16 July 2023 07:40:14 PM

hexahedron_witherden_rule_test():
  C++ version
  Test hexahedron_witherden_rule().

hexahedron_witherden_rule_test01():
  Quadrature rule for the unit hexahedron.
  Precision p = 5

  Number of nodes N = 14

     I      W          X           Y           Z

     0    0.110803    0.102089         0.5         0.5
     1    0.110803         0.5         0.5    0.897911
     2    0.110803         0.5    0.897911         0.5
     3    0.110803         0.5         0.5    0.102089
     4    0.110803    0.897911         0.5         0.5
     5    0.110803         0.5    0.102089         0.5
     6   0.0418975    0.879393    0.120607    0.120607
     7   0.0418975    0.120607    0.879393    0.879393
     8   0.0418975    0.120607    0.879393    0.120607
     9   0.0418975    0.120607    0.120607    0.120607
    10   0.0418975    0.120607    0.120607    0.879393
    11   0.0418975    0.879393    0.879393    0.120607
    12   0.0418975    0.879393    0.879393    0.879393
    13   0.0418975    0.879393    0.120607    0.879393

  Weight Sum = 1

hexahedron_witherden_rule_test02():
  Test the precision of a quadrature rule for the unit hexahedron.

  Number of nodes N = 14

  Stated precision of rule    = 5
  Number of quadrature points = 14

  Degree  Maximum error

   0               2.22045e-16
   1               3.33067e-16
   2               1.11022e-16
   3               1.66533e-16
   4               1.11022e-16
   5               8.32667e-17
   6               0.000420875
   7                0.00123527

hexahedron_witherden_rule_test03():
  Test the precision of quadrature rules for the unit hexahedron.
  Check rules of precision p = 0 through 11
  for error in approximating integrals of monomials.

              maximum                   maximum
   p          absolute                  relative
              error                     error

   0                         0                         0
   1                         0                         0
   2               2.22045e-16               3.33067e-16
   3               2.22045e-16               3.33067e-16
   4               3.33067e-16               8.32667e-16
   5               3.33067e-16               8.32667e-16
   6               2.22045e-16               5.55112e-16
   7               2.22045e-16               5.55112e-16
   8               3.33067e-16               1.04083e-15
   9               3.33067e-16               1.04083e-15
  10               8.88178e-16               3.69149e-15
  11               8.88178e-16               3.69149e-15

hexahedron_witherden_rule_test()
  Normal end of execution.

16 July 2023 07:40:14 PM