fill=green!20,draw=blue!50!black] %,inner sep=1ex]
      (init)
      {\begin{footnotesize}
       \begin{itemize}
       \item[]<alert@4> \hspace{-0.5cm} Set up coords
       \item[]<alert@5> \hspace{-0.5cm} Compute $\Delta t$
       \item[]<alert@6> \hspace{-0.5cm} Initial data
       \end{itemize}
       \end{footnotesize} };
      
      \draw[->,thick,draw=blue!50!black] (0,2.15) -- (-0.3,2.15) -- (-0.3,3.8) -- (-0.05,3.8);

      \draw (0,3) node 
      [anchor=north,right,text width=3cm,rounded corners,fill=green!20,draw=blue!50!black] %,inner sep=1ex]
      (evol)
      {\begin{footnotesize}
       \begin{itemize}
       \item[]<alert@7,12>   \hspace{-0.5cm} Rotate timelevels
       \item[]<alert@8-9>    \hspace{-0.5cm} Evolve GF, sync
       \item[]<alert@10> \hspace{-0.5cm} Apply BCs
       \item[]<alert@11> \hspace{-0.5cm} Output data
       \end{itemize}
       \end{footnotesize} };

      \scope[color=blue!50!black,thick]
        \draw[->,shorten >=2pt] (begin.south) -- (init.north);
        \draw[->,shorten >=2pt] (init.south)  -- (evol.north);
      \endscope
   \end{tikzpicture}
   \end{center}
   \end{figure}
 \end{columns}
}

%\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
% Implemented in \verb|CactusWave/WaveToy|:
% \begin{itemize}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToy/interface.ccl}{interface.ccl}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToy/schedule.ccl}{schedule.ccl}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToy/param.ccl}{param.ccl}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToy/src}{src/ directory}
% \end{itemize}
%}

\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
 Directory structure:
 \begin{alltt}
WaveToy/
|-- COPYRIGHT
|-- README
|-- configuration.ccl
|-- doc
|   `-- documentation.tex
|-- interface.ccl
|-- schedule.ccl
|-- param.ccl
`-- src
    |-- WaveToy.c
    `-- make.code.defn
\end{alltt}
}

\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
 Directory structure:
 \begin{alltt}
WaveToy/
|-- COPYRIGHT
|-- README
|-- configuration.ccl
|-- doc
|   `-- documentation.tex
\textcolor{blue}{|-- interface.ccl
|-- schedule.ccl
|-- param.ccl}
`-- src
    |-- WaveToy.c
    `-- make.code.defn
\end{alltt}
}

\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
 \begin{itemize}
  \item \verb|interface.ccl|:
   \tiny\begin{verbatim}
 IMPLEMENTS: wavetoy_simple
 INHERITS: grid

 PUBLIC:

 CCTK_REAL scalarevolve TYPE=gf TIMELEVELS=3
 {
   phi
 } "The evolved scalar field"

 CCTK_INT FUNCTION Boundary_SelectVarForBC( \
   CCTK_POINTER_TO_CONST IN GH, CCTK_INT IN faces, \
   CCTK_INT IN boundary_width, CCTK_INT IN table_handle, \
   CCTK_STRING IN var_name, CCTK_STRING IN bc_name)

 REQUIRES FUNCTION Boundary_SelectVarForBC\end{verbatim}
 \end{itemize}
}
\frame[containsverbatim]{ \frametitle{WaveToy Thorn cont.}
 \begin{itemize}
 \item \verb|schedule.ccl|:
  \tiny\begin{verbatim}
   STORAGE: scalarevolve[3]

   SCHEDULE WaveToy_InitialData AT CCTK_INITIAL
   {
     LANG: C
   } "Initial data for 3D wave equation"

   SCHEDULE WaveToy_Evolution AT CCTK_EVOL
   {
     LANG: C
     SYNC: scalarevolve
   } "Evolution of 3D wave equation"

   SCHEDULE WaveToy_Boundaries AT CCTK_EVOL AFTER WaveToy_Evolution
   {
     LANG: C
   } "Select boundary conditions for the evolved scalar"

