Re: [Getfem-users] new_interpolated_fem problem

[Andriy Andreykiv]

Dear Yves, 

        Thank you very much for your response. You were right and that helped. 
I just 
noticed that what I was trying to do was already done in 
test_interpolated_fem.cc (in function test2) in the tests directory. 
        One more question if I may. After I received a mass matrix M which was 
calculated from the shape fucntions of two overlapping meshes I have to 
relate somehow the rows and columns of that matrix to the global degrees of 
fredom of the original interpolated meshes. 
        If mq  is the original mesh_fem (say some quad mesh) and m_intrpolate 
is the 
interpolation of mq on some mesh_fem, called ml (segment mesh that crosses 
the quad mesh), then my mass matrix M has dimensions  
M(m_interpolate.nb_dof(), ml.nb_dof). Imagine that I'm using this matrix as a 
constraint matrix for an elliptical problem, where I'm imposing a Dirichlet 
boundary condition in a weak sense as in a fictitious domain method, with 
Lagrange multiplier:

| A     B | {   U     } 
| B^T  0 | {Lambda} 

here U is a solution, defined on mq, A is an elliptic stiffness (mq.nb_dof X 
mq.nb_dof)  matrix,  B is a constraint matrix and lambda is a Lagr.mult, 
defined on the segment mesh_fem ml. Clearly B is bigger than M, as B has 
dimentions B(mq.nb_dof, ml.nb_dof), so I have to relate rows of M to the 
corresponding rows of B. I've looked at the code for the interpolated_fem, 
but I didn't directly see how can I receive the index_of_dof for mq, that 
correspond to the rows of M (which is probably numbered as the DOF's of 
m_interpolate), so I can insert the rows of M into the correct places in B.

Would you be so kind to have a look at it?

Thank you very much in advance,
                                                         Andriy



On Wednesday 28 February 2007 15:38, you wrote:
> Le Mercredi 28 Février 2007 14:20, Andriy Andreykiv a écrit :
> > Good day gentlemen,
> >
> >     I'm having problems with interpolating a finite element method from one
> > mesh to the other (getfem::new_interpolated_fem). What I want to do is
> > the following, below there is a code that first defines two quad elements
> > (in 2D space) and a line elemnet that crosses it arbitrarily in the
> > middle (there is a picture bellow). I want to calculate a mass matrix
> > (used for fictitious domain method) which is evaluated on that segment 
> > element, but in fact is calculated as a product of shape functions from
> > the quads and the segment element (and the integration is over the
> > segment):
> >
> > M=\int_{segment} Base(the setment) X Base(the quads) dx
> >
> > I'm getting an error:
> >
> > interpolated_fem::update from context : convex_index = [0]
> > ============================================
> >
> > |      An error has been detected !!!      |
> >
> > ============================================
> > Error in ./gmm_opt.h, line 76 :
> > non invertible matrix
> >
> > I would really appreciate the help.
> > Best regards,
> >                     Andriy
>
> Hi Andriy,
>
> I see two errors in your program.
> The addition of the two quad element in the mesh should be writen:
>
>      ind1[0]=quad_mesh.add_point(bgeot::base_node(0.0,0.0));
>      ind1[1]=quad_mesh.add_point(bgeot::base_node(1.0,0.0));
>      ind1[2]=quad_mesh.add_point(bgeot::base_node(0.0,1.0));
>      ind1[3]=quad_mesh.add_point(bgeot::base_node(1.0,1.0));
>      ind2[0]=ind1[1];
>      ind2[1]=quad_mesh.add_point(bgeot::base_node(2.0,0.0));
>      ind2[2]=ind1[3];
>      ind2[3]=quad_mesh.add_point(bgeot::base_node(2.0,1.0));
>      ind3[0]=line_mesh.add_point(bgeot::base_node(0.5,0.5));
>      ind3[1]=line_mesh.add_point(bgeot::base_node(1.5,0.5));
>      quad_mesh.add_parallelepiped(2,ind1.begin());
>      quad_mesh.add_parallelepiped(2,ind2.begin());
>
> this particular numeration of the vertex come from the fact that
> quadrilaterons are defined as tensorial product of two segments in Getfem.
>
> Also, th line
> getfem::mesh_fem mq_interpolate(mq.linked_mesh());
>
> should be replaced by
> getfem::mesh_fem mq_interpolate(ml.linked_mesh());
>
> With this modifications, the program seems to  work !
>
> Best regards,
>
> 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
> -------------------------------------------------------------------------

-- 
__________________________________________
Andriy Andreykiv
Delft University of Technology
Faculty of Mechanical Engineering 
Fundamentals of Microsystems
Mekelweg 2
2628 CD  Delft
The Netherlands

E-mail  : address@hidden
Tel.    :   (31) 15 2786818
Fax.    :   (31) 15 2789475
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