dolfin team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

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

> > > On Thu, Apr 16, 2009 at 02:57:07PM -0400, Shawn Walker wrote:
> > > > Oh really?  And then I could call a direct solver on it?  Is there a
> > > > demo
> > > > somewhere that shows this?
> > > >
> > > > I could also use an Uzawa method.  But concatenating matrices would be
> > > > fine for me.
> > > >
> > > > - Shawn
> > > No, I don't expect direct solvers will work, but it should be possible
> > > to use with a Krylov solver. Kent knows about this.
> > >
> > > When I look at it now, BlockMatrix does not inherit from any of the
> > > KrylovMatrix base classes so it won't work with any of the solvers.
> > > Kent has his own GMRES/CG implementation in Python which uses the
> > > mult() operator provided by BlockMatrix. Maybe Kent can elaborate on
> > > this (and the code)?
> > >
> > > Moving this to dolfin-dev.
> > >
> > > --
> > > Anders
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> >
> >
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