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

[Matthew Knepley]

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.

   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
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