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Re: [Getfem-users] quadratic mesh, step 2

From: Yves Renard
Subject: Re: [Getfem-users] quadratic mesh, step 2
Date: Wed, 2 Jan 2019 13:57:42 +0100 (CET)

Dear Edouard,

If you need to evaluate the gradient on the center of a triangle, the best way 
is to interpolate it on a P0 fem, because its degree of freedom are located on 
the center of the triangle. Moreover, in that case, there is no inversion and 
the interpolation is fast (you can have location of dofs with mf.dof_nodes() 
method). You can either interpolate any value on the Gauss points of an 
integration method with the mim_data object, which is also fast. But, for the 
moment, there is no mean to interpolate on a point with its coordinates on the 
reference element, unfortunately.

Best regards,


----- Original Message -----
From: "EDOUARD OUDET" <address@hidden>
To: "yves renard" <address@hidden>
Cc: "getfem-users" <address@hidden>
Sent: Monday, December 31, 2018 6:44:30 PM
Subject: Re: [Getfem-users] quadratic mesh, step 2

Dear Yves,

Thanks a lot for your answer, that's perfectly clear now.. and works!

One more question: working on triangulated (curved) surface in R^3, I am 
interested to evaluate the gradient of a fem function at some point of 
this curved mesh. When my mesh was flat I used to build a model and call 
the interpolation of "Grad_u" on my mesh at a point P which was inside 
of the mesh.

Now that the mesh is curved, it is more tricky to produce a point which 
is exactly on the curved mesh like, for instance, the center of a curved 
triangle. Here are my (I hope last) questions:

1) Is it possible to generate points inside of a curved convex cell 
described by a mesh?
2) How to interpolate the gradient at these points. Does the same 
procedure work even if the point is never exactly on the curved mesh ?

Thanks a lot for your work and Happy new Year !!!



Le 29/12/2018 à 20:47, Yves Renard a écrit :
> Dear Edouard,
> The point ordering is the same that the corresponding fem. You can see the 
> dof ordering of fem in the page
> And yes, of course, it is possible to also mesh curved surfaces in 3D.
> Best regards,
> Yves
> ----- Original Message -----
> From: "EDOUARD OUDET" <address@hidden>
> To: "getfem-users" <address@hidden>
> Sent: Saturday, December 29, 2018 8:05:04 PM
> Subject: [Getfem-users] quadratic mesh, step 2
> I answer to the first part of my question: curved mesh seem to be
> implemented regarding examples in the tests/meshes folder. Great!!
> My remaining questions are:
> 1) How/where is defined the ordering point sequence which defines a
> curved convex cell in a getfem-mesh file?
> 2) curved mesh seem to be implemented in 2D, 3D but is it also the case
> for surfaces (triangulation in 3D)?
> Thanks!

Edouard Oudet :
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