13 July 2023 07:01:06 AM

pyramid_witherden_rule_test():
  C++ version
  Test pyramid_witherden_rule().

pyramid_witherden_rule_test01():
  Quadrature rule for the unit pyramid.
  Precision p = 5

  Number of nodes N = 15

     I      W          X           Y           Z

     0   0.0684354           0           0    0.729858
     1    0.169397           0           0    0.300401
     2   0.0587045           0           0  6.49177e-09
     3   0.0764413    0.706526           0       0.125
     4   0.0764413           0    0.706526       0.125
     5   0.0764413   -0.706526           0       0.125
     6   0.0764413           0   -0.706526       0.125
     7   0.0396709    0.705117    0.705117   0.0611119
     8   0.0396709    0.705117   -0.705117   0.0611119
     9   0.0396709   -0.705117    0.705117   0.0611119
    10   0.0396709   -0.705117   -0.705117   0.0611119
    11   0.0597536    0.432883    0.432883    0.423601
    12   0.0597536    0.432883   -0.432883    0.423601
    13   0.0597536   -0.432883    0.432883    0.423601
    14   0.0597536   -0.432883   -0.432883    0.423601

  Weight Sum = 1

pyramid_witherden_rule_test02():
  Test the precision of a quadrature rule for the unit pyramid.

  Number of nodes N = 15

  Stated precision of rule    = 5
  Number of quadrature points = 15

  Degree  Maximum error

   0               2.22045e-16
   1               1.11022e-16
   2               5.55112e-17
   3               1.52656e-16
   4               1.26635e-16
   5                3.1225e-17
   6                 0.0100361
   7               0.000702404

pyramid_witherden_rule_test03():
  Test the precision of quadrature rules for the unit pyramid.
  Check rules of precision p = 0 through 10
  for error in approximating integrals of monomials.

              maximum                   maximum
   p          absolute                  relative
              error                     error

   0                         0                         0
   1               1.66533e-16                 4.996e-16
   2               6.66134e-16                 4.996e-16
   3                 1.249e-16                1.8735e-15
   4               2.22045e-16               9.83588e-15
   5               2.22045e-16               9.97249e-15
   6               2.36356e-16               7.44522e-14
   7               6.66134e-16               7.38921e-14
   8               1.55431e-15               6.16444e-13
   9               1.55431e-15               1.06766e-12
  10               1.29844e-15                 4.704e-12

pyramid_witherden_rule_test()
  Normal end of execution.

13 July 2023 07:01:06 AM