On Thu, Apr 16, 2009 at 09:19:51PM -0400, Shawn Walker wrote:
On Fri, 17 Apr 2009, Garth N. Wells wrote:
kent-and@xxxxxxxxx wrote:
I would also like this capability! It is something that often shows up
in inverse/optimal control problems.
Written in FFC/UFL your first equation reads:
dot(u,v)*dx - p*div(v)*dx + lmbda*dot(v,n)*ds
where u, p, lmbda are trial functions.
You could form one system or create a block matrix. Anyhow
the term
lmbda*dot(v,n)*ds
would lead to a matrix with a very big kernel since you are not able to
restrict the dofs of lmbda only to the boundary.
What you can currently do is to restrict the functionspace for lmbda to
all the cells
associated with the boundary.
Using restricted functionspaces (in a simpler fashion) can be found in
demo/function/restriction.
The restriction does only work on cells for now.
We could discuss Uzawa and/or block matrices for this problem but I think
the simplest start is to create one system to begin with.
Whether it makes sense that lmbda lives on the whole cell associated with
the boundary, I don't know.
It should live only on the boundary. In practice this only becomes an
issue for higher-order elements with internal dofs.
Garth
Yes, I agree.
So how ridiculous is it to enable FFC/DOLFIN to have finite element
functions that are only defined on the boundary of the domain? I'm
guessing there would be some special DoFmappings to go from the global
domain numbering to a boundary numbering only. This would be really nice
to have. There are lots of cases in practice that have these kinds of
boundary functions.
- Shawn
It's not impossible but it requires some thought. I think Garth has
asked about this for a long time as well (to have function spaces that
only live on facets). I don't really know how to best handle it.
--
Anders
