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From 7th-19th order, the original conical product rules have been
replaced by rules published by Dunavant: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

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