-- FreeFem++ v4.14 (mer. 06 mars 2024 16:59:04 CET - git v4.14-1-g2b2052ae)
   file : laplace_periodic.edp
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  laplace_periodic.edp
    2 : //
    3 : //  Discussion:
    4 : //
    5 : //    Solve the Laplace equation in the square with periodic boundary
    6 : //    conditions, and writes the resulting data to files, using the 
    7 : //    ffmatlib() interface, for subsequent graphics processing by MATLAB or Octave.
    8 : //
    9 : //  Licensing:
   10 : //
   11 : //    Copyright (C) 2018 Chloros2 <chloros2@gmx.de>
   12 : //
   13 : //    This program is free software: you can redistribute it and/or modify it
   14 : //    under the terms of the GNU General Public License as published by
   15 : //    the Free Software Foundation, either version 3 of the License, or
   16 : //    (at your option) any later version.
   17 : //
   18 : //    This program is distributed in the hope that it will be useful, but
   19 : //    WITHOUT ANY WARRANTY; without even the implied warranty of
   20 : //    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   21 : //    GNU General Public License for more details.
   22 : //
   23 : //    You should have received a copy of the GNU General Public License
   24 : //    along with this program.  If not, see
   25 : //    <https://www.gnu.org/licenses/>.
   26 : //
   27 : //  Modified:
   28 : //
   29 : //    2018-05-19
   30 : //
   31 : // Author: 
   32 : //
   33 : //   Chloros2 <chloros2@gmx.de>
   34 : //
   35 : include "ffmatlib.idp"/*ffmatlib.idp Export Macros (Plot Solutions for Matlab and Octave)
    2 :  *
    3 :  * Author: Chloros2 <chloros2@gmx.de>
    4 :  * Created: 2018-12-21
    5 :  *
    6 :  *   This file is part of the ffmatlib which is hosted at
    7 :  *   https://github.com/samplemaker/freefem_matlab_octave_plot
    8 :  *
    9 :  * Copyright (C) 2018 Chloros2 <chloros2@gmx.de>
   10 :  *
   11 :  * This program is free software: you can redistribute it and/or modify it
   12 :  * under the terms of the GNU General Public License as published by
   13 :  * the Free Software Foundation, either version 3 of the License, or
   14 :  * (at your option) any later version.
   15 :  *
   16 :  * This program is distributed in the hope that it will be useful, but
   17 :  * WITHOUT ANY WARRANTY; without even the implied warranty of
   18 :  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   19 :  * GNU General Public License for more details.
   20 :  *
   21 :  * You should have received a copy of the GNU General Public License
   22 :  * along with this program.  If not, see
   23 :  * <https://www.gnu.org/licenses/>.
   24 :  *
   25 :  */
   26 : 
   27 : //Save finite element connectivity (j-th degree of freedom for i-th element)
   28 : macro ffSaveVh(Th, Vh, filename){
   29 #   {
   30 #   ofstream file(filename);
   31 #   file.precision(10);
   32 #   for (int i=0; i<Th.nt; i++){
   33 #     for (int j=0; j<Vh.ndofK; j++){
   34 #       file << Vh(i,j) << "\n";
   35 #     }
   36 #   }
   37 #   }
   38 # }  )  //EOM
   39 : 
   40 : //Save FE Space data
   41 : macro ffSaveData(u, filename){
   42 #   {
   43 #   ofstream file(filename);
   44 #   file.precision(10);
   45 #   for (int j=0; j<u[].n; j++){
   46 #     file << u[][j] << endl;
   47 #   }
   48 #   }
   49 # }  )  //EOM
   50 : 
   51 : macro ffSaveData2(u1, u2, filename){
   52 #   {
   53 #   ofstream file(filename);
   54 #   int datalen=u1[].n;
   55 #   if (u2[].n!=datalen){
   56 #     cout << "error: arguments must have same size" << endl;
   57 #     exit(1);
   58 #   }
   59 #   file.precision(10);
   60 #   for (int j=0; j<datalen; j++){
   61 #     file << u1[][j] << " " << u2[][j] << endl;
   62 #   }
