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" <[email protected]>
To: [email protected]
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 ([email protected]) 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
---------
