From: Lorenzo Botti <bottilorenzo@gm...>  20090530 00:50:25

> > It occurs to me that socalled "rotationalinvariant" quadrature rules > could be a great optimization for interior DG integration and some of > the integration routines in Kelly/JumpErrorEstimator. Such rules are > invariant under rotations of the reference element in the sense that: > if quadrature point q exists in the original rule, then it also exists > (and with the same weight) under all possible symmetrypreserving > rotations (and reflections, etc, in general) of the reference element. > > For example, the tensor product Gaussian quadrature rules on Quads > have this property, and a number of the rules for triangles do as > well. This implies that there is only a simple permutation matrix > needed to map between the rule on one side of the interior face and > the rule on the other. Since there are a finite number of possible > orientations that two face neighbors can share, these permutation > matrices could be precomputed and stored (as bitsets if you wanted) > ahead of time. > > >  > John I see what you mean but I have to warn about this practice. If you are using modal basis functions, even with rotationalinvariant quadrature rules, you have to take care of the orientation of the element not to integrate your odd modes differently on opposite sides. You could have also problems with nonlinear numerical fluxes when you compute the solution at a physical space side quadrature point for the element and his neighbor. The procedure I've written on the previous mail works well for conforming meshes and is faster than inverse mapping. It is simply a mapping to the reference space for the element and his neighbor (once the correct ordering of nodes is defined). For nonconforming meshes I don't know how to identify the side child number from the parent, the child and the side. With the side child number i could use embedding matrix to compute the neighbor nodes coordinates in reference space. Thank you for any suggestion. Lorenzo 