On Mon, Dec 2, 2013 at 8:31 PM, Jed Brown <[email protected]> wrote:
> Matthew Knepley <[email protected]> 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
