Hi Dave,
On Wed, Jun 18, 2008 at 11:50 AM, David Knezevic <[EMAIL PROTECTED]> 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
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