From: Derek Gaston <friedmud@gm...>  20081112 22:33:39

For now... I would vote for "do nothing"... maybe print a warning in debug mode. Having the library try to interpret what you "really" want might be trouble. Derek On Wed, Nov 12, 2008 at 3:24 PM, John Peterson <jwpeterson@...> wrote: > On Thu, Nov 6, 2008 at 11:18 AM, John Peterson <jwpeterson@...> > wrote: > > On Thu, Nov 6, 2008 at 11:03 AM, Roy Stogner <roystgnr@...> > wrote: > >> John Peterson wrote: > >>> Anyone know anything about the > >>> accuracy of quadrature for functions which are ratios of polynomials? > >> > >> We can derive custom quadrature rules which would integrate a mass > matrix > >> exactly... but would they then also integrate, say, a Laplacian matrix > >> exactly? The answer is an obvious "yes" for polynomial bases but I'd > expect > >> a "no" for pyramids. That could be bad. > >> > >> What are we doing for them now? > > > > The current quadrature rules have accuracies like you would expect for > > 1D elements, since they are conical products of Gausslike rules. So, > > for example, a 2x2x2 rule will integrate exactly all monomials of the > > form x^a y^b z^c, a+b+c <= 3. I have no idea what will happen when we > > try to integrate the rational basis functions... > > Just a quick update on the quadrature over pyramids stuff. > > After checking it with Maple, it appears that the "standard" > 2nd/3rdorder quadrature rule can exactly integrate the Pyramid5 mass > matrix. The laplace matrix, however, is a different story. I needed > to go up to 6/7thorder quadrature before I could get 910 digits of > precision from LibMesh. > > At first, this seems a little paradoxical since the Laplace matrix is > usually the easier of the two, but with rational basis functions, the > more derivatives you take the more poles you get in the denominator, > and the harder it is to integrate the functions. Since the default > quadrature rule is currently selected by the FEType without regard to > the geometric element type, it's not immediately obvious how we should > ensure the user gets accurate quadrature on pyramids. A couple > options... > > 1.) Just remember that higherthannormal order quadrature on pyramids > is required and your answer may be inaccurate. AKA "do nothing" :) > 2.) Redefine, within the pyramid quadrature rules, the meaning of > order. I.e. return a rule several orders higher than what the user > requests. > 3.) Research quadrature rules for rational functions. I have a few > papers on this but haven't looked into it too much yet. Phillipe > Devloo may be doing something special in his library, so I will check > there as well... > >  > John > >  > This SF.Net email is sponsored by the Moblin Your Move Developer's > challenge > Build the coolest Linux based applications with Moblin SDK & win great > prizes > Grand prize is a trip for two to an Open Source event anywhere in the world > http://moblincontest.org/redirect.php?banner_id=100&url=/ > _______________________________________________ > Libmeshdevel mailing list > Libmeshdevel@... > https://lists.sourceforge.net/lists/listinfo/libmeshdevel > 