On Mon, Dec 2, 2013 at 8:01 PM, Jed Brown <[email protected]> wrote:
> Matthew Knepley <[email protected]> writes: > >> 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. > > These issues are orthogonal. If the mapping is not affine, you need > separate Jacobians at each quadrature point. Non-affine elements are > required for high-order accuracy with curved boundaries, and in many > cases when using quad and hex elements. > I agree that non-affine stuff requires the linearization of the mapping at each quadrature. The interface Geoff suggested is the one I have been using for that. I am fine with it. > 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. 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
