Re: [Getfem-users] Build a mesh with quadrature points

[julien pommier]

Hi Giovani,

You can interpolate a mesh_fem at arbitrary locations using the function

void getfem::interpolation(const mesh_fem &mf_source, mesh_trans_inv &mti,
              const VECTU &U, VECTV &V, bool extrapolation = false)

It is defined in getfem_interpolation.h

Its mesh_trans_inv argument is where you will store the list of global 
coordinates to interpolate. U is the data on mf_source (U.size() == 
mf_source.nb_dof()), V is the interpolated data on the points stored in 
mti (V.size() == mti.nb_points()*mf_source.get_qdim()).

mti is filled like that:

mesh_trans_inv mti(mf_source.linked_mesh());
mti.add_point(base_node(42,42));
etc..

Now if you want to be able to perform this interpolation very quickly 
for a set of data vectors U, you can use the function

getfem::interpolation(const mesh_fem &mf_source,
            mesh_trans_inv &mti,
            const VECTU &U, VECTV &V, MAT &M,
            int version, bool extrapolation = false)

which is very similar, except that it, if you set version to 1, instead 
of filling V, it will fill the (preferably sparse) matrix M in such way 
that each row of M will contain the value of each base function on a 
point of mti. So this is indeed the answer to your first question. And 
of course, when you have that matrix M, you just have to multiply it 
with a vector U to obtain the interpolated values V, so you can perform 
many interpolations very quickly.

I hope I was clear ;)

Best regards,
Julien

Giovani wrote:
> Julien
>
> Thank you very much! That piece of code is helping a lot!
>
> If I may ask, I have another issue that requires enlightenment:
>
> Suppose you have a getfem::mesh, a getfem::mesh_fem linked with the 
> mesh, and a point in global coordinates whose location is not 
> identical to any of the mesh nodes. This point is, however, inside the 
> object that the mesh represents, so I can interpolate data from the 
> mesh nodes to it.
>
> --> How can I evaluate the shape functions of a single, specific 
> getfem::mesh_fem dof at this point's coordinates?
>
> --> If I multiply the result from the previous question by the value 
> of a field prescribed at that dof, I'll then have the contribution of 
> that dof to the interpolation of the field at the point. Just to be 
> sure, this result will be normalized, right? I mean, if I repeat this 
> for all dofs and simply sum the results, I'd obtain the same 
> interpolation that I'd get if I used getfem::interpolation instead, 
> although this explicit sum is probably more computationaly expensive 
> than using getfem::interpolation. Is that it?
>
> Best regards,
>
> Giovani
>
>
>
>
> julien pommier escreveu:
> > Hi Giovani,
> > If you want to retrieve the coordinates of the quadrature points of a 
> > convex cv, you can do:
> >
> >    /* get the approximate integration method for the convex */
> >    getfem::papprox_integration pai
> >      = mim.int_method_of_element(cv)->approx_method();
> >    /* prepare the geotrans_interpolation_context to apply the 
> > geometric transformation */
> >    bgeot::base_matrix G;
> >    bgeot::vectors_to_base_matrix(G, m.points_of_convex(cv));
> >    bgeot::geotrans_interpolation_context c(m.trans_of_convex(cv),
> >                        pai->point(0), G);
> >    /* apply the geotrans to each point of the integration method */
> >    for (size_type j = 0; j < pai->nb_points_on_convex(); ++j) {
> >      c.set_xref(pai->point(j));
> >      std::cout << " integration node " << j << " for convex " << cv 
> > << " is " << c.xreal() << "\n";
> >    }
> >
> > Best regards,
> > Julien
> >
> > Giovani wrote:
> > > Good day  gentlemen!
> > >
> > > Suppose I have a getfem::mesh object that has a getfem::mesh_fem 
> > > linked to it, and also a getfem::mesh_im that's also linked.
> > >
> > > I would like to build a new getfem::mesh, whose nodes are located at 
> > > the quadrature points of the previous mesh. Is there any simple way 
> > > of retrieving a list with the global coordinates of those quadrature 
> > > points?
> > >
> > > Best Regards,
> > >
> > > Giovani M. Faccin
> > >
> > > _______________________________________________
> > > Getfem-users mailing list
> > > address@hidden
> > > https://mail.gna.org/listinfo/getfem-users
>
>
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Julien Pommier, bureau 111
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