ffc team mailing list archive

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

On 16 June 2010 17:28, Garth N. Wells <gnw20@xxxxxxxxx> wrote:
>
>
> On 16/06/10 15:55, Kristian Oelgaard wrote:
>>
>> On 16 June 2010 16:45, Garth N. Wells<gnw20@xxxxxxxxx>  wrote:
>>>
>>>
>>> On 16/06/10 15:20, Marie Rognes wrote:
>>>>
>>>> On 16. juni 2010 15:51, Mehdi wrote:
>>>>>
>>>>> On Wed, 2010-06-16 at 14:03 +0200, Marie Rognes wrote:
>>>>>
>>>>>> On 16. juni 2010 13:41, Mehdi wrote:
>>>>>>
>>>>>>> On Tue, 2010-06-15 at 15:35 +0200, Marie Rognes wrote:
>>>>>>>
>>>>>>>
>>>>>>>> -------- Original Message --------
>>>>>>>>                           Subject:
>>>>>>>> Re: function on EnrichedElement
>>>>>>>>                              Date:
>>>>>>>> Tue, 15 Jun 2010 15:27:44 +0200
>>>>>>>>                              From:
>>>>>>>> Marie Rognes<meg@xxxxxxxxx>
>>>>>>>>                                To:
>>>>>>>> Mehdi<m.nikbakht@xxxxxxxxxx>
>>>>>>>>                                CC:
>>>>>>>> gnw20@xxxxxxxxx, Anders Logg
>>>>>>>> <logg@xxxxxxxxx>
>>>>>>>>
>>>>>>>>
>>>>>>>> On 15. juni 2010 15:12, Mehdi wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>> On Tue, 2010-06-15 at 14:26 +0200, Marie Rognes wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> On 14. juni 2010 19:57, Marie Rognes wrote:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> On 14. juni 2010 19:37, Mehdi wrote:
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>> On Mon, 2010-06-14 at 19:18 +0200, Marie Rognes wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> On 14. juni 2010 18:10, Mehdi wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hi Marie,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I have a function defined on Enriched Element. I want to have
>>>>>>>>>>>>>> access to
>>>>>>>>>>>>>> the subfunctions defined on this space. How ffc/ufl can be
>>>>>>>>>>>>>> extended to
>>>>>>>>>>>>>> handle this issue?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>> Could you give me a piece of sample code?
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>> The input is something like this,
>>>>>>>>>>>>
>>>>>>>>>>>> Elem1 = VectorElement("Lagrange", triangle, 2)
>>>>>>>>>>>> Elem2 = VectorElement("Lagrange", triangle, 1)
>>>>>>>>>>>>
>>>>>>>>>>>> Element = Elem1 + Elem2
>>>>>>>>>>>>
>>>>>>>>>>>> u = Coefficient(Element)
>>>>>>>>>>>>
>>>>>>>>>>>> # I want to have this functionality
>>>>>>>>>>>> u1, u2 = split(u)
>>>>>>>>>>>>
>>>>>>>>>>>> Thank you in advance.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>> Will see what I can do tomorrow.
>>>>>>>>>>>
>>>>>>>>>>> Note that functions on enriched spaces can be a bit treacherous
>>>>>>>>>>> since
>>>>>>>>>>> the basis is not a nodal basis.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>> I've been thinking some about this. Let me try to explain why this
>>>>>>>>>> is
>>>>>>>>>> nontrivial.
>>>>>>>>>>
>>>>>>>>>> Say, we have two element spaces
>>>>>>>>>>
>>>>>>>>>>     V = span ( {v_i} )
>>>>>>>>>>     Q = span ( {q_j})
>>>>>>>>>>
>>>>>>>>>> and create an "enriched space"
>>>>>>>>>>
>>>>>>>>>>     W = V + Q
>>>>>>>>>>
>>>>>>>>>> so that
>>>>>>>>>>
>>>>>>>>>>     W = span ( {v_i, q_j})
>>>>>>>>>>
>>>>>>>>>> We also define the degrees of freedom on W by taking the set of
>>>>>>>>>> all degrees of freedom on V (L_i) and all degrees of freedom on Q
>>>>>>>>>> (K_j)
>>>>>>>>>>
>>>>>>>>>>     ( {L_i}, {K_j} )
>>>>>>>>>>
>>>>>>>>>> At this point, we are starting to tweak the ffc element framework
>>>>>>>>>> a
>>>>>>>>>> bit,
>>>>>>>>>> because the basis for W is _not_ a nodal basis with respect to the
>>>>>>>>>> degrees of freedom: it might be (actually, quite often is) that
>>>>>>>>>>
>>>>>>>>>>     L_i (q_j) \not = 0
>>>>>>>>>>
>>>>>>>>>> for all i, j and vice versa for K_j (v_i).)
>>>>>>>>>>
>>>>>>>>>> A function f in W can be represented as
>>>>>>>>>>
>>>>>>>>>>     f = \alpha_i v_i + beta_j q_j
>>>>>>>>>>
>>>>>>>>>> However, note that for some degree of freedom L_k,
>>>>>>>>>>
>>>>>>>>>>     L_k(f) = \alpha_k + \beta_j L_k(q_j)
