Dear all,

I tried to calculate the second deri= vative in getfem using compute hessian. For linear elements, the second der= ivative 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 hes= sian computed in getfem for linear elements? Thanks.

Regards,I tried to calculate the second deri= vative in getfem using compute hessian. For linear elements, the second der= ivative 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 hes= sian computed in getfem for linear elements? Thanks.

Wen=A0

Sorry to clog your inbox. In my previous email I forg=
ot to tell that I used interpolator_on_mesh_fem to get the gradient and hes=
sian. Basically I would like the get the first derivative and second deriva=
tive of the displacement field at some points. I understand that the gradie=
nt is definitely discontinuous across elements so we have to use a disconti=
nuous fem as the targeted fem if the compute_gradient() is used. But I am n=
ot sure about how the gradient and hessian is calculated when calling inter=
polator_on_mesh_fem.eval(...) and .eval_hess(...). As I said, if the linear=
element is used, are those results still correct? Thanks.

Regards,Wen =A0

=

On Tue, Feb 11, 2014 at 9:55 AM, Wen Jiang <=
jiangwen84@domain.hid> wrote:

Dear all,Regards,

I tri= ed 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. C= ould you tell me how is the hessian computed in getfem for linear elements?= Thanks.

Wen=A0

Dear Prof Yves Renard,

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

Wen

On Wed, Feb 12, 2014 at 6:53=
AM, Yves Renard <yves.renard@domain.hid> wrote:

Dear Wen,

interpolator_on_mesh_fem is a structure which mainly allows to use a precom= puted solution to enrich a finite element space. It only interpolate the so= lution 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 interpo= late a gradient or a Hessian on a cloud of points, you should preferably us= e the functions in getfem_derivatives.h and getfem_interpolation.h but you = should first interpolate the gradient/Hessian on a discontinous finite elem= ent on the same mesh, then use the interpolation function in getfem_interpo= lation.h to interpolate on a cloud of points. Of course, it would be possib= le 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" <jia= ngwen84@domain.hid>

To: getfem-users@domain.hid

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 woul= d like the get the first derivative and second derivative of the displaceme= nt field at some points. I understand that the gradient is definitely disco= ntinuous across elements so we have to use a discontinuous fem as the targe= ted 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.ev= al(...) 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 < jiangwen84@domain.hid > 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 ze= ro. Could you tell me how is the hessian computed in getfem for linear elem= ents? Thanks.

Regards,

Wen

Getfem-users mailing list

Getfem-users@domain.hid

ht= tps://mail.gna.org/listinfo/getfem-users

Dear Yves

Why you are =A0describing it as=A0

Why you are =A0describing it as=A0

/* ***=
***************************************************************** */

=
=A0 /* Element RT0 on par=
allelepideds. =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =
=A0 =A0 */

=A0 /* ***************************************************************=
***** */

I became concerned over a word **parallelepide=
ds.**

Does it mean that element works only for affine trans=
itions? Like in 2D case the reference unit square element is transferred to=
a parallelogram but not to a trapezoid. Does it mean that passing of the t=
rapezoidal test described in Section 6 of MIXED FINITE ELEMENTS FOR ELASTIC=
ITY ON QUADRILATERAL MESHES paper by=A0DOUGLAS N. ARNOLD is not expected?

--bcaec51d2eb858798c04f3616fc2--
You(author) don't use the Piola transformation that=
should work fine so i'm wondering is there a reason for that?

I hav= e made a hardcoded implementation of more precise procedure(based on Piola = transformation) described in the paper mentioned above so now trapezoidal t= est passed. Let me know if you are interested in incorporation of =A0it.

I hav= e made a hardcoded implementation of more precise procedure(based on Piola = transformation) described in the paper mentioned above so now trapezoidal t= est passed. Let me know if you are interested in incorporation of =A0it.

Best Regards, Egor