dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

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

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