-- FreeFem++ v4.6 (Thu Apr  2 15:47:38 CEST 2020 - git v4.6)
 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 : //  Location:
    9 : //
   10 : //    http://people.sc.fsu.edu/~jburkardt/freefem_src/heat/heat.edp
   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 : //  Boundary.
   39 : //
   40 :   border Gamma1 ( t = 0.0, 2.0 * pi ) { x = cos ( t ); y = sin ( t ); }
   41 :   border Gamma2 ( t = 0.0, 1.0      ) { x = -0.5 + t; y = - 0.3; }
   42 : //
   43 : //  Define the mesh.
   44 : //
   45 :   mesh Th = buildmesh ( Gamma1 ( 100 ) + Gamma2 ( 60 ) );
   46 :   plot ( Th, wait = 1, ps = "heat_mesh.ps" );
   47 : //
   48 : //  Define the finite element space.
   49 : //
   50 :   fespace Vh ( Th, P1 );
   51 :   Vh uh;
   52 :   Vh uold;
   53 :   Vh vh;
   54 : //
   55 : //  The solution is taken to be constant at the initial time,
   56 : //  and at the "previous" timestep.
   57 : //
   58 :   uh = theta;
   59 :   uold = theta;
   60 : //
   61 : //  Define the weak form of the heat equation.
   62 : //
   63 :   problem heatstep ( uh, vh, solver = LU ) = 
   64 :     int2d ( Th ) ( uh * vh / dt )
   65 :   - int2d ( Th ) ( uold * vh / dt )
   66 :   + int2d ( Th ) ( kappa * dx ( uh ) * dx ( vh )
   67 :                  + kappa * dy ( uh ) * dy ( vh ) )
   68 :   + int1d ( Th, Gamma1 ) ( kappa * vh )
   69 :   + on ( Gamma2, uh = theta );
   70 : //
   71 : //  Perform 6 timesteps.
   72 : //
   73 :   for ( int it = 1; it <= 6; it++ )
   74 :   {
   75 :     heatstep;
   76 :     plot ( uh, nbiso = 50, fill = 1, value = 1, wait = 1, 
   77 :       ps = "heat_uh_" + it + ".ps" );
   78 :     uold = uh;
   79 :   }
   80 : //
   81 : //  Terminate.
   82 : //
   83 :   cout << "\n";
   84 :   cout << "HEAT:\n";
   85 :   cout << "  Normal end of execution.\n";
   86 : 
   87 :  sizestack + 1024 =2704  ( 1680 )

  --  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.
times: compile 0.004655s, execution 0.432698s,  mpirank:0
 CodeAlloc : nb ptr  3617,  size :478808 mpirank: 0
Ok: Normal End