>>>>>>>>>>
>>>>>>>>>> Hence, the coefficients in the vector do _not_ directly correspond
>>>>>>>>>> to
>>>>>>>>>> the degrees of freedom, unless L_k(q_j) = 0 for all k, j. This
>>>>>>>>>> means
>>>>>>>>>> that most kinds of function manipulation on enriched elements give
>>>>>>>>>> you
>>>>>>>>>> something different than what you might think you get.
>>>>>>>>>>
>>>>>>>>>> There are however exceptions where things are good: Take for
>>>>>>>>>> instance
>>>>>>>>>> continuous linears plus bubble:
>>>>>>>>>>
>>>>>>>>>>     V = FiniteElement("CG", "triangle", 1)
>>>>>>>>>>     Q = FiniteElement("B", "triangle", 3)
>>>>>>>>>>     W = V + Q
>>>>>>>>>>
>>>>>>>>>> Since the bubble basis functions are zero on the boundary of each
>>>>>>>>>> element, with the above notation
>>>>>>>>>>
>>>>>>>>>>     L_k (q_j) = 0
>>>>>>>>>>
>>>>>>>>>>
>>>>>>> This is not the case for the enrichment space(Q) in the partition of
>>>>>>> unity method. They are often defined on the same dofs that we have
>>>>>>> defined standard space V.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>>> for all k, j. This means that you can do
>>>>>>>>>>
>>>>>>>>>>     f = Function(W)
>>>>>>>>>>     g = interpolate(f, V)
>>>>>>>>>>
>>>>>>>>>> Then g will be what I think you want from
>>>>>>>>>>
>>>>>>>>>>     (g, h) = split(f)
>>>>>>>>>>
>>>>>>>>>> In order to get h, you could do
>>>>>>>>>>
>>>>>>>>>>     h = f - g
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It would be possible to extract the vectors {\alpha_i} and
>>>>>>>>>> {\beta_j}
>>>>>>>>>> from a Function on an enriched elements, but this requires quite a
>>>>>>>>>> bit
>>>>>>>>>> of work, and is mainly DOLFIN related (rather than FFC/UFL).
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>> To handle this inside DOLFIN, we extract required data form vectors.
>>>>>>> Why
>>>>>>> performing the approach inisde FFC/UFL is difficult? Isn't it just
>>>>>>> enough to pick up the components corresponding to a specific space
>>>>>>> from
>>>>>>> enriched space?
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> I don't see how to do this. If you or anyone else know how, go ahead
>>>>>> :)
>>>>>>
>>>>> OK. let me give it a try. Maybe this is a hack, but I think we may need
>>>>> to attach offsets for the sub functions derived from enriched space. Is
>>>>> there any reason why not this should work?
>>>>>
>>>>>
>>>>
>>>>
>>>> I probably misunderstood your original request, thinking that you wanted
>>>> to extract
>>>> (v, w) from {v + w}...
>>>>
>>>> One way of doing what I now _think_ that you want, is to add some
>>>> functionality to FFC/UFL to convert an enriched mixed element to a mixed
>>>> enriched element and then do split. This is feasible. But I still think
>>>> that this should _not_ be the default behaviour for enriched mixed
>>>> elements.
>>>>
>>>
>>> A simple example of what's missing is the Stokes mini element. It's not
>>> presently possible to prescribe only one of the displacement components
>>> (e.g. u_x) on the boundary. Using V.sub(0).sub(0) in DOLFIN to get the
>>> u_x
>>> component breaks.
>>
>> Could it work if instead of doing:
>>
>> P1 = VectorElement("Lagrange", triangle, 1)
>> B = VectorElement("Bubble", triangle, 3)
>> Q = FiniteElement("CG", triangle, 1)
>> Mini =  (P1 + B)*Q
>>
>> you did:
>>
>> P1 = FiniteElement("Lagrange", triangle, 1)
>> B = FiniteElement("Bubble", triangle, 3)
>> Mini = MixedElement([P1 + B], [P1 + B])*Q
>>
>
> Yes, that will work, but is it what we want? It's a bit clumsy and we lose
> the dimension-independence since in 3D we would need
>
>  P1 = FiniteElement("Lagrange", tetrahedron, 1)
>  B = FiniteElement("Bubble", tetrahedron, 3)
>  Mini = MixedElement([P1 + B], [P1 + B], [P1 + B])*Q

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.

Kristian

> Garth
>
>> Kristian
>>
>>> Garth
>>>
>>>
>>>
>>>>
>>>> --
>>>> Marie
>>>>
>>>>>  Mehdi
>>>>>
>>>>>
>>>>>> --
>>>>>> Marie
>>>>>>
>>>>>>
>>>>>>
>>>>>>> Mehdi
>>>>>>>
>>>>
>>>
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