ufl team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Mon, Feb 23, 2009 at 12:59:33PM +0100, Martin Sandve Alnæs wrote:
> On Mon, Feb 23, 2009 at 12:37 PM, Kristian Oelgaard
> <k.b.oelgaard@xxxxxxxxxx> wrote:
> > Quoting Martin Sandve Alnæs <martinal@xxxxxxxxx>:
> >
> >> On Mon, Feb 23, 2009 at 11:44 AM, Kristian Oelgaard
> >> <k.b.oelgaard@xxxxxxxxxx> wrote:
> >> > Quoting Martin Sandve Alnæs <martinal@xxxxxxxxx>:
> >> >
> >> >> On Mon, Feb 23, 2009 at 11:23 AM, Kristian Oelgaard
> >> >> <k.b.oelgaard@xxxxxxxxxx> wrote:
> >> >> > Quoting Kristian Oelgaard <k.b.oelgaard@xxxxxxxxxx>:
> >> >> >
> >> >> >> Quoting Anders Logg <logg@xxxxxxxxx>:
> >> >> >>
> >> >> >> > I thought about it some more and I think I might be able to generate
> >> >> >> > the indices on the fly as part of the monomial extraction so it
> >> might
> >> >> >> > not be necessary.
> >> >> >> >
> >> >> >> > So if it's not needed for quadrature it can be part of the monomial
> >> >> >> > extraction. Otherwise, it seems pretty simple to make a transformer
> >> >> >> > for index renumbering.
> >> >> >>
> >> >> >> I don't think index renumbering is needed for quadrature. A thing that
> >> is
> >> >> >> needed, however, is the component number of functions/basisfunctions
> >> but
> >> >> is
> >> >> >> this
> >> >> >> alway represented by index?
> >> >> >
> >> >> > Sorry, 'index' should be Indexed in the above.
> >> >> >
> >> >> > Kristian
> >> >>
> >> >> This question is too inaccurate for me to know what to say... But I'll
> >> try.
> >> >>
> >> >> A (basis) function never _has_ an index, but expressions
> >> >> may refer to a component of a function using Indexed.
> >> >> However, you can also have e.g. sums of Functions
> >> >> on vector elements, and Indexed outside that.
> >> >
> >> > Does this means that for
> >> >
> >> > a = V[0].dx(1)*dx
> >> >
> >> > one will have to return something like [V[0].dx(1), V[1].dx(1)] from
> >> > BasisFunction and then let Indexed pick the correct value? This looks very
> >> > inefficient and it makes it more complicated to know which variable names
> >> are
> >> > going to be used in the code.
> >>
> >> I'm not sure, but if I understand you right, you're talking about using
> >> the transformer framework. As I've suggested before, state can be
> >> kept on a stack, updated by Indexed and SpatialDerivative, and
> >> then basis_function can simply return the current component (0)
> >> and derivative (1).
> >
> > Yes, and I get all that. I just wanted to be sure that Indexed always referred
> > to components of basisfunctions. But I see now that Indexed is also used for the
> > components of ComponentTensor but in this case a second mapping of index values
> > is needed.
> 
> I think you've got it right, but just to be sure: It's a bit more
> general than this.
> 
> Indexed represents components of <any tensor-valued expression>,
> which can also be for example a Sum of other tensor-valued expressions,
> a ComponentTensor, or a ListTensor.
> 
> ComponentTensor represents a tensor-valued expression
> with components given by a scalar expression with free indices
> that are "bound" to tensor axes.
> 
> In a sense ComponentTensor and Indexed are opposite operations,
> Indexed mapping from tensor valued to scalar valued with free indices,
> and ComponentTensor mapping from scalar valued with free indices to
> tensor valued.

So why then are both needed in the current example? I would imagine
Indexed applied to ComponentTensor would cancel out so that we can get

 IndexSum
 (
  IndexSum
  (
    Product
    (
      Indexed
        (
        SpatialDerivative
        (
          BasisFunction(VectorElement('Lagrange',1, 2), -2)
          MultiIndex((Index(16),))
        )
        MultiIndex((Index(17),))

-- 
Anders

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