ffc team mailing list archive

[Kristian Oelgaard <k.b.oelgaard@xxxxxxxxx>]

On 18 June 2010 15:25, Mehdi <m.nikbakht@xxxxxxxxxx> wrote:
> On Fri, 2010-06-18 at 15:08 +0200, Kristian Oelgaard wrote:
>> On 18 June 2010 14:12, Marie Rognes <meg@xxxxxxxxx> wrote:
>> > On 18. juni 2010 13:43, Kristian Oelgaard wrote:
>> >
>> > On 18 June 2010 13:20, Mehdi <m.nikbakht@xxxxxxxxxx> wrote:
>> >
>> >
>> > On Fri, 2010-06-18 at 12:34 +0200, Marie Rognes wrote:
>> >
>> >
>> > On 18. juni 2010 12:23, Kristian Oelgaard wrote:
>> >
>> >
>> > On 18 June 2010 12:05, Marie Rognes <meg@xxxxxxxxx> wrote:
>> >
>> >
>> >
>> > On 18. juni 2010 11:38, Kristian Oelgaard wrote:
>> >
>> >
>> >
>> > On 18 June 2010 01:44, Marie Rognes <meg@xxxxxxxxx> wrote:
>> >
>> >
>> >
>> >
>> > On 17. juni 2010 15:44, Mehdi wrote:
>> >
>> > On Wed, 2010-06-16 at 18:04 +0200, Kristian Oelgaard wrote:
>> >
>> >
>> >
>> > Mehdi and I discussed this a bit, one way to get around this in FFC is to
>> > let
>> > VectorElement accept a FiniteElement as argument, then you can do
>> >
>> > element = VectorElement(V + Q)
>> >
>> > and still be dimension independent.
>> >
>> > Or in UFL we can tweak the '+' operator, such that enriching a
>> > VectorElement means enriching each of the components of 'self' with
>> > the components of 'other'. For this to work the dimension of the two
>> > vector elements must of course be identical but I guess that will
>> > always be the case, otherwise we throw an error.
>> >
>> >
>> > I will go for this option. This allows us to have simpler code and
>> > preserves accessing to the sub-elements of enriched mixed element.
>> >
>> >
>> >
>> > How do you plan on handling elements such as the following (relevant in
>> > connection with the PEERS element for linear elasticity) with this approach?
>> >
>> > V = FiniteElement("RT", "triangle", 1)
>> > Q = VectorElement("B", "triangle", 3)
>> > W = V + Q
>> >
>> >
>> >
>> >
>> > I was planning on throwing an error :)
>> >
>> >
>> >
>> >
>> > Please don't :)
>> >
>> >
>> >
>> >
>> > I did not know that one would ever want to enrich a scalar element
>> > with a vector bubble function,
>> >
>> >
>> >
>> > Since RT is a vector-valued element, enriching it with a vector bubble
>> > function
>> > is well-defined.
>> >
>> >
>> >
>> > Ha, I completely missed the 'RT', that's what you get for working with
>> > 'CG' only :)
>> > Now it makes a lot more sense to me.
>> >
>> >
>> >
>> >
>> > Ok :)
>> >
>> >
>> >
>> > Strictly speaking, my example is not the enrichment of one UFL VectorElement
>> > with another VectorElement. So, I guess you could overload + for
>> > VectorElement (and TensorElement) only. However, that would make
>> >
>> >
>> >
>> > Yes, that's what we had in mind, then instead of an error we just
>> > return an EnrichedElement, then it's up to the user to make sure that
>> > the enrichment makes sense. I haven't looked at the code in detail
>> > now, but maybe there are other things we need to check for.
>> >
>> >
>> >
>> >
>> >    V = FiniteElement("CG", "triangle", 1)
>> >    V = V*V
>> >    B = VectorElement("B", "triangle", 3)
>> >    W = V + B
>> >
>> > and
>> >
>> >    V2 = VectorElement("CG", "triangle", 1)
>> >    W = V2 + B
>> >
>> > behave differently, which I imagine could be rather confusing.
>> >
>> >
>> >
>> > They do?
>> >
>> >
>> >
>> > Assumption A: If you only overload + for VectorElement and TensorElement.
>> >
>> > Under A, yes.
>> >
>> >
>> > I think if we want to overload +, by default we should treat these two
>> > cases equally.
>> >
>> >
>> > Well, I never intended to overload '+' for just Vector and Tensor elements,
>> > I would overload the MixedElement class which is the base class for
>> > the two special types.
>> > Then the two cases will result in the same element, we should of
>> > course check for equal length of the two mixed elements, and in case
>> > of nested mixed elements, we let the '+' operator handle this on the
>> > sub elements.
>> >
>> >
>> >
>> > Ok, then what will be the effect for a mixed/vector version of my previous
>> > example? (which is even more relevant for the PEERS element ;) )
>> >
>> > V = FiniteElement("RT", "triangle", 1)
>> > V = V * V
>> > Q = VectorElement("B", "triangle", 3, 4)
>> >
>> > W = V + Q
>>
>> This will (and should) crash for sure, len(V) = 2, len(Q) = 4; so it
>> makes no sense to enrich the sub elements.
>>
>> > The above W will then be an EnrichedElement of vector-valued elements?
>> >
>> > V = FiniteElement("RT", "triangle", 1)
>> > V = V * V
>> > Q = VectorElement("B", "triangle", 3)
>> > Q = Q * Q
>> >
>> > W = V + Q
>>
>> V0 = FiniteElement("RT", "triangle", 1)
>> V = V0 * V0
>> Q0 = VectorElement("B", "triangle", 3)
>> Q = Q0 * Q0
>> W = V + Q
>>
>> This is will end up as:
>>
>> E0 = V0 + Q0 # EnrichedElement([V0, Q0])
>> W = MixedElement( [E0,  E0] )
>>
>> and the example we had before:
>>
>> V0 = FiniteElement("CG", "triangle", 1)
>> V = V0 * V0
>> B0 = FiniteElement("B", "triangle", 3)
>> B  = B0 * B0
>> W = V + B
>>
>> will be:
>> E0 = V0 + B0
>> W = MixedElement([E0, E0])
>>
>> > While this will be a MixedElement of vector-valued Enriched elements?
>> >
>> > My main interest is just to keep the + operator "predictable".
>>
>> That looks pretty predictable to me, but there might be other elements
>> that I'm unaware of for which the logic breaks.
>
> If we want to address this issue, the same concept should be also
> considered for ElementRestriction. What would we expect if we enrich a
> vector element with a restricted vector element?
>
>  V = VectorElement("CG", "triangle", 1)
>  B = ElementRestriction(V, dc)
>
>  W = V + B
>
> Since this restricted element is not vector element anymore.

