ffc team mailing list archive

[Marie Rognes <meg@xxxxxxxxx>]

On 17. juni 2010 15:44, Mehdi wrote:
> On Wed, 2010-06-16 at 18:04 +0200, Kristian Oelgaard wrote:
>   
>> 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.
>>     
> 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

    v = TestFunction(W)
    u = TrialFunction(W)
    a = dot(v, u)*dx


--
Marie




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