Re: [Getfem-users] gradient interpolation matrix

[Yves Renard]

Dear Edouard,

No, you cannot specify the location of points to the interpolation function. Of 
course, if you make this operation more than once, it would save some 
computational time to store the result of the localisation of the points. 
However, it is  not available for the moment (Not very difficult to do, but 
this means to store the element number and the location inside the element fo 
each point). Alternatively, for a linear interpolation, extracting the 
interpolation matrix would be also intersting as you suggested, of course. 

If you need to interpolate on the center of each element, use the interpolation 
on a P0 Lagrange element instead which will avoid this localisation.

Best,

Yves.

----- Original Message -----
From: "EDOUARD OUDET" <address@hidden>
To: "yves renard" <address@hidden>
Cc: "getfem-users" <address@hidden>
Sent: Thursday, November 16, 2017 5:28:52 PM
Subject: Re: [Getfem-users] gradient interpolation matrix

Dear Yves, 

The solution you proposed worked perfectly to interpolate gradient on points 
pts: 

GU = md.interpolation('Grad_u', pts.T, tmesh) 

I understood that localization of the points in the mesh is a time consuming 
and I read in the documentation the optional fields "int region[, int 
extrapolation[, int rg_source]]]". 
I wonder if giving the element number in which the point pts is located could 
speed up the call ? If it is the case, how should I definie these optional 
fields: I only get empty answer array with a call like 

GU = md.interpolation('Grad_u', pts.T in the element num, tmesh, num) 

Thanks, 

best. 

-- 
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) 


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)