On 16 June 2010 16:45, Garth N. Wells <gn...@cam.ac.uk> 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<m...@simula.no>
>>>>>> To:
>>>>>> Mehdi<m.nikba...@tudelft.nl>
>>>>>> CC:
>>>>>> gn...@cam.ac.uk, Anders Logg
>>>>>> <l...@simula.no>
>>>>>>
>>>>>>
>>>>>> 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
Kristian
> Garth
>
>
>
>>
>> --
>> Marie
>>
>>> Mehdi
>>>
>>>
>>>> --
>>>> Marie
>>>>
>>>>
>>>>
>>>>> Mehdi
>>>>>
>>
>
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