Can't we just check, inside the '+' operator, if an element is an
ElementRestriction and then if the restricted element is a
VectorElement
BTW, shouldn't it be RestrictedElement (like EnrichedElement) rather
than ElementRestriction?

Another possibility is to propagate the restriction to the subelements
when creating the restricted element and then return a VectorElement
with restricted sub elements. Did we try that and fail at some point?
I forgot.

Kristian

>
> Yours,
> Mehdi
>
>
>>
>> Kristian
>>
>> >
>> > Another advantages of using this approach is we don't need to define
>> > unnecessary scaler elements to just get mixed enriched element. The
>> > approach of defining scaler elements can be annoying, if we want to use
>> > both enriched and non-enriched vector elements(which is the case often
>> > for me).
>> >
>> > If we overload +, it is just enough to have:
>> >
>> > V = VectorElement("CG", "triangle", 1)
>> > B = VectorElement("B", "triangle", 3)
>> > M = V + B
>> >
>> > We can use M and V both to define our functions.
>> >
>> >
>> > This is definitely and advantage.
>> >
>> >
>> >
>> > If we want to extend VectorElement, this would be,
>> >
>> > V1 = FiniteElement("CG", "triangle", 1)
>> > B1 = FiniteElement("B", "triangle", 3)
>> > M = VectorElemnet(V1 + B1)
>> >
>> >
>> > But we can still extend the vector element to enable this it you think
>> > it will be useful, that was the essence of my earlier and confusing
>> > remark which should have been:
>> >
>> > 'We CAN of course still do this even if we decide on option 1)'
>> >
>> >
>> > Ok, sentence makes sense now!
>> >
>> > --
>> > Marie
>> >
>
>