ffc team mailing list archive

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

On 18 June 2010 15:19, Marie Rognes <meg@xxxxxxxxx> wrote:
> On 18. juni 2010 15:08, 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.
>>
>>
>
> This will not (and I think should not) crash at the moment: both V and Q
> has rank dimension 4, and so enrichment makes sense.

I think it should, because you will make FFC guess how you want to
enrich your element V because the number of sub-elements is not equal.
Using the same logic as in the first 'RT' example:

V = FiniteElement("RT", "triangle", 1)
Q = VectorElement("B", "triangle", 3)
W = V + Q

Which is an EnrichedElement([V, Q])

What you want should be implemented as:

V0 = FiniteElement("RT", "triangle", 1)
V = V0 * V0
Q = VectorElement("B", "triangle", 3)

W = V + (Q * Q)

Then FFC will know what to do because it sees two VectorElements with
two sub elements and it will proceed to enrich sub elements such that:

W = MixedElement([ V0 + Q, V0 + Q ])

which is a vector version of the first example.

> However, if you try to progagate the enrichment to sub-elements, you
> will run into trouble.
> Hence, I assume that you will either throw an error (which I would not
> like, since the construction is not erranous) or return just the
> original EnrichedElement.
>
>
>>> 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])
>>
>>
>
> Agree.
>
>>> 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.
>>
>>
>
> In the vector RT/B example above, the first version becomes an
> EnrichedElement while the second becomes a MixedElement. I don't find
> that transparent.

It is if you use MY definition :)

> I would really prefer to have the conversion from enriched to mixed be
> explicit. But I'll stop arguing now ;)

So you would prefer if we just implemented

W = VectorElement(V + Q) ?

Kristian

> --
> Marie
>
>
>> 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
>>>
>>>
>
>