Re: [Getfem-users] gradient interpolation matrix

[EDOUARD OUDET]

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.

--
Edouard Oudet : http://www-ljk.imag.fr/membres/Edouard.Oudet/
IMAG - Bureau 164
700 avenue Centrale
38400 Saint Martin d'Hères
+33 (0)4 57 42 17 71  (office LJK)
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De: "Yves Renard" <address@hidden>
À: "EDOUARD OUDET" <address@hidden>
Cc: "getfem-users" <address@hidden>
Envoyé: Dimanche 5 Novembre 2017 16:11:07
Objet: Re: [Getfem-users] gradient interpolation matrix

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.

--
Edouard Oudet : http://www-ljk.imag.fr/membres/Edouard.Oudet/
IMAG - Bureau 164
700 avenue Centrale
38400 Saint Martin d'Hères
+33 (0)4 57 42 17 71 (office LJK)
+33 (0)4 79 68 82 06 (home)