From: John P. <jwp...@gm...> - 2008-06-18 18:31:36
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Hi Dave, On Wed, Jun 18, 2008 at 11:50 AM, David Knezevic <dav...@gm...> 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 14-point rule in Table 2.1. I didn't see it explicitly stated anywhere that it was a 15-point 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 15-point rule. I'm still skeptical of the accuracy-order claims in any case. >> Anyway, I agree with you: this does appear to be different from the >> 15-point 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 15-point 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 |