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Re: [Getfem-users] second derivative of linear elements


From: Yves Renard
Subject: Re: [Getfem-users] second derivative of linear elements
Date: Wed, 12 Feb 2014 19:53:23 +0100 (CET)


Dear Wen,

You have first to fill a mesh_trans_inv object (defined in 
bgeot_geotrans_inv.h) with a cloud of points then to call interpolation 
function such as
getfem::interpolation(mf_source, mti, U, V)
where mti is a mesh_trans_inv object and V a vector of the right size.

But you are right, in the case of the crack-tip enrichment, it is not a good 
idea to first interpolate the gradient on a non-enriched finite element. The 
better would be to adapt getfem::interpolation to directly interpolate the 
gradient.

Best regards,

Yves.

----- Original Message -----
From: "Wen Jiang" <address@hidden>
To: "Yves Renard" <address@hidden>
Cc: address@hidden
Sent: Wednesday, February 12, 2014 5:13:37 PM
Subject: Re: [Getfem-users] second derivative of linear elements





Dear Prof Yves Renard, 

Thanks for your suggestions. However I still have some concerns about the 
accuracy of the interpolation. 

Basically I would like to extract the displacement and strain field at the 
crack tip. At the crack tip the field is spanned by the sum of the standard 
basis function and enriched basis functions(like Heaviside and tip enrichment). 
I do not know how the accuracy would be if we first interpolate the 
gradient/Hessian of the original finite element on a discontinuous finite 
element with only standard shape function. I think that is the reason that 
previously I used interpolator_on_mesh_fem to get the gradient/Hessian because 
I guess that function uses the original finite elements for interpolation. Any 
suggestions? 

Also I am not very clear about how to use the interpolation function in 
getfem_interpolation.h to interpolate on a cloud of points. Which function 
should I call exactly and how to define those points as the input of such 
function? Thanks. 

Regards, 
Wen 



On Wed, Feb 12, 2014 at 6:53 AM, Yves Renard < address@hidden > wrote: 





Dear Wen, 

interpolator_on_mesh_fem is a structure which mainly allows to use a 
precomputed solution to enrich a finite element space. It only interpolate the 
solution and its gradient. It is an interpolation, thus the gradient of a P1 
function will be constant over an element, yes. If you just need to interpolate 
a gradient or a Hessian on a cloud of points, you should preferably use the 
functions in getfem_derivatives.h and getfem_interpolation.h but you should 
first interpolate the gradient/Hessian on a discontinous finite element on the 
same mesh, then use the interpolation function in getfem_interpolation.h to 
interpolate on a cloud of points. Of course, it would be possible to provide a 
function which performs both the two operations in only one step, but it does 
not exist for the moment. 

Best regards, 

Yves. 







----- Original Message ----- 
From: "Wen Jiang" < address@hidden > 
To: address@hidden 
Sent: Tuesday, February 11, 2014 11:41:55 PM 
Subject: Re: [Getfem-users] second derivative of linear elements 




Sorry to clog your inbox. In my previous email I forgot to tell that I used 
interpolator_on_mesh_fem to get the gradient and hessian. Basically I would 
like the get the first derivative and second derivative of the displacement 
field at some points. I understand that the gradient is definitely 
discontinuous across elements so we have to use a discontinuous fem as the 
targeted fem if the compute_gradient() is used. But I am not sure about how the 
gradient and hessian is calculated when calling 
interpolator_on_mesh_fem.eval(...) and .eval_hess(...). As I said, if the 
linear element is used, are those results still correct? Thanks. 

Regards, 
Wen 




On Tue, Feb 11, 2014 at 9:55 AM, Wen Jiang < address@hidden > wrote: 




Dear all, 

I tried to calculate the second derivative in getfem using compute hessian. For 
linear elements, the second derivative of the shape function should be zero but 
it seems that the results of hessian computed in getfem is not zero. Could you 
tell me how is the hessian computed in getfem for linear elements? Thanks. 

Regards, 
Wen 


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