[petsc-dev] 2D finite elements in 3D ambient space

[Matthew Knepley]

On Mon, Dec 2, 2013 at 8:45 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Dec 2, 2013 at 8:31 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
>
>> Matthew Knepley <knepley at gmail.com> writes:
>>
>> [added context]
>>
>> >>>> Unfortunately, something more is required for higher order accuracy,
>> >>>> since naively the coordinate section itself would have to be higher
>> >>>> order, and this would require lots of changes (the equivalent of
>> >>>> DMPlexComputeCellGeometry would be called once per quadrature point
>> >>>> instead of once per element).
>> >>>
>> >>> I have never been convinced that isoperimetric stuff produces enough
>> benefit
>> >>> for its complication. Polynomials are not good approximators for the
>> >>> Jacobian of these transforms. NURBS are so much better.
>> >>
>> >> The value of NURBS is that (a) some coordinate transformations can be
>> >> represented exactly and (b) for certain problems, the rest solution can
>> >> be represented exactly in the ansatz space.  Quadrature error does not
>> >> magically vanish.
>> >
>> > My point is that trying to resolve particular geometry with polynomials
>> is
>> > very slowly convergent. NURBS are much better. It depends on how
>> > complicated your geometry is.
>>
>> I thought you were objecting to "the equivalent of
>> DMPlexComputeCellGeometry would be called once per quadrature point
>> instead of once per element".  If you were in fact agreeing with this,
>> and the talk of NURBS was just a tangent, then we are now on the same
>> page.
>>
>
> I am agreeing with that. I just hate isoperimetric. Its terrible at really
> resolving geometry.
>

This is called "nonaffine" in PetscFE. I just merged it to next.

   Matt


>    Matt
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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