Wed Jul 12 08:43:08 2023

tetrahedron_witherden_rule_test():
  Python version: 3.8.10
  Test tetrahedron_witherden_rule().

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

     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  1.0

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

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

  Degree  Maximum error

   0                         0
   1     6.938893903907228e-18
   2     3.469446951953614e-18
   3     1.734723475976807e-18
   4     1.734723475976807e-18
   5     4.336808689942018e-19
   6     1.361833211602735e-05
   7     3.762506581633795e-05

tetrahedron_witherden_rule_test03():
  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     3.469446951953614e-18     2.081668171172169e-16
   3     1.734723475976807e-18     2.081668171172169e-16
   4     6.938893903907228e-18     5.464378949326943e-16
   5     6.938893903907228e-18     5.464378949326943e-16
   6     8.326672684688674e-17     4.996003610813204e-16
   7     2.775557561562891e-17     6.830473686658676e-16
   8     2.775557561562891e-17      9.36750677027476e-16
   9     8.326672684688674e-17     8.050201130704872e-16
  10     2.775557561562891e-17     8.139647809934924e-16

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 0.24005891016200295
  Volume of tetrahedron is 0.16666666666666666

   P    N     Q     |Q-Exact]

   0    1    0.2532785618838642   0.01321965172186121
   1    1    0.2532785618838642   0.01321965172186121
   2    4    0.2442781387638714  0.004219228601868463
   3    8    0.2422436873187426  0.002184777156739648
   4   14     0.241442689571049  0.001383779409046021
   5   14     0.241442689571049  0.001383779409046021
   6   24    0.2403540555991645  0.0002951454371615259
   7   35    0.2396527439280942  0.0004061662339087946
   8   46    0.2404524584761408  0.0003935483141378759
   9   59    0.5672984490527833    0.3272395388907803
  10   81     0.239965007217433  9.390294456992909e-05

tetrahedron_witherden_rule_test():
  Normal end of execution.
Wed Jul 12 08:43:08 2023