Re: [Getfem-users] Hermite element implementation doubts

[Yves Renard]

Dear Roman,

The fact that the gradient is not necessarily the same at the two different 
points comes from the fact that an arbitrary geometric transformation can be 
applied, including a nonlinear one.

But you are right, it should be gmm::mat_col(K,0) instead of gmm::mat_row(K,0)
in the second expression. This means that the element has only been tested in 
dimension 1 ...

And you are also right, the signum function is here to give a unique 
orientation of the "tangent" derivative between two elements.

Yves.




On vendredi 28 mai 2010, Roman Putanowicz wrote:
> Dear All,
>
> I am trying to understand the implementation of Hermite element
> and have a problem with the following fragment of the method:
> void hermite_segment__::mat_trans(/* skip *)
>
>
>  gmm::copy(gmm::identity_matrix(), M);
>  // gradient at point 0
>  gmm::mult(G, pgp->grad(1), K);
>  if (N == 1) M(1, 1) = K(0,0);
>  else  M(1, 1) = gmm::mat_euclidean_norm(K)
>     * gmm::sgn(gmm::vect_sp(gmm::mat_col(K, 0), r));
>  // gradient at point 1
>  if (!(pgt->is_linear())) gmm::mult(G, pgp->grad(3), K);
>  if (N == 1) M(3, 3) = K(0,0);
>  else M(3, 3) = gmm::mat_euclidean_norm(K)
>     * gmm::sgn(gmm::vect_sp(gmm::mat_row(K, 0), r));
>
> Why the scheme for gradient at point 0 and 1 differ -- that is why
> in case of point 1 we take gmm:mat_row(K,0) and not gmm::mat_col(K,0)?
> Isn't the matrix K of the size Nx1 where N is the dimension of the
> real space?
>
> And also this computatno with signum function -- are they to take into
> account the order of poins in respet to the local coordinate system?
>
> I would appreciate any hint.
>
> Regards
>
> Roman



-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
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  http://math.univ-lyon1.fr/~renard

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