[Getfem-users] vectorial problem with interpolated fem

[Andreykiv, A.]

Dear Yves,

A question on interpolated fem if I may. I need to use interpolated fem with a vectorial problem, something that getfem currently does not allow.
Some time ago I was already asking you about this and you suggested to reformulate my problem into a scalar one, so I won't need the vector feature.

I have a code now, which I'm, say, "enhancing" with interpolated fem and reformulation of this code in scalar terms would be a considerable time investment.
Therefore, would you be kind to briefly explain how difficult it is to develop a vectorial interpolated fem and what steps need to be undertaken.
Despite my experience with getfem, I still have problems understanding the internal structures, as the ones you have in getfem_interpolated_fem.h/cc.

Is this, by any chance, anything you would be planning to include in the next versions of getfem?

Best regards,
                Andriy

------------------------------------------------------------------------
Andriy Andreykiv,
Postdoctoral researcher  

Leiden University Medical Center   |   Delft University of Technology
Biomechanics and Imaging Gr.       |   Fundamentals and Microsystems Gr.
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Le mercredi 11 juillet 2007 19:14, Andriy Andreykiv a écrit :
> Dear Yves,
>
>         What I want to do with interpolated fem is the following. I want to
> simulate a composite material (something like a car distribution belt),
> where the matrix of the composite is simulated with hexahedral elements
> while the fibers, that enforce the composite material are simulated with
> trusses. I want those trusses not to be conformal with the mesh of the
> matrix material, hence I want to impose a weak constraint that displacement
> of the fibers should be equal to the displacement of the matrix material
> in the location where those trusses fibers cross the matrix (this way I
> would attach the fibers inside the matrix  material). Hence, again this is
> conceptually similar to fictitious domain method for fluid-structure
> interection, where velocity of the fluid on the boundary of the structure
> should be equal the velocity of the structure and this constraint is
> imposed in a weak sence.
>         I probably can reformulate my vectorial problem into a  set of
> scalar problems and then use interpolated fem, and then assemble a
> vectorial problem again. Would that be a solution?

>I suppose you need the mass matrix beetween the two elements ?  (because, if
>you only need a basic interpolation, in the sense of Lagrange elements, you
>can have the interpolation matrix without using interpolated fems).

>Yes, you can indeed try to reformulate your problem as a set of scalar
>problems and use the scalar interpolated fem. However, if you use only scalar
>element (not intric vectorial ones), the adaptation of interpolated fems to
>vectorial fems should not be to much complicated. If you need, i can have a
>look to this when i will not be too busy.


>Yves.

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>  Yves Renard (address@hidden)       tel : (33) 04.72.43.80.11
>  Pole de Mathematiques,                       fax : (33) 04.72.43.85.29
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