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From: John Peterson <jwpeterson@gm...>  20080618 22:18:13

On Wed, Jun 18, 2008 at 1:52 PM, David Knezevic <dave.knez@...> wrote: > > hehe, well the way the paper is written doesn't inspire me with confidence > in their results, so I'd be very interested to hear the results of the > comparisons. So far, so good. This 14point rule described by Walkington returns the same results for polynomials of fifth order as the 15 point rule we already have in LibMesh. Can anyone suggest some good test functions to integrate so I can test it further? Preferably something that has an analytical solution over the reference tet but that's not crucial. It's not a huge gain but the fifthorder rule is used a lot for integrating quadratics in say NavierStokes.  John 
From: David Knezevic <dave.knez@gm...>  20080618 18:52:51

Hi John, > I think this is actually a 14point rule in Table 2.1. I didn't see > it explicitly stated anywhere that it was a 15point rule, and it > turns out that > > 4*w_1 + 4*w_2 + 6*w_3 = 1/6 > > where 4 and 6 are the cardinality of the \Xi_1 and \Xi_{11} sets, > respectively. (Awful notation BTW!) > > This is equal to the volume of the Tet4 (=1/d!) so I don't think > there's a 15th point. Well that's sorted then, thanks. I assumed based on equation (2.1) that it would be a 15point rule because (2.1) gives the fifth order quadrature rule defined in arbitrary dimension, and that includes the w_0 term. But they mention that Table 2.1 gives "simplified" versions of the quadrature rules in 2D or 3D, so I guess the w_0 term drops out in this simplified form. > This would also explain why it doesn't match our 15point rule. I'm > still skeptical of the accuracyorder claims in any case. hehe, well the way the paper is written doesn't inspire me with confidence in their results, so I'd be very interested to hear the results of the comparisons.  Dave 
From: John Peterson <jwpeterson@gm...>  20080618 18:31:36

Hi Dave, On Wed, Jun 18, 2008 at 11:50 AM, David Knezevic <dave.knez@...> wrote: > >> Did you see where w_0 is given for this degree 5 tet rule? I suppose >> I can figure it out by summing the other 14 and subtracting from the >> volume... >> > > Good question, I'm not sure. Is it intended to imply that w_0 is the same in > for both rows of Table 2.1? If so, it's not very clearly written... I think this is actually a 14point rule in Table 2.1. I didn't see it explicitly stated anywhere that it was a 15point rule, and it turns out that 4*w_1 + 4*w_2 + 6*w_3 = 1/6 where 4 and 6 are the cardinality of the \Xi_1 and \Xi_{11} sets, respectively. (Awful notation BTW!) This is equal to the volume of the Tet4 (=1/d!) so I don't think there's a 15th point. This would also explain why it doesn't match our 15point rule. I'm still skeptical of the accuracyorder claims in any case. >> Anyway, I agree with you: this does appear to be different from the >> 15point rule in the library. If you haven't already, I think I will >> take a closer look at this one's accuracy claims. >> > > I haven't tested out the 15point rule in Walkington's paper. Are you going > to compare it to the 5th order rule that is already in libMesh (hopefully > they both integrate degree 5 polynomials exactly!) That's my next step...will let you know how it goes.  John 
From: David Knezevic <dave.knez@gm...>  20080618 16:50:10

> Did you see where w_0 is given for this degree 5 tet rule? I suppose > I can figure it out by summing the other 14 and subtracting from the > volume... > Good question, I'm not sure. Is it intended to imply that w_0 is the same in for both rows of Table 2.1? If so, it's not very clearly written... > Anyway, I agree with you: this does appear to be different from the > 15point rule in the library. If you haven't already, I think I will > take a closer look at this one's accuracy claims. > I haven't tested out the 15point rule in Walkington's paper. Are you going to compare it to the 5th order rule that is already in libMesh (hopefully they both integrate degree 5 polynomials exactly!)  Dave 
From: John Peterson <jwpeterson@gm...>  20080618 16:26:33

Hi Dave, On Wed, Jun 18, 2008 at 5:27 AM, David Knezevic <dave.knez@...> wrote: > > The report by Walkington, "Quadrature on Simplices of Arbitrary > Dimension" has a quadrature rule on tets that is exact for polynomials > of degree 5, and has 15 points (i.e., see Table 2.1, but note that the > 15th point is the w_0 point), but it looks like it's not the quadrature Did you see where w_0 is given for this degree 5 tet rule? I suppose I can figure it out by summing the other 14 and subtracting from the volume... Anyway, I agree with you: this does appear to be different from the 15point rule in the library. If you haven't already, I think I will take a closer look at this one's accuracy claims. > On a related note, I've been using the 4th order quadrature rule on tets > with 11 quadrature points, does anyone know where that one came from? No idea...I guess we could've used a little more documentation when writing these!  John 
From: David Knezevic <dave.knez@gm...>  20080618 10:28:07