   SCHEDULE GROUP ApplyBCs as WaveToy_ApplyBCs AT CCTK_EVOL AFTER WaveToy_Boundaries
   {
   } "Apply boundary conditions"\end{verbatim}
 \end{itemize}
}
\frame[containsverbatim]{ \frametitle{WaveToy Thorn cont.}
 \begin{itemize}
  \item \verb|param.ccl|:
   \tiny\begin{verbatim}
   CCTK_REAL amplitude "The amplitude of the waves"
   {
    *:* :: "Anything"
   } 1.0

   CCTK_REAL radius "The radius of the gaussian wave"
   {
    0:* :: "Positive"
   } 0.0

   CCTK_REAL sigma "The sigma for the gaussian wave"
   {
    0:* :: "Positive"
   } 0.1\end{verbatim}
 \end{itemize}
}

\frame[containsverbatim]{ \frametitle{WaveToy Thorn cont.}
 \begin{itemize}
  \item Example parameter file:
   \tiny\begin{verbatim}
  Cactus::cctk_run_title = "Simple WaveToy"

  ActiveThorns = "time boundary Carpet CarpetLib CartGrid3D"
  ActiveThorns = "CoordBase ioutil CarpetIOBasic CarpetIOASCII"
  ActiveThorns = "CarpetIOHDF5 SymBase wavetoy"

  cactus::cctk_itlast = 10000
  time::dtfac = 0.5

  IO::out_dir             = $parfile
  IOBasic::outInfo_every  = 1
  IOASCII::out1D_every    = 1
  IOASCII::out1D_vars     = "wavetoy_simple::phi"

  iohdf5::out_every = 10
  iohdf5::out_vars        = "grid::coordinates{out_every=10000000} wavetoy_simple::phi"\end{verbatim}
  \end{itemize}
}
%\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
% \begin{enumerate}
%   \item Define a new variable in \verb|interface.ccl|, and allocate storage
%         for it in \verb|schedule.ccl|.
%   \item Schedule the energy calculation in the appropriate time bin, also in 
%         \verb|schedule.ccl|.
%\item Code up the energy calculation procedure in a file under the \verb|src/|
%         subdirectory, and request its compilation in \verb|make.code.defn|.
% \end{enumerate}
%}

%\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
% Modified thorn:
% \begin{itemize}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToyEnergy/interface.ccl}{interface.ccl}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToyEnergy/schedule.ccl}{schedule.ccl}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToyEnergy/param.ccl}{param.ccl}
%  \item \href{http://www.cct.lsu.edu/~bentivegna/WaveToyEnergy/src}{src/ directory}
% \end{itemize}
%}
%
%\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
% Running this example:
% \begin{enumerate}
%  \item Download the thornlist, optionlist and parameter file:
%
%  \small{\url{www.cct.lsu.edu/~bentivegna/ICCS09Demo/wavetoy.th}}
%
%  \small{\url{www.cct.lsu.edu/~bentivegna/ICCS09Demo/wavetoy.op}}
%
%  \small{\url{www.cct.lsu.edu/~bentivegna/ICCS09Demo/wavetoy.par}}
%
%  \item Configure and compile:
%  
%  \verb|cd $CACTUS_DIR|
%
%  \verb|make wave-config options=wavetoy.op THORNLIST=wavetoy.th|
%
%  \verb|make wave|
%  \item Run:
% 
%  \verb|./exe/cactus_wave wavetoy.par|
% \end{enumerate}
%}
%
%\frame[containsverbatim]{ \frametitle{WaveToy Thorn}
% Visualize the results:
% \begin{itemize}
%  \item ASCII output with gnuplot. 
%  \item HDF5 output with VisIt and visitCarpetHDF5.
%  \includegraphics[height=3cm]{viz1.png}
%  \quad
%  \includegraphics[height=3cm]{viz3.png}
%  \quad
%  \includegraphics[height=3cm]{viz6.png}
% \end{itemize}
%}