On Mon, Feb 16, 2009 at 10:17 AM, John Peterson <[email protected]> wrote: > On Mon, Feb 16, 2009 at 9:59 AM, David Knezevic <[email protected]> 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 ------------------------------------------------------------------------------ Open Source Business Conference (OSBC), March 24-25, 2009, San Francisco, CA -OSBC tackles the biggest issue in open source: Open Sourcing the Enterprise -Strategies to boost innovation and cut costs with open source participation -Receive a $600 discount off the registration fee with the source code: SFAD http://p.sf.net/sfu/XcvMzF8H _______________________________________________ Libmesh-devel mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-devel
