Re: [Libmesh-devel] Quadrature on simplices From: John Peterson - 2009-02-16 16:41:15 ```On Mon, Feb 16, 2009 at 10:17 AM, John Peterson wrote: > On Mon, Feb 16, 2009 at 9:59 AM, David Knezevic 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 ```

 [Libmesh-devel] Quadrature on simplices From: David Knezevic - 2009-02-16 16:06:16 ```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). - Dave ```
 Re: [Libmesh-devel] Quadrature on simplices From: John Peterson - 2009-02-16 16:17:36 ```On Mon, Feb 16, 2009 at 9:59 AM, David Knezevic 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). Nice! Thanks David! -- John ```
 Re: [Libmesh-devel] Quadrature on simplices From: John Peterson - 2009-02-16 16:41:15 ```On Mon, Feb 16, 2009 at 10:17 AM, John Peterson wrote: > On Mon, Feb 16, 2009 at 9:59 AM, David Knezevic 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 ```