ffc team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

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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