From: John Peterson <jwpeterson@gm...>  20090216 16:41:15

On Mon, Feb 16, 2009 at 10:17 AM, John Peterson <jwpeterson@...> wrote: > On Mon, Feb 16, 2009 at 9:59 AM, David Knezevic <dknez@...> 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. 8996. >> http://www.globalsci.org/jcm/volumes/v27n1/pdf/27189.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 16point, 8thorder rule on the triangle will be useful. There's also a 28point/11thorder triangle rule claimed (but not tabulated) which would be better than our present 11thorder rule. Similarly for the 52point/15thorder, 55point/16thorder, and 91point/21storder triangle rules claimed. The 46point/8thorder rule for the tet I don't believe I've seen before. Ditto for the 236point/14thorder rule for tets: the best rules we have for that one contain 512 (allpositive) points and 330 (somenegative) points, respectively. The 7thorder/36point (untabulated) rule is also better than anything we currently have. Nice find!!  John 