-- FreeFem++ v4.14 (mer. 06 mars 2024 16:59:04 CET - git v4.14-1-g2b2052ae)
   file : heat.edp
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : // heat.edp
    2 : //
    3 : //  Discussion:
    4 : //
    5 : //    Time dependent heat equation with inhomogeneous Dirichlet
    6 : //    and Neumann flux boundary conditions.
    7 : //
    8 : //  Licensing:
    9 : //
   10 : //    This code is distributed under the MIT license.
   11 : //
   12 : //  Modified:
   13 : //
   14 : //    14 June 2015
   15 : //
   16 : //  Author:
   17 : //
   18 : //    Florian De Vuyst
   19 : //
   20 : //  Reference:
   21 : //
   22 : //    Florian De Vuyst,
   23 : //    Numerical modeling of transport problems using freefem++ software -
   24 : //    with examples in biology, CFD, traffic flow and energy transfer,
   25 : //    HAL id: cel-00842234
   26 : //    https://cel.archives-ouvertes.fr/cel-00842234
   27 : //
   28 : //  Parameters:
   29 : //
   30 : //    real KAPPA, the thermal conductivity.
   31 : //
   32 : //    real THETA, the initial and boundary temperature.
   33 : //
   34 : real theta = 20.0;
   35 : real kappa = 0.1;
   36 : real dt = 0.5;
   37 : 
   38 : cout << "\n";
   39 : cout << "heat():\n";
   40 : cout << "  FreeFem++ version.\n";
   41 : cout << "  Solve the time dependent heat equation with inh
  ... : omogeneous\n";
   42 : cout << "  Dirichlet and Neumann flux boundary conditions.
  ... : \n";
   43 : //
   44 : //  Boundary.
   45 : //
   46 : border Gamma1 ( t = 0.0, 2.0 * pi ) { x = cos ( t ); y = sin ( t ); }
   47 : border Gamma2 ( t = 0.0, 1.0      ) { x = -0.5 + t; y = - 0.3; }
   48 : //
   49 : //  Define the mesh.
   50 : //
   51 : mesh Th = buildmesh ( Gamma1 ( 100 ) + Gamma2 ( 60 ) );
   52 : plot ( Th, wait = true, ps = "heat_mesh.ps" );
   53 : //
   54 : //  Define the finite element space.
   55 : //
   56 : fespace Vh ( Th, P1 );
   57 : Vh uh;
   58 : Vh uold;
   59 : Vh vh;
   60 : //
   61 : //  The solution is taken to be constant at the initial time,
   62 : //  and at the "previous" timestep.
   63 : //
   64 : uh = theta;
   65 : uold = theta;
   66 : //
   67 : //  Define the weak form of the heat equation.
   68 : //
   69 : problem heatstep ( uh, vh, solver = LU ) = 
   70 :   int2d ( Th ) ( uh * vh / dt )
   71 : - int2d ( Th ) ( uold * vh / dt )
   72 : + int2d ( Th ) ( kappa * dx ( uh ) * dx ( vh )
   73 :                + kappa * dy ( uh ) * dy ( vh ) )
   74 : + int1d ( Th, Gamma1 ) ( kappa * vh )
   75 : + on ( Gamma2, uh = theta );
   76 : //
   77 : //  Perform 6 timesteps.
   78 : //
   79 : for ( int it = 1; it <= 6; it++ )
   80 : {
   81 :   heatstep;
   82 :   plot ( uh, nbiso = 50, fill = true, value = true, wait = true, 
   83 :     ps = "heat_uh_" + it + ".ps" );
   84 :   uold = uh;
   85 : }
   86 : //
   87 : //  Terminate.
   88 : //
   89 : cout << "\n";
   90 : cout << "heat():\n";
   91 : cout << "  Normal end of execution.\n";
   92 : 
   93 : exit ( 0 );
   94 : 
   95 :  sizestack + 1024 =2704  ( 1680 )


heat():
  FreeFem++ version.
  Solve the time dependent heat equation with inhomogeneous
  Dirichlet and Neumann flux boundary conditions.
  --  mesh:  Nb of Triangles =   5236, Nb of Vertices 2669
  SkyLineMatrix: size pL/pU: 2669 173034 173034 moy=64.831
  -- Solve : 
          min 19.7447  max 20
  SkyLineMatrix: size pL/pU: 2669 173034 173034 moy=64.831
  -- Solve : 
          min 19.5993  max 20
  SkyLineMatrix: size pL/pU: 2669 173034 173034 moy=64.831
  -- Solve : 
          min 19.4794  max 20
  SkyLineMatrix: size pL/pU: 2669 173034 173034 moy=64.831
  -- Solve : 
          min 19.3721  max 20
  SkyLineMatrix: size pL/pU: 2669 173034 173034 moy=64.831
  -- Solve : 
          min 19.2731  max 20
  SkyLineMatrix: size pL/pU: 2669 173034 173034 moy=64.831
  -- Solve : 
          min 19.1807  max 20

heat():
  Normal end of execution.
  current line = 93
exit(0)
 err code 0 ,  mpirank 0
 CodeAlloc : nb ptr  3996,  size :527112 mpirank: 0
Ok: Normal End