-- FreeFem++ v4.14 (mer. 06 mars 2024 16:59:04 CET - git v4.14-1-g2b2052ae)
   file : membrane.edp
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  membrane.edp
    2 : //
    3 : //  Discussion:
    4 : //
    5 : //    Let an ellipse have semimajor axis 2 and semiminor axis 1:
    6 : //      (x/2)^2 + (y/1)^2 = 1.
    7 : //    Let Gamma1 be the ellipse boundary from 0 to 4pi/3, and
    8 : //    Gamm2 the boundary from 4pi/3 to 2pi.
    9 : //
   10 : //    Solve:
   11 : //      -uxx - uyy = f in Gamma1 + Gamma2,
   12 : //      u = x on Gamma1.
   13 : //      du/dn = 0, natural boundary condition on Gamma2.
   14 : //
   15 : //  Licensing:
   16 : //
   17 : //    This code is distributed under the MIT license.
   18 : //
   19 : //  Modified:
   20 : //
   21 : //    18 June 2015
   22 : //
   23 : //  Reference:
   24 : //
   25 : //    Frederic Hecht,
   26 : //    Freefem++,
   27 : //    Third Edition, version 3.22
   28 : //
   29 : cout << "\n";
   30 : cout << "membrane():\n";
   31 : cout << "  freefem++ version\n";
   32 : cout << "  Model the deflection of an elastic membrane ins
  ... : ide an ellipse..\n";
   33 : //
   34 : //  Define Gamma1 and Gamma2, the boundaries.
   35 : //  A and B are the lengths of the semimajor and semiminor axes:
   36 : //  THETA specifies the angle at which we switch from GAMMA1 to GAMMA2.
   37 : //
   38 : real a = 2.0;
   39 : real b = 1.0;
   40 : real theta = 4.0 * pi / 3.0;
   41 : border Gamma1 ( t = 0, theta )    { x = a * cos(t); y = b*sin(t); }
   42 : border Gamma2 ( t = theta, 2*pi ) { x = a * cos(t); y = b*sin(t); }
   43 : //
   44 : //  Th: the triangulation of the "left" side of the boundaries.
   45 : //
   46 : mesh Th = buildmesh ( Gamma1(100) + Gamma2(50) );
   47 : //
   48 : //  Plot the mesh.
   49 : //
   50 : plot ( Th, wait = true, ps = "membrane_mesh.ps", cmm = "membrane mesh" );
   51 : //
   52 : //  Define Vh, the finite element space defined over Th, using P2 basis functions.
   53 : //
   54 : fespace Vh ( Th, P2 );
   55 : //
   56 : //  Define U, V, and F, piecewise P2 continuous functions over Th.
   57 : //  F is a constant function.
   58 : //
   59 : Vh u;
   60 : Vh v;
   61 : Vh f = 1.0;
   62 : //
   63 : //  Define G, a function for the Dirichlet boundary conditions.
   64 : //
   65 : func g = x;
   66 : //
   67 : //  Define the weak form of the PDE.
   68 : //
   69 : problem poisson ( u, v ) 
   70 :   = int2d ( Th ) ( dx(u)*dx(v) + dy(u)*dy(v) )
   71 :   - int2d ( Th ) ( f * v ) 
   72 :   + on ( Gamma1, u = g );
   73 : //
   74 : //  Solve the PDE.
   75 : //
   76 : poisson;
   77 : //
   78 : //  Plot the solution.
   79 : //
   80 : plot ( u, fill = true, wait = true, 
   81 :   ps = "membrane_u.ps", cmm = "membrane solution" );
   82 : //
   83 : //  Save the mesh file.
   84 : //
   85 : savemesh ( Th, "membrane.msh" );
   86 : //
   87 : //  Terminate.
   88 : //
   89 : cout << "\n";
   90 : cout << "membrane():\n";
   91 : cout << "  Normal end of execution.\n";
   92 : 
   93 : exit ( 0 );
   94 :  sizestack + 1024 =1896  ( 872 )


membrane():
  freefem++ version
  Model the deflection of an elastic membrane inside an ellipse..
  --  mesh:  Nb of Triangles =   2568, Nb of Vertices 1360
  -- Solve : 
          min -2  max 2
  number of required edges : 0

membrane():
  Normal end of execution.
  current line = 93
exit(0)
 err code 0 ,  mpirank 0
 CodeAlloc : nb ptr  3951,  size :523960 mpirank: 0
Ok: Normal End