On 16/set/09, at 15:33, Till Heinemann wrote:
I have a specific problem, where I want to combine a boundary
element integration and a finite element integration on one domain.
I was going to use two different triangulations for this (is this at
all necessary?).
Yes. For now, deal.II supports coupling BEM and FEM only by using
separate meshes and dofhandlers. I have never had the need to do this,
but in principle it should be possible to have a "TriangulationView"
or something like this that behaves like a codimension one
triangulation, built on top of the boundary of a standard
triangulation...
The BEM is supposed to share displacement variables at the vertices
the two domains coincide on (i.e. the boundary nodes).
You will have to do this by hand, but it is not too complicated.
So my idea was to create a dim and a dim-1 triangulation (and
dofhandlers, fes…) and somehow use the dof_handler to exchange this
displacement variable information.
The latest distribution of deal.II supports BEM as codimension one
grids, that is Triangulation<dim-1, dim> objects. You want a
triangulation with vertices in dim space, and cells in dim-1 space.
The next difficulty would be assembling and solving a common system
of equations to be solved for all the dofs appearing in the 2
systems, which would resolve in combining a full matrix from BEM and
a sparse matrix from FEM – given respect to the size of the FEM
matrix, I think it may still be advantageous to use a sparse matrix
representation of the combined system matrix?
In some of my applications I use deal.II sparse matrix also for BEM
problems. This does not seem to be too much of an overhead, compared
to the assembly of the full system.
So I’m not asking you to solve my problem for me, but maybe someone
has already attempted sth similar and can tell me if I’m thinking in
the right direction here or if there’s a simpler / more efficient
approach to it – or he knows why my ideas won’t work.
Where can I find more information on this whole problem, which
examples may treat aspects of this?
The example you should look at is step-34, where a potential flow
problem is solved (Laplace equation for outer domain) using BEM. Part
of your problem will be very similar to that. As far as coupling is
concerned, I think your ideas seem reasonable.
Best,
Luca.
_______________________________________________
dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
