On Fri, Jan 29, 2010 at 10:54:54AM +0000, Garth N. Wells wrote: > > > Anders Logg wrote: > > On Fri, Jan 29, 2010 at 10:31:05AM +0000, Garth N. Wells wrote: > >> > >> Anders Logg wrote: > >>> On Fri, Jan 29, 2010 at 10:10:37AM +0000, Garth N. Wells wrote: > >>> > >>>>> Sub domains seem to be very different, but the other two cases just > >>>>> seem to be a matter of some dofs being "active" and the other zeroed > >>>>> out. This is what Marie suggested yesterday, that a restricted element > >>>>> only considers a subset of the dofs of some given element. > >>>>> > >>>> Sounds good. > >>>> > >>>>> The thing I don't understand yet is the selection of which dofs should > >>>>> be active. If we think of the case with restriction to facets, then > >>>>> the element needs to be restricted to different facets depending on > >>>>> which facet we are integrating over, or are we always mapping one > >>>>> specific facet of the reference cell to the current facet? > >>>>> > >>>> It works the same way as the DG elements, just the internal dofs are > >>>> thrown away, which is the latter if the above, right? > >>>> > >>>>> Say we have P1 elements in 2D which have 3 dofs. Then we could > >>>>> restrict that element to the dofs on the first facet (facet 0). These > >>>>> dofs are then labeled 1 and 2. But sometimes a facet in the mesh will > >>>>> correspond to the edge between 0 and 1 or 0 and 2. > >>>>> > >>>> We don't restrict to individual facets, but to all facts of a cell. > >>> That makes sense, but one thing still confuses me. Say that we have a > >>> P1 element and restrict it to facets. Then all dofs are on the facets > >>> so the result of the restriction is just a new P1 element. Same for P2 > >>> where the result again is a new P2 element. > >> Yes. > >> > >>> For P3, the result is P3 > >>> element minus just one dof. > >> Yes. > >> > >>> So does this make much difference for > >>> other than very high degree elements? > >>> > >> It is only needed for k > 2. It's important because everything in > >> FFC/UFL works for arbitrary orders. > > > > Yes, it should work for any order. I was just questioning the > > usefulness of it if it results in standard P1 and P2 elements for > > k = 1,2. > > > > Then I think I understand how it all works. > > > > But does the FFC demo make any sense? > > We have a demo?
Yes, it's called ElementRestriction.ufl. :-) > > Could we simplify it so that it > > just defines a finite element restricted to a facet and then some dS > > integral? > > > > Sounds good. Could you post something simple and I'll add it. > > It currently breaks the code we added for RestrictedElement yesterday > > because it has a complex nesting of restriction, then mixed with > > another element and then restricted again. It looks like this is not > > how you are using it in your solver. > > > > The concept is very simple, so its implementation should be pretty > simple too. Yes. -- Anders
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