ffc team mailing list archive

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

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?

> Could we simplify it so that it
> just defines a finite element restricted to a facet and then some dS
> integral?
> 

Sounds good.

> 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.

Garth

> --
> Anders