On Mon, Dec 2, 2013 at 8:45 PM, Matthew Knepley <[email protected]> wrote:
> 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. > 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
