-- FreeFem++ v4.6 (Thu Apr  2 15:47:38 CEST 2020 - git v4.6)
 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 : //  Location:
   13 : //
   14 : //    http://people.sc.fsu.edu/~jburkardt/freefem_src/poisson_1d/poisson_1d.edp
   15 : //
   16 : //  Licensing:
   17 : //
   18 : //    This code is distributed under the GNU LGPL license.
   19 : //
   20 : //  Modified:
   21 : //
   22 : //    25 July 2015
   23 : //
   24 : //  Reference:
   25 : //
   26 : //    Frederic Hecht,
   27 : //    Freefem++,
   28 : //    Third Edition, version 3.22
   29 : //
   30 : cout << "\n";
   31 : cout << "poisson_1d\n";
   32 : cout << "  FreeFem++ version\n";
   33 : cout << "  Trick FreeFem++ into solving a 1D Poisson probl
  ... : em.\n";
   34 : //
   35 : //  Define the 1D problem on a long rectangular strip.
   36 : //  Use 100 intervals in X, and 1 in Y.
   37 : //  The parameters X and Y run from 0 to 1.
   38 : //  The [ ] option allows us to rescale X or Y.
   39 : //
   40 : int n = 100;
   41 : mesh Th = square ( n, 1, [ x, (-1+2*y) / 10 ] );
   42 : //
   43 : //  Plot the mesh.
   44 : //
   45 : plot ( Th, wait = 1, aspectratio = 1, ps = "poisson_1d_mesh.ps" );
   46 : //
   47 : //  Define Vh, the finite element space defined over Th, using P1 basis functions.
   48 : //
   49 : fespace Vh ( Th, P1 );
   50 : //
   51 : //  Define u and v, piecewise P1 continuous functions over Th.
   52 : //
   53 : Vh u, v;
   54 : //
   55 : //  Define f, the right hand side function.
   56 : //
   57 : func f = x;
   58 : //
   59 : //  Request a solution of the discrete weak system.
   60 : //  Note that the boundary condition is included, 
   61 : //  defined on sides 2 and 4 of the square boundary.
   62 : //
   63 : solve Poisson ( u, v, solver = LU ) 
   64 :   = int2d(Th) ( dx(u)*dx(v) + u*v )
   65 :   - int2d(Th) ( f*v )
   66 :   + on ( 2, 4, u = 0.0 );
   67 : //
   68 : //  Plot the solution.
   69 : //
   70 : plot ( u, wait = 1, dim = 3, fill = 1, ps = "poisson_1d_u.ps" );
   71 : //
   72 : //  Save the mesh file.
   73 : //
   74 : savemesh ( Th, "poisson_1d.msh" );
   75 : //
   76 : //  Terminate.
   77 : //
   78 : cout << "\n";
   79 : cout << "poisson_1d\n";
   80 : cout << "  Normal end of execution.\n";
   81 : 
   82 :  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.
times: compile 0.004571s, execution 0.005494s,  mpirank:0
 CodeAlloc : nb ptr  3524,  size :472912 mpirank: 0
Ok: Normal End