Re: [Getfem-users] Lineic boundary conditions

[Renard Yves]

Dear Jean-Francois,


Yes, the problem is that integration method in getfem are defined on  
the element
and the boundary of the element not in n-2 dimension structures. If  
you have a mean
to define an integration method on this polyline, then you can  
assemble your Neumann term.
But the only mean, for the moment, to define a 1D integration method  
on a 3D domain is to define
some 1D elements. The problem if you do so is that this integration  
method will only be defined
on the 1D elements, not a the 3D elements on which you want to  
integrate. So, I think, the only mean
which exists right now is to use an interpolation of the 3D fem on the  
1D elements and assemble the term.
(see interpolation of a fem) It is rather tricky for such a simple  
operation, but I do not see another
"simple" possibility.

For Dirichlet condition, you can indeed use add_explicit_matrix to add  
a constraint
on certain nodes or add a constraint brick. For non Lagrange element,  
you can use
the previous strategy to build the constraint matrix, I think.


Yves.

Jean-Francois Barthelemy <address@hidden> a écrit :

> Dear Getfem users,
>
> Is there any simple way in Getfem to impose lineic boundary conditions on a
> 3D problem ?
> To be more precise, I have a 3D mesh and I want to impose either Dirichlet
> or Neumann boundary conditions on a polyline. The first problem that arises
> is that, if I'm not wrong, the mesh_regions in 3D can be either volumes
> (convexes) or surfaces (convexe faces) but not 1D elements. However, as I
> can gather all the dof corresponding to the polyline, Dirichlet conditions
> can rather easily be handled by add_explicit_matrix and add_explicit_rhs
> methods. But the case of Neumann conditions may be a bit more difficult. Is
> there any straightforward method to do so ?
> Thank you very much
>
> Jean-Francois Barthelemy