fiat team mailing list archive

[Kristian Oelgaard <k.b.oelgaard@xxxxxxxxxx>]

Quoting 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.

quadrature representation mirrors more or less the tensor contraction, the
difference is that it loops the quadrature points (to compute the 'reference
tensor') runtime. But still it might be easier to adapt things in the quadrature
module to other elements.

Kristian
 
> 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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