On Thu, Apr 16, 2009 at 09:19:51PM -0400, Shawn Walker wrote: > > On Fri, 17 Apr 2009, Garth N. Wells wrote: > > > [email protected] 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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