11 July 2023 08:04:27 PM

tetrahedron_witherden_rule_test():
  C++ version
  Test tetrahedron_witherden_rule().

tetrahedron_witherden_rule_test01():
  Quadrature rule for the tetrahedron,
  given in barycentric coordinates.
  Precision p = 5

  Number of nodes N = 14

     I      W          A           B           C           D

     0    0.112688    0.310886    0.310886   0.0673422    0.310886
     1    0.112688    0.310886   0.0673422    0.310886    0.310886
     2    0.112688   0.0673422    0.310886    0.310886    0.310886
     3    0.112688    0.310886    0.310886    0.310886   0.0673422
     4    0.073493   0.0927353   0.0927353    0.721794   0.0927353
     5    0.073493   0.0927353    0.721794   0.0927353   0.0927353
     6    0.073493    0.721794   0.0927353   0.0927353   0.0927353
     7    0.073493   0.0927353   0.0927353   0.0927353    0.721794
     8    0.042546   0.0455037    0.454496    0.454496   0.0455037
     9    0.042546    0.454496   0.0455037    0.454496   0.0455037
    10    0.042546   0.0455037   0.0455037    0.454496    0.454496
    11    0.042546   0.0455037    0.454496   0.0455037    0.454496
    12    0.042546    0.454496   0.0455037   0.0455037    0.454496
    13    0.042546    0.454496    0.454496   0.0455037   0.0455037

  Weight Sum = 1

tetrahedron_witherden_rule_test02():
  Test the precision of a quadrature rule for the unit tetrahedron.

  Number of nodes N = 14

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

  Degree  Maximum error

   0               8.32667e-17
   1               2.77556e-17
   2               1.73472e-17
   3               6.93889e-18
   4               5.20417e-18
   5               3.46945e-18
   6               1.36183e-05
   7               3.76251e-05

tetrahedron_witherden_rule_test02():
  Test the precision of quadrature rules for the unit tetrahedron.
  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                         0                         0
   2               3.46945e-18               2.08167e-16
   3               2.77556e-17               2.08167e-16
   4               8.32667e-17               1.27502e-15
   5               8.32667e-17               1.27502e-15
   6               1.38778e-16                1.7486e-15
   7               1.66533e-16                 3.747e-15
   8               3.05311e-16               2.65413e-15
   9               1.11022e-16               9.44557e-15
  10               1.38778e-16               2.23259e-14

tetrahedron_witherden_rule_test04():
  Integrate 1/sqrt(r) over the reference tetrahedron.
  Witherden rule #9 fails because a quadrature point is
  very near the singularity at the origin.
  Exact integral value is 0.240059
  Volume of tetrahedron is 0.166667

   P    N     Q     |Q-Exact]

   0    1              0.253279             0.0132197
   1    1              0.253279             0.0132197
   2    4              0.244278            0.00421923
   3    8              0.242244            0.00218478
   4   14              0.241443            0.00138378
   5   14              0.241443            0.00138378
   6   24              0.240354           0.000295145
   7   35              0.239653           0.000406166
   8   46              0.240452           0.000393548
   9   59              0.567298               0.32724
  10   81              0.239965           9.39029e-05

tetrahedron_witherden_rule_test()
  Normal end of execution.

11 July 2023 08:04:27 PM