# Title: Convergence of the Poisson solver with solid boundaries
#
# Description:
#
# Another of the test cases presented in Popinet \cite{popinet2003}. A
# circular solid boundary of radius 0.25 is embedded in the
# domain. The same right-hand-side is used.
# 
# This time the problem does not have an analytical solution and we
# use Richardson extrapolation to estimate the error for a given
# resolution.
#
# \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 circle.gfs
# Version: 1.1.0
# Required files: circle.sh res-7.ref error.ref order.ref solution.gfv
# Generated files: residual.eps rate.eps error.eps order.eps solution.eps
#
1 0 GfsPoisson GfsBox GfsGEdge {} {
  Time { iend = 10 }
  Refine LEVEL
  Solid (ellipse (0, 0, 0.25, 0.25))
  ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 erelax = 2 }
  Init {} {
    Div = {
      int k = 3, l = 3;
      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 {}