dolfin team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

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

> Kent
>
>
> > 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
> > _______________________________________________
> > DOLFIN-dev mailing list
> > DOLFIN-dev@xxxxxxxxxx
> > http://www.fenics.org/mailman/listinfo/dolfin-dev
>
>
> _______________________________________________
> DOLFIN-dev mailing list
> DOLFIN-dev@xxxxxxxxxx
> http://www.fenics.org/mailman/listinfo/dolfin-dev