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From: John Peterson <jwpeterson@gm...>  20081112 22:45:40

On Wed, Nov 12, 2008 at 4:38 PM, Roy Stogner <roystgnr@...> wrote: > > On Wed, 12 Nov 2008, John Peterson wrote: > >> 1.) Just remember that higherthannormal order quadrature on pyramids >> is required and your answer may be inaccurate. AKA "do nothing" :) > > Not a good answer, but probably a fair one. > >> 2.) Redefine, within the pyramid quadrature rules, the meaning of >> order. I.e. return a rule several orders higher than what the user >> requests. > > Maybe an "extra_pyramid_quadrature_order()" option? So we can give it > a safe default but still let users override it for efficiency if they > know what they're doing. Yeah, this sounds like a good idea, at least until something useful comes out of option 3... Maybe a flag in QBase, similar to the way we let knowledgable users disallow the use of rules with negative weights? >> 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... > > This could be ideal.  John 
From: Roy Stogner <roystgnr@ic...>  20081112 22:39:46

On Wed, 12 Nov 2008, John Peterson wrote: > 1.) Just remember that higherthannormal order quadrature on pyramids > is required and your answer may be inaccurate. AKA "do nothing" :) Not a good answer, but probably a fair one. > 2.) Redefine, within the pyramid quadrature rules, the meaning of > order. I.e. return a rule several orders higher than what the user > requests. Maybe an "extra_pyramid_quadrature_order()" option? So we can give it a safe default but still let users override it for efficiency if they know what they're doing. > 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... This could be ideal.  Roy 
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 > 
From: John Peterson <jwpeterson@gm...>  20081112 22:25:12

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 
From: Tim Kroeger <tim.kroeger@ce...>  20081112 16:38:19

Dear all, Good news: I was finally able to get my application running on the cluster. Well, "running" means that it doesn't crash due to problems of the cluster nor due to problems of our institute's software. It crashes as soon as I make use of a ShellMatrix, though. I'll debug that in the next days and will certainly send you more patches. Best Regards, Tim  Dr. Tim Kroeger Phone +494212187710 tim.kroeger@..., tim.kroeger@... Fax +494212184236 MeVis Research GmbH, Universitaetsallee 29, 28359 Bremen, Germany Amtsgericht Bremen HRB 16222 Geschaeftsfuehrer: Prof. Dr. H.O. Peitgen 