dolfin team mailing list archive

["Martin Sandve Alnæs" <martinal@xxxxxxxxx>]

2007/4/12, Garth N. Wells <g.n.wells@xxxxxxxxxx>:
> Anders Logg wrote:
> > On Wed, Apr 11, 2007 at 06:15:30PM +0200, Garth N. Wells wrote:
> >> Anders Logg wrote:
> >>> On Tue, Apr 10, 2007 at 06:14:12PM +0200, Garth N. Wells wrote:
> >>>> Connected to Kristian's work on quadrature in FFC, we should think about
> >>>> how to work with functions which do not come from a finite element
> >>>> space. Such functions (like stress for a plasticity model or viscosity
> >>>> for a non-Newtonian flow) are evaluated at quadrature points, rather
> >>>> than at nodes.
> >>>>
> >>>> Garth
> >>> The current design (including UFC) assumes that all functions can be
> >>> interpolated to a finite element basis, but I think it will work for
> >>> the quadrature code generation to imagine that you have a finite
> >>> element basis where the quadrature points are the same as the nodes.
> >>> (But you never need to know the basis functions.)
> >>>
> >>> The array of coefficients (double** w) that comes in to the function
> >>> tabulate_tensor() should contain the coefficients, but for the
> >>> quadrature these will be the same as the values at the quadrature
> >>> points, and this should work out fine since the values that go in to w
> >>> are decided by the evaluate_dof() function that also gets
> >>> generated.
> >>>
> >>> So the quadrature code generator just needs to make sure that
> >>> evaluate_dof() picks the values at the quadrature points.
> >>>
> >> The problem with this approach is that it's not possible to create a
> >> consistent linearisation when dofs and integration points do not
> >> coincide. Kristian and I went through this in detail a while ago.
> >>
> >> Garth
> >
> > Yes, I remember, but my suggestion was that the dofs and the points
> > should coincide. Then the linearization should be ok?
> >
>
> I don't see how this can work. The locations of the dofs and the Gauss
> quadrature points do not in general coincide.

The idea is to construct an "artificial finite element" where the dofs
_are_ values in the Gauss quadrature points. By generating a
corresponding implementation of ufc::finite_element where
evaluate_dof(i, f, ...) evaluates the function f in dof (quadpoint) i,
and local_dimension() returns the number of quadrature points, this
should work.

Some functions like evaluate_basis can have empty implementations,
perhaps raising an exception, if no sensible implementation is
possible.

martin