On Wed, 2010-06-16 at 18:04 +0200, Kristian Oelgaard wrote: > On 16 June 2010 17:28, Garth N. Wells <[email protected]> wrote: > > > > > > On 16/06/10 15:55, Kristian Oelgaard wrote: > >> > >> On 16 June 2010 16:45, Garth N. Wells<[email protected]> 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<[email protected]> > >>>>>>>> To: > >>>>>>>> Mehdi<[email protected]> > >>>>>>>> CC: > >>>>>>>> [email protected], Anders Logg > >>>>>>>> <[email protected]> > >>>>>>>> > >>>>>>>> > >>>>>>>> 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. Mehdi > > Kristian > > > Garth > > > >> Kristian > >> > >>> Garth > >>> > >>> > >>> > >>>> > >>>> -- > >>>> Marie > >>>> > >>>>> Mehdi > >>>>> > >>>>> > >>>>>> -- > >>>>>> Marie > >>>>>> > >>>>>> > >>>>>> > >>>>>>> Mehdi > >>>>>>> > >>>> > >>> > >>> _______________________________________________ > >>> Mailing list: https://launchpad.net/~ffc > >>> Post to : [email protected] > >>> Unsubscribe : https://launchpad.net/~ffc > >>> More help : https://help.launchpad.net/ListHelp > >>> > > > > > > _______________________________________________ > Mailing list: https://launchpad.net/~ffc > Post to : [email protected] > Unsubscribe : https://launchpad.net/~ffc > More help : https://help.launchpad.net/ListHelp _______________________________________________ Mailing list: https://launchpad.net/~ffc Post to : [email protected] Unsubscribe : https://launchpad.net/~ffc More help : https://help.launchpad.net/ListHelp
