Re: [Libmesh-devel] Quadrature on simplices

[John P. <jwp...@gm...>]

On Mon, Feb 16, 2009 at 10:17 AM, John Peterson <jwp...@gm...> wrote:
> On Mon, Feb 16, 2009 at 9:59 AM, David Knezevic <dk...@mi...> wrote:
>> The quadrature rules for simplices in libmesh have been recently
>> refurbished I think (thanks John!) and with that in mind I thought I'd
>> just pass on a link to a new paper I saw about this topic:
>>
>> Linbo Zhang, Tao Cui and Hui Liu
>> A Set of Symmetric Quadrature Rules on Triangles and Tetrahedra.
>> J. Comp. Math., 27 (2009), pp. 89-96.
>> http://www.global-sci.org/jcm/volumes/v27n1/pdf/271-89.pdf
>>
>> It's got a nice description of their algorithm for finding symmetric
>> quadrature rules, and they list a bunch of them. However, happily, their
>> quadrature rules don't offer much of an improvement over the ones
>> already available in libMesh (except that they have explicitly found
>> quadrature rules on tets up to order 14).
>

The extra precision for the 16-point, 8th-order rule on the triangle
will be useful.  There's also a 28-point/11th-order triangle rule
claimed (but not tabulated) which would be better than our present
11th-order rule.  Similarly for the 52-point/15th-order,
55-point/16th-order, and 91-point/21st-order triangle rules claimed.

The 46-point/8th-order rule for the tet I don't believe I've seen
before.  Ditto for the 236-point/14th-order rule for tets: the best
rules we have for that one contain 512 (all-positive) points and 330
(some-negative) points, respectively.  The 7th-order/36-point
(untabulated) rule is also better than anything we currently have.

Nice find!!

-- 
John