   63 #   }
   64 # }  )  //EOM
   65 : 
   66 : macro ffSaveData3(u1, u2, u3, filename){
   67 #   {
   68 #   ofstream file(filename);
   69 #   int datalen=u1[].n;
   70 #   if ((u2[].n!=datalen) | (u3[].n!=datalen)){
   71 #     cout << "error: arguments must have same size" << endl;
   72 #     exit(1);
   73 #   }
   74 #   file.precision(10);
   75 #   for (int j=0; j<datalen; j++){
   76 #     file << u1[][j] << " " << u2[][j] << " " << u3[][j] << endl;
   77 #   }
   78 #   }
   79 # }  )  //EOM
   80 : 
   81 : macro ffSaveData4(u1, u2, u3, u4, filename){
   82 #   {
   83 #   ofstream file(filename);
   84 #   int datalen=u1[].n;
   85 #   if ((u2[].n!=datalen) | (u3[].n!=datalen) | (u4[].n!=datalen)){
   86 #     cout << "error: arguments must have same size" << endl;
   87 #     exit(1);
   88 #   }
   89 #   file.precision(10);
   90 #   for (int j=0; j<datalen; j++){
   91 #     file << u1[][j] << " " << u2[][j] << " " << u3[][j] << " " << u4[][j] << endl;
   92 #   }
   93 #   }
   94 # }  )  //EOM
   95 : 
   36 : 
   37 : cout << endl;
   38 : cout << "laplace_periodic():" << endl;
   39 : cout << "  FreeFem++ version." << endl;
   40 : cout << "  Solve the Laplace equation on a periodic domain
  ... : ." << endl;
   41 : cout << "  Using the ffmatlib interface, export the data f
  ... : or graphic" << endl;
   42 : cout << "  processing by MATLAB/Octave." << endl;
   43 : //
   44 : //  The region is 2*pi x 2*pi square.
   45 : //
   46 : mesh Th = square ( 30, 30, [ 2 * x * pi, 2 * y * pi ] );
   47 : //
   48 : //  Define a finite element space of periodic elements.
   49 : //
   50 : fespace Vh ( Th, P1, periodic = [ [ 2, y ], [ 4, y ], [ 1, x ], [ 3, x ] ] );
   51 : 
   52 : Vh u, v;
   53 : 
   54 : func f = sin ( x + pi / 4.0 ) * cos ( y + pi / 2.0 );
   55 : 
   56 : problem laplace ( u, v ) = int2d(Th)(dx(u)*dx(v)+dy(u)*dy(v))
   57 :                       +int2d(Th)(-f*v);
   58 : 
   59 : laplace;
   60 : 
   61 : plot ( u, value = true, fill = true,
   62 :   ps = "laplace_periodic.ps" );
   63 : //
   64 : //  Write out data for later processing by MATLAB/Octave.
   65 : //  
   66 : savemesh ( Th, "laplace_periodic.msh" );
   67 : ffSaveVh ( Th, Vh, "laplace_periodic_vh.txt" )
   29 @   
   30 @    
   31 @   
   32 @       
   33 @         
   34 @           
   35 @     
   36 @   
   37 @   
   38 @  {
   29 @   {
   30 @   ofstream file( "laplace_periodic_vh.txt");
   31 @   file.precision(10);
   32 @   for (int i=0; i< Th.nt; i++){
   33 @     for (int j=0; j< Vh.ndofK; j++){
   34 @       file <<  Vh(i,j) << "\n";
   35 @     }
   36 @   }
   37 @   }
   38 @ } ;
   68 : ffSaveData ( u, "laplace_periodic_data.txt" )
   42 @   
   43 @    
   44 @   
   45 @       
   46 @         
   47 @   
   48 @   
   49 @  {
   42 @   {
   43 @   ofstream file( "laplace_periodic_data.txt");
   44 @   file.precision(10);
   45 @   for (int j=0; j< u[].n; j++){
   46 @     file <<  u[][j] << endl;
   47 @   }
   48 @   }
   49 @ } ;
   69 : //
   70 : //  Terminate.
   71 : //
   72 : cout << "\n";
   73 : cout << "laplace_periodic():\n";
   74 : cout << "  Normal end of execution.\n";
   75 : 
   76 : exit ( 0 );
   77 : 
   78 :  sizestack + 1024 =2144  ( 1120 )


laplace_periodic():
  FreeFem++ version.
  Solve the Laplace equation on a periodic domain.
  Using the ffmatlib interface, export the data for graphic
  processing by MATLAB/Octave.
  -- Square mesh : nb vertices  =961 ,  nb triangles = 1800 ,  nb boundary edges 120
  -- Solve : 
          min -1.85337  max -0.863816
  number of required edges : 0

laplace_periodic():
  Normal end of execution.
  current line = 76
exit(0)
 err code 0 ,  mpirank 0
 CodeAlloc : nb ptr  3984,  size :522832 mpirank: 0
Ok: Normal End