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

 From: Yves Renard Subject: Re: [Getfem-users] quadratic mesh, step 2 Date: Fri, 4 Jan 2019 10:49:28 +0100 (CET)

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Dear Edouard,

Yes, apart from the specific case of Newton-Cotes integration methods, all the
Gauss points are in the interior of the elements.

Best regards,

Yves

----- Original Message -----
Sent: Friday, January 4, 2019 9:54:42 AM
Subject: Re: [Getfem-users] quadratic mesh, step 2

Dear Yves,
Thanks, that sounds perfect for me!
Just to be sure: Gauss integration points are inside points of the
curved convex where the fem are smooth?
All the best,
Edouard.

Le 02/01/2019 à 13:57, Yves Renard a écrit :
> 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,
>
> Yves
>
>
>
> ----- Original Message -----
> 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 !!!
>
> Best,
>
> Edouard.
>
> 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
>>
>> http://getfem.org/userdoc/appendixA.html
>>
>> And yes, of course, it is possible to also mesh curved surfaces in 3D.
>>
>>
>> Best regards,
>>
>> Yves
>>
>> ----- Original Message -----
>> 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 : http://www-ljk.imag.fr/membres/Edouard.Oudet/
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