Re: [Getfem-users] Periodic BC

[Yves Renard]

On mercredi 15 septembre 2010, Artur A. Poźniak wrote:
> Hello All,
> 
> I would like to impose periodic BC to my linear elastic system (2D). I need
> the *derivative* of one component of the displacement field to be equal on
> respective edges, i.e. {u_y},x on left = {u_y},x on right. ,x denotes
> partial derivative along x and u_y is the y-component of the displacement
> vector u.
> I know that there is no brick responsible for this in GetFEM, so I kindly
> ask for some help. I would expect it to be done with the use of additional
> system of Lagrange multipliers. Is that correct?
> 
> Thanks in advance
> Artur Pozniak


You are right, there is no specific brick to prescribe a periodic boundary 
condition (this would be possible to build one). 
You do not have to prescribe the equality of a derivative (or a stress in 
elasticity), the continuity of the unknown is sufficient.
If the degrees of freedom correspond from a boundary to the other (in the case 
of a regular mesh for instance) then you can easily bouild the constraint 
matrix prescribing the eaqulity of these degrees of freedom (and add a 
constraint brick). If the mesh is not the same, you have to prescribe the 
equality in a weak form with a multiplier which is more difficult.

Yves.



-- 

  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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