Re: [Getfem-users] Interpolation

[Renard Yves]

Selon Giovani <address@hidden>:

> Yves:
> 
> Thank you very much for the quick reply!
> 
> I've prepared a simplified version of the program, which I've posted here:
> 
> http://www.ifi.unicamp.br/~gfaccin/download/interpolation.tar.gz
> 

Using a sparse matrix, the following piece of code allows to see the
correspondance between nodes of the small mesh and node of the large mesh:

gmm::row_matrix< gmm::rsvector<double> >
    N( S_meshfem.nb_dof(), L_meshfem.nb_dof()  );
getfem::interpolation( L_meshfem, S_meshfem, N);

for (unsigned i = 0; i < S_meshfem.nb_dof(); ++i) {
  gmm::linalg_traits<gmm::rsvector<double> >::const_iterator
    it = gmm::vect_const_begin(N[i]),
    ite = gmm::vect_const_end(N[i]);
  for (; it != ite; ++it) {
    cout << "S dof " << i << " localized at  " << S_meshfem.point_of_dof(i)
                 << " influenced by L dof " << it.index() << " localized at  "
                 << L_meshfem.point_of_dof(it.index()) << endl;
  }
}

I tried and the result is normal. I did not detect some correspondance between
nodes that are far away from each other.

> This version will load 2 meshes from the disk (which are also provided 
> in the file) and solve their movement equations with a central 
> difference scheme. The calculation's output is sent to the disk in 
> opendx format, and can be viewed using an opendx program that's also 
> provided in the file.
> 
> I've also added the resulting movies for the default situation (happens 
> if you simply compile the program and run, without changing anything), 
> in avi format.
> 
> One curiosity: you said that  "gmm::mult( gmm::transposed(N), S_ax , 
> L_ax); is not strictly speaking an interpolation of the solution on the 
> fine mesh onto the coarse mesh". If I were to build an interpolation 
> matrix, which I call here "N" that strictly speaking does the 
> interpolation, how should I proceed in order to do it?

the function getfem::interpolation( L_meshfem, S_meshfem, N) gives you the
matrix with allows to compute the interpolation of a solution on the large mesh
on the small mesh. i.e. gmm::mult( N, L_az , S_az) really does this
interpolation. The meaning of gmm::mult( gmm::transposed(N), S_az , L_az) is
not strictly speaking speaking an interpolation. If fact, in your case, this
operation will sum the contribution of a lot of point of the small mesh without
making a mean of this contributions. I think you would better use
getfem::interpolation( S_meshfem, L_meshfem, N). (even if there is some
warnings ... !  you can suppress the warning by invoking
dal::set_warning_level(0))



Best,

Yves.

-------------------------------------------------------------------------
  Yves Renard (address@hidden)       tel : (33) 04.72.43.80.11
  Pole de Mathematiques, INSA de Lyon          fax : (33) 04.72.43.85.29
  Institut Camille Jordan - CNRS UMR 5208
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard
-------------------------------------------------------------------------