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Re: [Getfem-users] Hermite element implementation doubts
From: |
Yves Renard |
Subject: |
Re: [Getfem-users] Hermite element implementation doubts |
Date: |
Fri, 28 May 2010 10:01:46 +0200 |
User-agent: |
KMail/1.9.9 |
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
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard
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