-- FreeFem++ v4.6 (Thu Apr  2 15:47:38 CEST 2020 - git v4.6)
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  Discussion:
    2 : //
    3 : //    -uxx-uyy = f on the unit square.
    4 : //    u = g on the boundary.
    5 : //
    6 : //    f = - gxx - gyy
    7 : //    g = exp(-alpha*(x-xc)^2+(y-yc)^2)
    8 : //
    9 : //    Suggested parameter values:
   10 : //    * alpha = 1000,   (xc,yc) = (0.5,0.5)
   11 : //    * alpha = 100000, (xc,yc) = (0.51,0.117)
   12 : //
   13 : //  Location:
   14 : //
   15 : //    http://people.sc.fsu.edu/~jburkardt/freefem_src/mitchell_04/mitchell_04b.edp
   16 : //
   17 : //  Licensing:
   18 : //
   19 : //    This code is distributed under the GNU LGPL license.
   20 : //
   21 : //  Modified:
   22 : //
   23 : //    17 December 2014
   24 : //
   25 : //  Author:
   26 : //
   27 : //    John Burkardt
   28 : //
   29 : //  Reference:
   30 : //
   31 : //    Frederic Hecht,
   32 : //    Freefem++,
   33 : //    Third Edition, version 3.22
   34 : //
   35 : //    William Mitchell,
   36 : //    A collection of 2D elliptic problems for testing adaptive
   37 : //    grid refinement algorithms,
   38 : //    Applied Mathematics and Computation,
   39 : //    Volume 220, 1 September 2013, pages 350-364.
   40 : //
   41 : cout << "\n";
   42 : cout << "mitchell_04a\n";
   43 : cout << "  FreeFem++ version\n";
   44 : cout << "  The Peak problem\n";
   45 : 
   46 : border bottom ( t = 0.0, 1.0 )   { x = t;   y = 0.0;  label = 1; }
   47 : border right  ( t = 0.0, 1.0 )   { x = 1.0; y = t;    label = 1; }
   48 : border top    ( t = 1.0, 0.0 )   { x = t;   y = 1.0;  label = 1; }
   49 : border left   ( t = 1.0, 0.0 )   { x = 0.0; y = t;    label = 1; }
   50 : //
   51 : //  Define Th, the triangulation of the "left" side of the boundaries.
   52 : //
   53 : int n = 20;
   54 : mesh Th = buildmesh ( bottom ( n ) + right ( n ) + top ( n ) + left ( n ) );
   55 : //
   56 : //  Define Vh, the finite element space defined over Th, using P1 basis functions.
   57 : //
   58 : fespace Vh ( Th, P1 );
   59 : //
   60 : //  Define U, V, and F, piecewise continuous functions over Th.
   61 : //
   62 : Vh u;
   63 : Vh v;
   64 : //
   65 : //  Define problem parameters.
   66 : //
   67 : real xc = 0.51;
   68 : real yc = 0.117;
   69 : real alpha = 100000.0;
   70 : //
   71 : //  Define the right hand side function F.
   72 : //
   73 : func f = 4.0 * alpha * ( 1.0 - alpha * ( pow ( x - xc, 2 ) + pow ( y - yc, 2 ) ) )
   74 :   * exp ( - alpha * ( pow ( x - xc, 2 ) + pow ( y - yc, 2 ) ) );
   75 : //
   76 : //  Define the boundary function G.
   77 : //
   78 : func g = exp ( - alpha * ( pow ( x - xc, 2 ) + pow ( y - yc, 2 ) ) );
   79 : //
   80 : //  Solve the variational problem.
   81 : //
   82 : solve Laplace ( u, v ) 
   83 :   = int2d ( Th ) ( dx(u)*dx(v) + dy(u)*dy(v) )
   84 :   - int2d ( Th ) ( f * v ) 
   85 :   + on ( 1, u = g );
   86 : //
   87 : //  Plot the solution.
   88 : //
   89 : plot ( u, wait = 1, fill = true, ps = "mitchell_04b_u.eps" );
   90 : //
   91 : //  Plot the mesh.
   92 : //
   93 : plot ( Th, wait = 1, ps = "mitchell_04b_mesh.eps" );
   94 : //
   95 : //  Save the mesh file.
   96 : //
   97 : savemesh ( Th, "mitchell_04b.msh" );
   98 : //
   99 : //  Terminate.
  100 : //
  101 : cout << "\n";
  102 : cout << "mitchell_04b\n";
  103 : cout << "  Normal end of execution.\n";
  104 : 
  105 : cout << "mitchell_04a\n";
  106 : cout << "  Normal end of execution.\n";
  107 :  sizestack + 1024 =3672  ( 2648 )


mitchell_04a
  FreeFem++ version
  The Peak problem
  --  mesh:  Nb of Triangles =    952, Nb of Vertices 517
  -- Solve : 
          min -0.012953  max -1.62203e-65
  number of required edges : 0

mitchell_04b
  Normal end of execution.
mitchell_04a
  Normal end of execution.
times: compile 0.005856s, execution 0.320936s,  mpirank:0
 CodeAlloc : nb ptr  3682,  size :479440 mpirank: 0
Ok: Normal End