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["Robert Kirby" <robert.c.kirby@xxxxxxxxx>]

Still, in this case you have to handle a non-affine mapping so the jacobian
varies spatially.  The quadrature module will have to be generalized.  I
imagine that isn't too hard once the geometry is in place.

Rob

On Jan 24, 2008 10:58 AM, Anders Logg <logg@xxxxxxxxx> wrote:

> On Thu, Jan 24, 2008 at 10:06:19AM -0600, Robert Kirby wrote:
> > I will also point out that, even if FIAT had these element shapes, it
> would be
> > some work for FFC to adapt to use them.  We would be in the world of
> non-affine
> > transformations, which means that the tensor representation in FFC would
> not
> > work.  It can be generalized, but with some cost in run-time operation
> count.
> >
> > Rob
>
> Yes, or we could just go for quadrature in that case (ffc -r quadrature).
>
> --
> Anders
>
>
> > On Jan 24, 2008 9:15 AM, Martin Sandve Aln s <martinal@xxxxxxxxx> wrote:
> >
> >     2008/1/24, Anders Logg <logg@xxxxxxxxx>:
> >     > On Thu, Jan 24, 2008 at 07:57:43AM -0600, Robert Kirby wrote:
> >     > > Well, FIAT really does simplices because they're hard.  Hexes
> and
> >     rectangles
> >     > > have tensor-product bases for H(div), H(curl), and H1, so you
> should
> >     really be
> >     > > doing spectral-type techniques.  See the thesis of Heintsch
> (sp?) at
> >     NYU for
> >     > > some interesting work on high order H(div) and H(curl) a few
> years ago.
> >      Not
> >     > > sure if it got published, but it was very good
> >     > >
> >     > > I now have a user at Sandia who wants the other shapes, so I
> will be
> >     looking at
> >     > > doing this, either in Python or else with straight
> tensor-products in
> >     C++.  Of
> >     > > course, pyramids and prisms present wrinkles of being somewhere
> >     in-between.
> >     >
> >     > There has also been some interest in adding quads and hexes to the
> DOLFIN
> >     > mesh library (which should not be very hard) so this might also
> happen
> >     > (if someone has time to implement it).
> >     >
> >
> >     As a sidenote, SyFi supports code generation for quads and hexes (at
> >     least Lagrange elements).
> >
> >
> >
> >     > > On Jan 23, 2008 9:07 PM, Harish Narayanan <harish@xxxxxxxxxxx >
> wrote:
> >     > >
> >     > >     Greetings,
> >     > >
> >     > >     I understand from the documentation in FIAT that all its
> reference
> >     > >     elements treat spaces as simplicial complexes. Is there an
> obvious
> >     > >     difficulty in extending this to non-simplicial elements
> (assuming
> >     the
> >     > >     mesh is suitably generated elsewhere)?
> >     > >
> >     > >     I would be curious to read some literature on this topic if
> someone
> >     were
> >     > >     willing to point me to it.
> >     > >
> >     > >     Thanks,
> >     > >     Harish
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