# Title: Convergence with a refined circle
#
# Description:
#
# Same as the previous test but in order to test the accuracy of the
# gradient operator at coarse/fine boundaries, two levels of
# refinement are added in a circle centered on the origin and of
# radius 0.25.
#
# The solver still shows second-order accuracy in all norms (Figure \ref{order}).
#
# \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 ../poisson.sh circle.gfs
# Version: 0.8.0
# Required files: res-7.ref error.ref order.ref
# Generated files: residual.eps rate.eps error.eps order.eps
#
1 0 GfsPoisson GfsBox GfsGEdge {} {
  Time { iend = 10 }
  Refine (x*x + y*y <= 0.25*0.25 ? LEVEL + 2 : LEVEL)
  ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 }
  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
  }
  OutputErrorNorm { start = end } {
    awk '{print LEVEL " " $5 " " $7 " " $9}' >> error 
  } { v = P } {
    s = (sin (M_PI*3.*x)*sin (M_PI*3.*y))
    unbiased = 1
  }
}
GfsBox {}