-- FreeFem++ v4.14 (mer. 06 mars 2024 16:59:04 CET - git v4.14-1-g2b2052ae)
   file : poisson_1d.edp
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  poisson_1d.edp
    2 : //
    3 : //  Discussion:
    4 : //
    5 : //    Solve the Poisson equation over a 1D interval.
    6 : //
    7 : //    - uxx + u = x, 0 < x < 1
    8 : //    u(0) = u(1) = 0
    9 : //
   10 : //    Exact solution is u(x) = x - sinh(x)/sinh(1)
   11 : //
   12 : //  Licensing:
   13 : //
   14 : //    This code is distributed under the MIT license.
   15 : //
   16 : //  Modified:
   17 : //
   18 : //    25 July 2015
   19 : //
   20 : //  Reference:
   21 : //
   22 : //    Frederic Hecht,
   23 : //    Freefem++,
   24 : //    Third Edition, version 3.22
   25 : //
   26 : cout << "\n";
   27 : cout << "poisson_1d():\n";
   28 : cout << "  FreeFem++ version\n";
   29 : cout << "  Trick FreeFem++ into solving a 1D Poisson probl
  ... : em.\n";
   30 : //
   31 : //  Define the 1D problem on a long rectangular strip.
   32 : //  Use 100 intervals in X, and 1 in Y.
   33 : //  The parameters X and Y run from 0 to 1.
   34 : //  The [ ] option allows us to rescale X or Y.
   35 : //
   36 : int n = 100;
   37 : mesh Th = square ( n, 1, [ x, (-1+2*y) / 10 ] );
   38 : //
   39 : //  Plot the mesh.
   40 : //
   41 : plot ( Th, wait = true, aspectratio = 1, ps = "poisson_1d_mesh.ps" );
   42 : //
   43 : //  Define Vh, the finite element space defined over Th, using P1 basis functions.
   44 : //
   45 : fespace Vh ( Th, P1 );
   46 : //
   47 : //  Define u and v, piecewise P1 continuous functions over Th.
   48 : //
   49 : Vh u, v;
   50 : //
   51 : //  Define f, the right hand side function.
   52 : //
   53 : func f = x;
   54 : //
   55 : //  Request a solution of the discrete weak system.
   56 : //  Note that the boundary condition is included, 
   57 : //  defined on sides 2 and 4 of the square boundary.
   58 : //
   59 : solve Poisson ( u, v, solver = LU ) 
   60 :   = int2d(Th) ( dx(u)*dx(v) + u*v )
   61 :   - int2d(Th) ( f*v )
   62 :   + on ( 2, 4, u = 0.0 );
   63 : //
   64 : //  Plot the solution.
   65 : //
   66 : plot ( u, wait = true, dim = 3, fill = true, ps = "poisson_1d_u.ps" );
   67 : //
   68 : //  Save the mesh file.
   69 : //
   70 : savemesh ( Th, "poisson_1d.msh" );
   71 : //
   72 : //  Terminate.
   73 : //
   74 : cout << "\n";
   75 : cout << "poisson_1d():\n";
   76 : cout << "  Normal end of execution.\n";
   77 : 
   78 : exit ( 0 );
   79 : 
   80 :  sizestack + 1024 =1744  ( 720 )


poisson_1d():
  FreeFem++ version
  Trick FreeFem++ into solving a 1D Poisson problem.
  -- Square mesh : nb vertices  =202 ,  nb triangles = 200 ,  nb boundary edges 202
  SkyLineMatrix: size pL/pU: 202 10401 10401 moy=51.4901
  -- Solve : 
          min 1.48326e-32  max 0.0585228
  number of required edges : 0

poisson_1d():
  Normal end of execution.
  current line = 78
exit(0)
 err code 0 ,  mpirank 0
 CodeAlloc : nb ptr  3890,  size :520928 mpirank: 0
Ok: Normal End