On Mon, 20 Apr 2009, Anders Logg wrote: > 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
ok. I just implemented what I needed in MATLAB and that formulation works. But it would certainly be great to have it in FENICS. - Shawn _______________________________________________ DOLFIN-dev mailing list [email protected] http://www.fenics.org/mailman/listinfo/dolfin-dev