> Do any of you have access to "The finite element method" vol. 1 by > Zienkiewicz & Taylor? Pg. 222 is referenced as the source for orders > 15, > and I want to make sure that the 5thorder rule has only 15 points... > The report by Walkington, "Quadrature on Simplices of Arbitrary Dimension" has a quadrature rule on tets that is exact for polynomials of degree 5, and has 15 points (i.e., see Table 2.1, but note that the 15th point is the w_0 point), but it looks like it's not the quadrature rule used in the code. The report is located here: http://www.math.cmu.edu/~nw0z/publications/00CNA023/023abs/ and it is cited in the libmesh source code for fifth order gauss quadrature on triangles. On a related note, I've been using the 4th order quadrature rule on tets with 11 quadrature points, does anyone know where that one came from? Cheers, Dave 
From: David Knezevic <david.knezevic@ba...>  20080618 10:26:15

> Do any of you have access to "The finite element method" vol. 1 by > Zienkiewicz & Taylor? Pg. 222 is referenced as the source for orders 15, > and I want to make sure that the 5thorder rule has only 15 points... > The report by Walkington, "Quadrature on Simplices of Arbitrary Dimension" has a quadrature rule on tets that is exact for polynomials of degree 5, and has 15 points (i.e., see Table 2.1, but note that the 15th point is the w_0 point), but it looks like it's not the quadrature rule used in the code. The report is located here: http://www.math.cmu.edu/~nw0z/publications/00CNA023/023abs/ and it is cited in the libmesh source code for fifth order gauss quadrature on triangles. On another note, I've been using the 4th order quadrature rule on tets with 11 quadrature points, does anyone know where that one came from? Cheers, Dave >  > Check out the new SourceForge.net Marketplace. > It's the best place to buy or sell services for > just about anything Open Source. > http://sourceforge.net/services/buy/index.php > _______________________________________________ > Libmeshdevel mailing list > Libmeshdevel@... > https://lists.sourceforge.net/lists/listinfo/libmeshdevel > > 
From: John Peterson <jwpeterson@gm...>  20080618 02:29:49

On Tue, Jun 17, 2008 at 4:16 PM, John Peterson <jwpeterson@...> wrote: > On Tue, Jun 17, 2008 at 4:02 PM, Roy Stogner <roy@...> wrote: >> >> On Tue, 17 Jun 2008, John Peterson wrote: >> >>> On Tue, Jun 17, 2008 at 2:11 PM, Benjamin Kirk <benjamin.kirk@...> >>> wrote: >>> >>>> Do any of you have access to "The finite element method" vol. 1 by >>>> Zienkiewicz & Taylor? Pg. 222 is referenced as the source for orders >>>> 15, >>>> and I want to make sure that the 5thorder rule has only 15 points... >>> >>> I found one of Zienkiewicz's books on google books >>> >>> The Finite Element Method: Its Basis and Fundamentals >>> >>> Redacted from the book preview is pg. 167, which should contain Table >>> 5.4  tetrahedral quadrature formulae... this always seems to happen >>> to me with Google Books. >>> >>> Maybe Roy can send Vikram to get one of the many copies from the UT >>> Engineering Library: TA 640.2 Z5 >> >> No luck; at least in the editions on the shelves (3rd through 6th), >> the quadrature for tets only runs up through 3rdorder. > > Crappy... I guess the comment in the code only applied to the rules up > to that order. I'll search around a bit. I actually have a Gaussian > quadrature textbook at home, so I'll look there too. Well, that (Stroud's quadrature book) was a bust. It really only has onedimensional quadrature rules for integrals with nonstandard weighting functions. I'm not sure when I'll next be on campus, and this article is too old to be available online yet, but if somebody wants to take a look, it should have tet rules up to at least 8th order. And a warning, the eighthorder rule's centroid weighting apparently has the wrong sign. @article{17769, author = {P Keast}, title = {Moderatedegree tetrahedral quadrature formulas}, journal = {Comput. Methods Appl. Mech. Eng.}, volume = {55}, number = {3}, year = {1986}, issn = {00457825}, pages = {339367}, doi = {http://dx.doi.org/10.1016/00457825(86)900599}, publisher = {Elsevier Sequoia S. A.}, address = {Lausanne, Switzerland, Switzerland}, }  John 