-- FreeFem++ v4.14 (mer. 06 mars 2024 16:59:04 CET - git v4.14-1-g2b2052ae)
   file : laplace_circle.edp
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  laplace_circle.edp
    2 : //
    3 : //  Discussion:
    4 : //
    5 : //    Solve the Poisson equation on the unit disk.
    6 : //
    7 : //    Robin boundary conditions are applied.
    8 : //
    9 : //  Licensing:
   10 : //
   11 : //    This code is distributed under the MIT license.
   12 : //
   13 : //  Modified:
   14 : //
   15 : //    01 October 2024
   16 : //
   17 : //  Author:
   18 : //
   19 : //    Original FreeFem++ version by Florian De Vuyst.
   20 : //    This version by John Burkardt.
   21 : //
   22 : //  Reference:
   23 : //
   24 : //    Numerical modeling of transport problems using freefem++ software -
   25 : //    with examples in biology, CFD, traffic flow and energy transfer,
   26 : //    HAL id: cel-00842234
   27 : //    https://cel.archives-ouvertes.fr/cel-00842234
   28 : //
   29 : cout << "\n";
   30 : cout << "laplace_circle():\n";
   31 : cout << "  FreeFem++ version:\n";
   32 : cout << "  Solve the Laplace equation inside the unit circ
  ... : le.\n";
   33 : 
   34 : real epsilon = 1.0E-02;
   35 : //
   36 : //  Define the region.
   37 : //
   38 : border domega ( t = 0.0, 2.0 * pi ) { x = cos(t); y = sin(t); }
   39 : //
   40 : //  Mesh the region.
   41 : //
   42 : mesh Th = buildmesh ( domega ( 100 ) );
   43 : //
   44 : //  Plot the mesh.
   45 : //
   46 : plot ( Th, wait = true, ps = "laplace_circle_mesh.ps" );
   47 : //
   48 : //  Define the finite element space.
   49 : //
   50 : fespace Vh ( Th, P1 );
   51 : Vh uh;
   52 : Vh vh;
   53 : 
   54 : func f = 1.0;
   55 : 
   56 : real cpu1 = clock ( );
   57 : 
   58 : solve poisson ( uh, vh, solver = LU ) =
   59 :   int2d ( Th ) ( dx ( uh ) * dx ( vh ) + dy ( uh ) * dy ( vh ) )
   60 : + int1d ( Th, domega ) ( epsilon * uh * vh )
   61 : - int2d ( Th ) ( f * vh );
   62 : 
   63 : real cpu2 = clock ( );
   64 : 
   65 : cout << "  CPU seconds = " << cpu2 - cpu1 << "\n";
   66 : //
   67 : //  Plot the solution.
   68 : //
   69 : plot ( uh, nbiso = 50, fill = false, value = 1.0, wait = true, 
   70 :   ps = "laplace_circle_uh.ps" );
   71 : //
   72 : //  Terminate.
   73 : //
   74 : cout << "\n";
   75 : cout << "laplace_circle():\n";
   76 : cout << "  Normal end of execution.\n";
   77 : 
   78 : exit ( 0 );
   79 : 
   80 :  sizestack + 1024 =1856  ( 832 )


laplace_circle():
  FreeFem++ version:
  Solve the Laplace equation inside the unit circle.
  --  mesh:  Nb of Triangles =   1750, Nb of Vertices 926
  SkyLineMatrix: size pL/pU: 926 28862 28862 moy=31.1685
  -- Solve : 
          min 49.9751  max 50.2254
  CPU seconds = 0.053975

laplace_circle():
  Normal end of execution.
  current line = 78
exit(0)
 err code 0 ,  mpirank 0
 CodeAlloc : nb ptr  3920,  size :522976 mpirank: 0
Ok: Normal End