Re: [Getfem-users] gradient interpolation matrix

[Yves Renard]

Dear Edouard,

No, such a matrix in not available for the moment. It is not very 
difficult to implement, but it has to be done in C++ by extending the 
function in the file getfem_interpolation.h which do the job for the 
value, but not for a derivative.

May be you can be more accurate on the use of this matrix. May be there 
is some alternative to avoid it.

For instance, what I mentionned in my previous e-mail was to use instead 
a projection matrix. A projection matrix can be easily assembled with a 
expression such as for instance

"Grad_u(1)Test_v"

in term of the generic assembly language where "Grad_u(1)" is the 
derivative with respect to the first direction and "Test_v" should 
correspond to a P_0 discontinuous finite element method to obtain a 
unique value on each element. But of course, in that case, it will be a 
mean value of the derivative on the element, not the interpolation at 
the center of the element.

Best regards,

Yves



Le 05/11/2017 à 22:32, Edouard Oudet a écrit :
> Dear Yves,
> Thanks a lot for your fast answer!
> I am not sure I follow your suggestion. My goal is to obtain a 
> description of the linear operator from my dof to the evaluation of, 
> let say, the first derivative of my fem at the centers of my elements. 
> Is this what you call discontinuous fem ?
> If my fem is described by an object femk, I understood that a (python) 
> call to
>
> M = asm_interpolation_matrix(femk, fem0)
>
> gives me the interpolaation matrix from femk to fem0 but I do not see 
> how to use this for my derivative "\partial_1 femk" ? Which matrix 
> should be inverted ? I apologize for the naivety of my questions,
> best,
> Edouard.
>
> Le 05/11/2017 à 16:11, Yves Renard a écrit :
> > Dear Edouard,
> >
> > No, unfortunately, there is no function in Getfem that gives the 
> > interpolation matrix for a derivative of a field. You can perform the 
> > interpolation itself with the high level generic assembly, but it 
> > does not give an interpolation matrix. If you want to interpolate on 
> > a discontinuous fem, you can instead compute the projection matrix 
> > which will be easy to invert because it will be local (a small matrix 
> > on each element). Then if your projection is exact, then the inverse 
> > will also be an interpolation matrix ...
> >
> > Best regards,
> >
> > Yves.
> >
> >
> >
> > ----- Original Message -----
> > From: "EDOUARD OUDET" <address@hidden>
> > To: address@hidden
> > Sent: Friday, November 3, 2017 11:43:34 AM
> > Subject: [Getfem-users] gradient interpolation matrix
> >
> > Dear all,
> > Is there a way with the getfem python interface to assembly the 
> > matrix associated to the interpolation matrix of a first derivative 
> > evaluation of a fem (or its full gradient).
> > I found
> >
> > Mi = asm_interpolation_matrix(MeshFem mf, vec pts)
> >
> > for the evaluation of the function u = MeshFem mf itself, but I was 
> > not able to identify the relevant generalization for derivatives of 
> > u: \partial u_x, \partial u_y, etc.
> > Thanks a lot for this great library,
> > best, Edouard.

--

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard

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