-- FreeFem++ v4.6 (Thu Apr  2 15:47:38 CEST 2020 - git v4.6)
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  Location:
    2 : //
    3 : //    http://people.sc.fsu.edu/~jburkardt/freefem_src/exec_test/exec_test.edp
    4 : //
    5 : //  Discussion:
    6 : //
    7 : //    We solve the Poisson equation in a square.
    8 : //
    9 : //      - uxx - uyy = u
   10 : //
   11 : //    and then:
   12 : //
   13 : //    * sample the solution, writing the data to a file.
   14 : //    * use EXEC() to run GNUPLOT and create a plot of the data.
   15 : //
   16 : //  Licensing:
   17 : //
   18 : //    This code is distributed under the GNU LGPL license.
   19 : //
   20 : //  Modified:
   21 : //
   22 : //    27 January 2015
   23 : //
   24 : //  Reference:
   25 : //
   26 : //    John Chrispell, Jason Howell,
   27 : //    Finite Element Approximation of Partial Differential Equations
   28 : //    Using FreeFem++, or, How I Learned to Stop Worrying and Love
   29 : //    Numerical Analysis.
   30 : //
   31 : //    Frederic Hecht,
   32 : //    New development in FreeFem++,
   33 : //    Journal of Numerical Mathematics,
   34 : //    Volume 20, Number 3-4, 2012, pages 251-265.
   35 : //
   36 : cout << "\n";
   37 : cout << "exec_test\n";
   38 : cout << "  FreeFem++ version.\n";
   39 : cout << "  Use the exec() function to issue an external co
  ... : mmand\n";
   40 : cout << "  In this case, call gnuplot() to plot some resul
  ... : ts.\n";
   41 : //
   42 : //  Define Th, the triangulation of the square.
   43 : //
   44 : int n = 10;
   45 : 
   46 : mesh Th = square ( n, n );
   47 : //
   48 : //  Define Vh, the finite element space for 
   49 : //    2D velocity vector (piecewise linear "bubble") and 
   50 : //    pressure (piecewise linear).
   51 : //
   52 : fespace Vh ( Th, P1 );
   53 : //
   54 : //  Define UH, the trial function.
   55 : //
   56 : Vh uh;
   57 : //
   58 : //  Define VH, test function.
   59 : //
   60 : Vh vh;
   61 : //
   62 : //  Define F(X,Y), the right hand side function.
   63 : //
   64 : func f = 
   65 :   +      sin(5*pi*x*(1-x)) *      sin(4*pi*y*(1-y)) * pow(5*pi*(1-x)-5*pi*x,2)
   66 :   + 10 * cos(5*pi*x*(1-x)) * pi * sin(4*pi*y*(1-y))
   67 :   +      sin(5*pi*x*(1-x)) *      sin(4*pi*y*(1-y)) * pow(4*pi*(1-y)-4*pi*y,2) 
   68 :   + 8  * sin(5*pi*x*(1-x)) * pi * cos(4*pi*y*(1-y));
   69 : //
   70 : //  Define G(X,Y), the boundary condition function.
   71 : //
   72 : func g = 0.0;
   73 : //
   74 : //  Define POISSON, the problem to be solved.
   75 : //
   76 : problem poisson ( uh, vh ) 
   77 :   = int2d ( Th ) 
   78 :   ( 
   79 :     dx(uh) * dx(vh) 
   80 :   + dy(uh) * dy(vh)
   81 :   )
   82 :   - int2d ( Th )
   83 :   (
   84 :     f * vh 
   85 :   )
   86 :   + on ( 1, 2, 3, 4, uh = g );
   87 : //
   88 : //  Solve the POISSON problem.
   89 : //  This puts the solution into UH.
   90 : //
   91 : poisson;
   92 : //
   93 : //  Define DATAFILE, the name to use for the file storing the data.
   94 : //
   95 : string datafile = "poisson" + n + ".txt";
   96 : //
   97 : //  Define PLOTUNIT, an output device associated with "poissonN.sol"
   98 : //
   99 : {
  100 : ofstream plotunit ( datafile );
  101 : //
  102 : //  Write a list of X, Y, UH(X,Y) values to the datafile.
  103 : //
  104 : {
  105 :   for ( int i = 0; i <= n ; i++ )
  106 :   {
  107 :     real xx = real ( i ) / real ( n );
  108 :     for ( int j = 0; j <= n ; j++ )
  109 :     {
  110 :       real yy = real ( j ) / real ( n );
  111 :       plotunit << xx << " " << yy << " " << uh( xx, yy ) << endl;
  112 :     }
  113 :     plotunit << endl;
  114 :   }
  115 : }
  116 : }
  117 : //
  118 : //  Define PLOTFILE, the name of a graphics file to be created.
  119 : //
  120 : string plotfile = "poisson" + n + ".png";
  121 : //
  122 : //  Using EXEC ( "command" ) create a stream of input to gnuplot.
  123 : //
  124 : exec
  125 : (
  126 :   "echo"
  127 :   + " '"
  128 :   +   "set parametric\n" 
  129 :   +   "set term png\n"
  130 :   +   "set hidden\n"
  131 :   +   "set contour base\n"
  132 :   +   "set style data lines\n"
  133 :   +   "set output \""
  134 :   +   plotfile
  135 :   +   "\"\n"
  136 :   +   "splot \""
  137 :   +   datafile
  138 :   +   "\"\n"
  139 :   + " ' | gnuplot"
  140 : ); 
  141 : //
  142 : //  Terminate.
  143 : //
  144 : cout << "\n";
  145 : cout << "exec_test\n";
  146 : cout << "  Normal end of execution.\n";
  147 :  sizestack + 1024 =6592  ( 5568 )


exec_test
  FreeFem++ version.
  Use the exec() function to issue an external command
  In this case, call gnuplot() to plot some results.
  -- Square mesh : nb vertices  =121 ,  nb triangles = 200 ,  nb boundary edges 40
  -- Solve : 
          min -0.617154  max 0.856647
exec: echo 'set parametric
set term png
set hidden
set contour base
set style data lines
set output "poisson10.png"
splot "poisson10.txt"
 ' | gnuplot

exec_test
  Normal end of execution.
times: compile 0.005277s, execution 0.003653s,  mpirank:0
 CodeAlloc : nb ptr  3783,  size :479136 mpirank: 0
Ok: Normal End