Re: [Getfem-users] [Fwd: Re: combining 2D and 1D elements]]

[Yves Renard]

Dear Till,

The algorithm which enumerate the degrees of freedom indentifies the degrees 
of freedom even for element with different dimensions. This means in 
particular that if the 1D and the 2D elements share a Lagrange dof on the 
same node, they will coincide normally. At least of course if they are 
declared on the same mesh_fem. Note that if the identification is not done 
correctly for some reason, you can use the reduction matrix of the mesh_fem 
to prescribe it (or if the indentifications implies a linear combination of 
dofs). 

A second possibility, of course, is to declare separate mesh_fems. This may be 
more natural becasue the equation on the 2D domain and on the 1D domain will 
not be the same (if you define only one mesh_fem you can also use mesh 
regions to assemble some terms specifically on the 1D and 2D part).
With separate mesh_fems, you will have to prescribe some constraints on your 
dof using for instance a constraint brick.

Best Regards,

Yves.


On vendredi 23 avril 2010, Till Heinemann wrote:
> Hi,
>
> I have a follow-up question about putting 1D elements on 2D mesh:
> I want to create a relation between the 1D and 2D element I have on my
> 2D mesh. How would this element matrix generic_assembly work? If it
> works on each convex, there are four 1D line elements on this convex,
> so...? How is this done?
>
> After all, all I want to do is:
> - have equal displacement dofs on the nodes on 1D and 2D elements (on
> boundary).
> - elastostatic relation on 2D domain
> - "bar-element" relation on 1D domain, which is the boundary of the 2D
> domain. 1D dofs that are not on the boundary are to be dropped / left
> zero
> - bubble dofs on 1D Lagrange defined in some other way
>
> So I think besides the self-related bricks for elastostatic and bar
> behavior, I need some brick defining the equality of the boundary node
> dofs in 1D and 2D -- or any other function, that relates the 1D dof to
> the value on the geometrically identical 2D dof on that node, since I
> actually wouldn't need to explicitly store the same values twice...
>
> Up to now I've been working with 2 meshes (1D and 2D) and some manual
> method that searches the entire "other" mesh for the locally
> corresponding dof on the same node, same component. But I'm afraid
> that's really inefficient and I get too many problems, if my (now also
> manual) assembly of the system matrix becomes more complex.
>
> So I was wondering, how I'd cleverly do this with generic getfem++
> methods?
>
> I hope my question is understandable!
>
> Thank you, best regards
> Till
>
> > Dear Till,
> >
> > You can indeed mix into the same mesh 2D and 1D elements. But you cannot
> > affect a 1D finite element method directly on the boundary of a 2D
> > element. You have to add explicitely the 1D element first to the mesh.
> > If you use Lagrange elements, the correspodance between the dof of 1D and
> > 2D elements will be taken into account correctly.
> >
> > Of course, this means that you will have a PDE solved in your 2D domain
> > and also a PDE on the boundary of your domain.
> >
> > Yves.
> >
> > On lundi 22 février 2010, Till Heinemann wrote:
> > > Hello!
> > >
> > > I'm pretty new to this library and I would like to do the following:
> > > Implement a 2D domain (mesh) with standard lagrange elements plus 1D
> > > lagrange (with bubble function) elements on this domain's boundary!
> > >
> > > Could I somehow do this on one mesh (compiler says no),
> > >
> > > Incompatibility between fem FEM_PK_WITH_CUBIC_BUBBLE(1,1) and mesh
> > > element GT_LINEAR_QK(2)
> > >
> > > and if not, is there later for the assembly of the system description
> > > an easy way to know which node-dofs interface at the same spacial
> > > position (i.e. without looping twice and checking their positions /
> > > thus writing a connection table of some sort)? I mean, the elements
> > > need to know that they have an existing neighbor (on a different mesh).
> > > Also, I don't see yet how to write a mesh from a mesh_region (i.e.
> > > boundary), but I'm sure I'll figure that out sooner or later.
> > >
> > > Now I thought there must be a standardized way for this, as I read in
> > > http://download.gna.org/getfem/doc/getfem_project/getfem_project_5.html
> > >#id9 connecting neighboring elements of different dimensions is already
> > > implemented?
> > >
> > > Thank you for any suggestions on which methods or types that might help
> > > me,
> > >
> > > best regards
> > > Till
> > >
> > >
> > > _______________________________________________
> > > Getfem-users mailing list
> > > address@hidden
> > > https://mail.gna.org/listinfo/getfem-users
>
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-- 

  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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