Re: [Getfem-users] interpolated fem again

[Yves Renard]

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
  Institut Camille Jordan - CNRS UMR 5208
  INSA de Lyon, Universite de Lyon
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  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard
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