Re: [Getfem-users] Interpolation

[Giovani]

Yves

Using that piece of code with the mesh correspondences you gave me, I 
played with the program and found out the error: I was supposing that 
the numeration of the getfem::mesh points and getfem::mesh_fem dofs were 
the same. Once I figured this out, it was simple to write a class that 
would map these correspondences, thus allowing the program to work as it 
should. That's why nodes far away were moving when they should not.

Thank you very much!

Best,

Giovani


Renard Yves escreveu:
> 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
> -------------------------------------------------------------------------
>
>    
>
>
>
>
>
>
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