ufl team mailing list archive

[Kent-Andre Mardal <kent-and@xxxxxxxxx>]

tir, 06.05.2008 kl. 10.38 +0200, skrev Martin Sandve Alnæs:
> 2008/5/6 Anders Logg <logg@xxxxxxxxx>:
> > On Tue, May 06, 2008 at 10:26:27AM +0200, Martin Sandve Alnæs wrote:
> >> 2008/5/6 Anders Logg <logg@xxxxxxxxx>:
> >> > On Mon, May 05, 2008 at 10:45:25PM +0200, Martin Sandve Alnæs wrote:
> >> >> 2008/5/5 Anders Logg <logg@xxxxxxxxx>:
> >> >> > On Mon, May 05, 2008 at 03:34:41PM +0200, Martin Sandve Alnæs wrote:
> >> >> >> 2008/5/5 Anders Logg <logg@xxxxxxxxx>:
> >> >> >> > On Mon, May 05, 2008 at 03:05:24PM +0200, Martin Sandve Alnæs wrote:
> >> >> >> >> 2008/5/5 Anders Logg <logg@xxxxxxxxx>:
> >> >> >> >> > On Mon, May 05, 2008 at 02:02:39PM +0200, Martin Sandve Alnæs wrote:
> >> >> >> >> >> 2008/5/2 UFL <ufl@xxxxxxxxxx>:
> >> >> >> >> >> > One or more new changesets pushed to the primary ufl repository.
> >> >> >> >> >> > A short summary of the last three changesets is included below.
> >> >> >> >> >> >
> >> >> >> >> >> > changeset:   99:ab1f19b9eb5545605d2651bf95508956aa27ad0b
> >> >> >> >> >> > tag:         tip
> >> >> >> >> >> > user:        Anders Logg <logg@xxxxxxxxx>
> >> >> >> >> >> > date:        Fri May 02 23:16:10 2008 +0200
> >> >> >> >> >> > files:       ufl/basisfunctions.py ufl/finiteelement.py
> >> >> >> >> >> > description:
> >> >> >> >> >> > Implement recursive initialization of tensor elements.
> >> >> >> >> >> > Unit tests pass, but see what you think of it.
> >> >> >> >> >>
> >> >> >> >> >> I don't agree with this, we want to have e.g. symmetric
> >> >> >> >> >> second order tensor elements, which do not fit into this.
> >> >> >> >> >
> >> >> >> >> > In what way do they not fit?
> >> >> >> >> >
> >> >> >> >> > The flag is_symmetric() is still there.
> >> >> >> >> >
> >> >> >> >>
> >> >> >> >> For a symmetric tensor in 3D, there should be only 6 subelements,
> >> >> >> >> and this recursive initialization will create 9.
> >> >> >> >
> >> >> >> > Does that matter? Creating an UFL element is very lightweight so it
> >> >> >> > shouldn't matter that we have a few extra elements. The important
> >> >> >> > thing is for algorithms (and form compilers) to look at is_symmetric
> >> >> >> > and use that to optimize.
> >> >> >>
> >> >> >> I'm not sure, but I feel that this should closely match the resulting
> >> >> >> UFC element hierarchy that comes out at the other side.
> >> >> >
> >> >> > Then what should the hierarchy look like for a symmetric 2x2 tensor
> >> >> > element?
> >> >> >
> >> >> > We could do
> >> >> >
> >> >> >  [[e, e], [None, e]]
> >> >> >
> >> >> > if we like.
> >> >> >
> >> >>
> >> >> Basically, yes, but I'm not sure what you mean with the []'s?
> >> >
> >> > I mean that we have a mixed element which has two sub elements,
> >> > each consisting of two (scalar) elements.
> >> >
> >> >> But if I interpret this correctly as Python list, I don't see the
> >> >> advantage of storing this kind of list with None values.
> >> >
> >> > No, it's nested classes. The list notation was just shorthand (and
> >> > confusing).
> >> >
> >> >> I'd rather store a single list of subelements, which can
> >> >> be handled like in any MixedElement most of the time,
> >> >> and store the subelement indices like:
> >> >
> >> > How would you store a simple Taylor-Hood element that way?
> >>
> >> Irrelevant. A Taylor-Hood element is not a TensorElement.
> >
> > No, it's not irrelevant if a TensorElement should be a subclass of
> > MixedElement (which I think it should since it is a special case).
> >
> >> > I think the natural thing would be to have a MixedElement which has
> >> > two sub elements. The first one of these (for u) will be a
> >> > VectorElement (which is a special case of a MixedElement) and that
> >> > element will have a list of two scalar sub elements. The second one
> >> > (for p) will be a FiniteElement (a scalar).
> >> >
> >> > Similarly, one can take a vector-valued BDM-element for u and a scalar
> >> > element for p and combine them into a MixedElement. In that case, each
> >> > of the two sub elements will be a FiniteElement, but one will be
> >> > vector-valued and one scalar.
> >>
> >> I completely agree with that for a general MixedElement.
> >>
> >> I just don't agree that a TensorElement should be
> >> represented as a nested hierarchy of MixedElements,
> >> since this will not be simple as intended for symmetric elements.
> >>
> >> Actually, I'm still not quite comfortable with VectorElement meaning
> >> "vector of element" instead of "vector valued element", and I don't
> >> think that matches what people would expect. Our different opinions
> >> here may be related to this.
> >
> > It's very convenient if one can take any scalar element and use that
> > to create a vector-valued element, and it's also convenient if one can
> > have a single base class (MixedElement) which takes care of it all
> > and have VectorElement and TensorElement as special cases.
> >
> > --
> > Anders
> 
> I never said TensorElement shouldn't be a MixedElement.
> I just want it to be a single MixedElement, instead of
> containing a nested hierarchy of MixedElements.
> The reason is that I don't think symmetric elements will fit
> nicely into the hierarchic approach. I suspect using "None"
> as you suggested above will lead to all sorts of special cases.
> 
> --
> Martin

I think a mixed element is a collection of (typically different)
elements, a vector element is an element with values that are vectors, a
tensor element is an element with values that are tensors. Symmetric
tensors are useful because then appear often.  

You can of course create a 2D vector element as a mixed element
containing two scalar elements. This is not typical, but can be done.
Still this should not make VectorElement a subclass of MixedElement or
vica versa.  

The famous AFW elasticity elements is a mixed element where the first
element is a (possibly symmetric) tensor, the second element is a vector
element and additionally you can have a scalar element if you want. 

Kent