# Title: Thin wall at box boundary
#
# Description:
#
# Boxes are used to setup a similar problem but with an infinitely
# thin wall.
#
# \begin{figure}[htbp]
# \caption{\label{solution}Solution of the Poisson equation.}
# \begin{center}
# \includegraphics[width=0.6\hsize]{solution.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{residual}Evolution of the residual.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{residual.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{rate}Average reduction factor.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{rate.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{error}Evolution of the error as a function of resolution.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{error.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{order}Corresponding convergence order.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{order.eps}
# \end{center}
# \end{figure}
#
# Author: St\'ephane Popinet
# Command: sh ../circle.sh thin.gfs
# Version: 0.8.0
# Required files: res-7.ref error.ref order.ref solution.gfv
# Generated files: residual.eps rate.eps error.eps order.eps solution.eps
#
4 3 GfsPoisson GfsBox GfsGEdge {} {
  Time { iend = 10 }
  Refine LEVEL
  ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 erelax = 2 }
  Init {} {
    Div = {
      int k = 3, l = 3;
      x = (x - 0.5)/2.;
      y = (y + 0.5)/2.;
      return -M_PI*M_PI*(k*k + l*l)*sin (M_PI*k*x)*sin (M_PI*l*y);
    }
  }
  OutputTime { istep = 1 } {
    awk '{print n++, $8}' > time
  }
  OutputProjectionStats { istep = 1 } {
    awk '{
      if ($1 == "niter:") printf ("%d ", $2);
      if ($1 == "residual.infty:") print $3 " " $4;
    }' > proj
  }
  OutputSimulation { start = end } sim-LEVEL { variables = P }
}
GfsBox {}
GfsBox {}
GfsBox {}
GfsBox {}
1 2 right
2 3 bottom
3 4 left