[Libmesh-devel] Updates to quadrature rules on TRIs From: John Peterson - 2008-06-24 19:50:58 ```Hi all, I've just checked in some changes to the quadrature classes. The most general change was the addition of a public bool allow_rules_with_negative_weights; to the QBase class. By default this is true, and you will obtain the same behavior which has been present in the past. If you set this to false you can use more expensive (but potentially safer) quadrature rules with all positive weights. I think there may be a few places I haven't placed if statements around negative weight rules but I'll be replacing those soon as well. The other change affects very high-order quadrature on triangles. >From 7th-19th order, the original conical product rules have been replaced by rules published by Dunavant: Dunavant, "High degree efficient symmetrical Gaussian quadrature rules for the triangle", IJNME 21 p. 1129--1148, 1985. with significantly fewer evaluation points. Anyone using very high p in 2D could benefit from using these rules, some of which have up to 50% fewer points than comparable order conical product rules. The table below has details about the numbers of points saved at various orders. (You may need to view it in a fixed-width font.) degree Dunavant Conical % Savings 6 12 16 33.33 7 13 16 23.08 8 16 25 56.25 9 19 25 31.58 10 25 36 44.00 11 33 36 9.09 12 33 49 48.48 13 37 49 32.43 14 42 64 52.38 15 61 64 4.92 16 61 81 32.79 17 61 81 32.79 18 73 100 36.99 19 73 100 36.99 -- John ```

 [Libmesh-devel] Updates to quadrature rules on TRIs From: John Peterson - 2008-06-24 19:50:58 ```Hi all, I've just checked in some changes to the quadrature classes. The most general change was the addition of a public bool allow_rules_with_negative_weights; to the QBase class. By default this is true, and you will obtain the same behavior which has been present in the past. If you set this to false you can use more expensive (but potentially safer) quadrature rules with all positive weights. I think there may be a few places I haven't placed if statements around negative weight rules but I'll be replacing those soon as well. The other change affects very high-order quadrature on triangles. >From 7th-19th order, the original conical product rules have been replaced by rules published by Dunavant: Dunavant, "High degree efficient symmetrical Gaussian quadrature rules for the triangle", IJNME 21 p. 1129--1148, 1985. with significantly fewer evaluation points. Anyone using very high p in 2D could benefit from using these rules, some of which have up to 50% fewer points than comparable order conical product rules. The table below has details about the numbers of points saved at various orders. (You may need to view it in a fixed-width font.) degree Dunavant Conical % Savings 6 12 16 33.33 7 13 16 23.08 8 16 25 56.25 9 19 25 31.58 10 25 36 44.00 11 33 36 9.09 12 33 49 48.48 13 37 49 32.43 14 42 64 52.38 15 61 64 4.92 16 61 81 32.79 17 61 81 32.79 18 73 100 36.99 19 73 100 36.99 -- John ```