-- FreeFem++ v4.14 (mer. 06 mars 2024 16:59:04 CET - git v4.14-1-g2b2052ae)
   file : schwarz_overlap.edp
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  schwarz_overlap.edp
    2 : //
    3 : //  Discussion:
    4 : //
    5 : //    This script implements the Schwarz method.
    6 : //    In this example, the domain is decomposed into two subdomains,
    7 : //    with overlap.
    8 : //
    9 : //  Licensing:
   10 : //
   11 : //    This code is distributed under the MIT license.
   12 : //
   13 : //  Modified:
   14 : //
   15 : //    03 February 2016
   16 : //
   17 : //  Author:
   18 : //
   19 : //    Frederic Hecht
   20 : //
   21 : //  Reference:
   22 : //
   23 : //    Frederic Hecht,
   24 : //    Freefem++,
   25 : //    Third Edition, version 3.22
   26 : //
   27 : cout << "\n";
   28 : cout << "schwarz_overlap():\n";
   29 : cout << "  FreeFem++ version\n";
   30 : cout << "  The Schwarz method of domain decomposition is u
  ... : sed, replacing\n";
   31 : cout << "  the problem domain by two overlapping subdomain
  ... : s.\n";
   32 : //
   33 : //  Region labels.
   34 : //
   35 : int inner = 2;
   36 : int outer = 1;
   37 : //
   38 : //  Define the border.
   39 : //
   40 : border a  ( t = 1,    2 )    { x = t;         y = 0;         label = outer; };
   41 : border b  ( t = 0,    1 )    { x = 2;         y = t;         label = outer; };
   42 : border c  ( t = 2,    0 )    { x = t;         y = 1;         label = outer; };
   43 : border d  ( t = 1,    0 )    { x = 1-t;       y = t;         label = inner; };
   44 : border e  ( t = 0,    pi/2 ) { x = cos ( t ); y = sin ( t ); label = inner; };
   45 : border e1 ( t = pi/2, 2*pi ) { x = cos ( t ); y = sin ( t ); label = outer; }; 
   46 : 
   47 : int n = 4;
   48 : mesh Th1 = buildmesh ( a ( 5 * n ) + b ( 5 * n ) + c ( 10 * n ) + d ( 5 * n ) );
   49 : mesh Th2 = buildmesh ( e ( 5 * n ) + e1 ( 25 * n ) );
   50 : //
   51 : //  Plot the mesh.
   52 : //
   53 : plot ( Th1, Th2, wait = true, ps = "schwarz_overlap_mesh.eps" );
   54 : //
   55 : //  Define the finite element spaces.
   56 : //
   57 : int i = 0;
   58 : 
   59 : fespace Vh1 ( Th1, P1 );
   60 : Vh1 u1 = 0.0;
   61 : Vh1 v1;
   62 : 
   63 : fespace Vh2 ( Th2, P1 );
   64 : Vh2 u2 = 0.0;
   65 : Vh2 v2;
   66 : 
   67 : problem pb1 ( u1, v1, init = i, solver = Cholesky ) = 
   68 :     int2d ( Th1 ) ( dx ( u1 ) * dx ( v1 ) + dy ( u1 ) * dy ( v1 ) )
   69 :   + int2d ( Th1 ) ( -v1 )
   70 :   + on ( inner, u1 = u2 ) 
   71 :   + on ( outer, u1 = 0.0 );
   72 : 
   73 : problem pb2 ( u2, v2, init = i, solver = Cholesky ) = 
   74 :     int2d ( Th2 ) ( dx ( u2 ) * dx ( v2 ) + dy ( u2 ) * dy ( v2 ) )
   75 :   + int2d ( Th2 ) ( -v2 ) 
   76 :   + on ( inner, u2 = u1 )
   77 :   + on ( outer, u2 = 0.0 ) ;
   78 : 
   79 : for ( i = 0; i < 10; i++ ) 
   80 : {   
   81 :   pb1; 
   82 :   pb2;
   83 :   plot ( u1, u2, wait = true );
   84 : };
   85 : 
   86 : plot ( u1, u2, ps = "schwarz_overlap_u.eps" );
   87 : //
   88 : //  Terminate.
   89 : //
   90 : cout << "\n";
   91 : cout << "schwarz_overlap():\n";
   92 : cout << "  Normal end of execution.\n";
   93 : 
   94 : exit ( 0 );
   95 :  sizestack + 1024 =2368  ( 1344 )


schwarz_overlap():
  FreeFem++ version
  The Schwarz method of domain decomposition is used, replacing
  the problem domain by two overlapping subdomains.
  --  mesh:  Nb of Triangles =   1164, Nb of Vertices 633
  --  mesh:  Nb of Triangles =   2000, Nb of Vertices 1061
  SkyLineMatrix: size pL/pU: 633 12396 12396 moy=19.5829
  -- Solve : 
          min 3.2567e-65  max 0.0949787
  SkyLineMatrix: size pL/pU: 1061 35085 35085 moy=33.0679
  -- Solve : 
          min 2.23119e-32  max 0.258194
  -- Solve : 
          min 4.82284e-63  max 0.15581
  -- Solve : 
          min 2.26832e-32  max 0.270668
  -- Solve : 
          min 4.86586e-63  max 0.197845
  -- Solve : 
          min 2.27815e-32  max 0.274581
  -- Solve : 
          min 4.88084e-63  max 0.210987
  -- Solve : 
          min 2.28138e-32  max 0.276041
  -- Solve : 
          min 4.88615e-63  max 0.215473
  -- Solve : 
          min 2.28249e-32  max 0.276548
  -- Solve : 
          min 4.88805e-63  max 0.217024
  -- Solve : 
          min 2.28288e-32  max 0.276728
  -- Solve : 
          min 4.88873e-63  max 0.217573
  -- Solve : 
          min 2.28302e-32  max 0.276793
  -- Solve : 
          min 4.88898e-63  max 0.217769
  -- Solve : 
          min 2.28307e-32  max 0.276816
  -- Solve : 
          min 4.88907e-63  max 0.21784
  -- Solve : 
          min 2.28309e-32  max 0.276825
  -- Solve : 
          min 4.8891e-63  max 0.217866
  -- Solve : 
          min 2.2831e-32  max 0.276828

schwarz_overlap():
  Normal end of execution.
  current line = 94
exit(0)
 err code 0 ,  mpirank 0
 CodeAlloc : nb ptr  4131,  size :534072 mpirank: 0
Ok: Normal End