-- 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 : //    Let an ellipse have semimajor axis 2 and semiminor axis 1:
    4 : //      (x/2)^2 + (y/1)^2 = 1.
    5 : //    Let Gamma1 be the ellipse boundary from 0 to 4pi/3, and
    6 : //    Gamm2 the boundary from 4pi/3 to 2pi.
    7 : //
    8 : //    Solve:
    9 : //      -uxx - uyy = f in Gamma1 + Gamma2,
   10 : //      u = x on Gamma1.
   11 : //      du/dn = 0, natural boundary condition on Gamma2.
   12 : //
   13 : //  Location:
   14 : //
   15 : //    http://people.sc.fsu.edu/~jburkardt/freefem_src/membrane/membrane.edp
   16 : //
   17 : //  Licensing:
   18 : //
   19 : //    This code is distributed under the GNU LGPL license.
   20 : //
   21 : //  Modified:
   22 : //
   23 : //    18 June 2015
   24 : //
   25 : //  Reference:
   26 : //
   27 : //    Frederic Hecht,
   28 : //    Freefem++,
   29 : //    Third Edition, version 3.22
   30 : //
   31 : cout << "\n";
   32 : cout << "membrane:\n";
   33 : cout << "  Solve the Poisson equation on an ellipse.\n";
   34 : //
   35 : //  Define Gamma1 and Gamma2, the boundaries.
   36 : //  A and B are the lengths of the semimajor and semiminor axes:
   37 : //  THETA specifies the angle at which we switch from GAMMA1 to GAMMA2.
   38 : //
   39 : real a = 2.0;
   40 : real b = 1.0;
   41 : real theta = 4.0 * pi / 3.0;
   42 : border Gamma1 ( t = 0, theta )    { x = a * cos(t); y = b*sin(t); }
   43 : border Gamma2 ( t = theta, 2*pi ) { x = a * cos(t); y = b*sin(t); }
   44 : //
   45 : //  Th: the triangulation of the "left" side of the boundaries.
   46 : //
   47 : mesh Th = buildmesh ( Gamma1(100) + Gamma2(50) );
   48 : //
   49 : //  Plot the mesh.
   50 : //
   51 : plot ( Th, wait = true, ps = "membrane_mesh.ps", cmm = "membrane mesh" );
   52 : //
   53 : //  Define Vh, the finite element space defined over Th, using P2 basis functions.
   54 : //
   55 : fespace Vh ( Th, P2 );
   56 : //
   57 : //  Define U, V, and F, piecewise P2 continuous functions over Th.
   58 : //  F is a constant function.
   59 : //
   60 : Vh u;
   61 : Vh v;
   62 : Vh f = 1.0;
   63 : //
   64 : //  Define G, a function for the Dirichlet boundary conditions.
   65 : //
   66 : func g = x;
   67 : //
   68 : //  Define the weak form of the PDE.
   69 : //
   70 : problem poisson ( u, v ) 
   71 :   = int2d ( Th ) ( dx(u)*dx(v) + dy(u)*dy(v) )
   72 :   - int2d ( Th ) ( f * v ) 
   73 :   + on ( Gamma1, u = g );
   74 : //
   75 : //  Solve the PDE.
   76 : //
   77 : poisson;
   78 : //
   79 : //  Plot the solution.
   80 : //
   81 : plot ( u, fill = true, wait = true, 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 :  sizestack + 1024 =1896  ( 872 )


membrane:
  Solve the Poisson equation on 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.
times: compile 0.004188s, execution 1.06127s,  mpirank:0
 CodeAlloc : nb ptr  3576,  size :475752 mpirank: 0
Ok: Normal End