11 July 2023 11:55:43 AM

tetrahedron_jaskowiec_rule_test():
  C version
  Test tetrahedron_jaskowiec_rule().

tetrahedron_jaskowiec_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    0.310886   0.0673422
     1    0.112688   0.0673422    0.310886    0.310886    0.310886
     2    0.112688    0.310886   0.0673422    0.310886    0.310886
     3    0.112688    0.310886    0.310886   0.0673422    0.310886
     4    0.073493   0.0927353   0.0927353   0.0927353    0.721794
     5    0.073493    0.721794   0.0927353   0.0927353   0.0927353
     6    0.073493   0.0927353    0.721794   0.0927353   0.0927353
     7    0.073493   0.0927353   0.0927353    0.721794   0.0927353
     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    0.454496    0.454496   0.0455037   0.0455037
    12    0.042546   0.0455037    0.454496   0.0455037    0.454496
    13    0.042546    0.454496   0.0455037   0.0455037    0.454496

  Weight Sum = 1

tetrahedron_jaskowiec_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                         0
   1     6.938893903907228e-18
   2     3.469446951953614e-18
   3     1.734723475976807e-18
   4     8.673617379884035e-19
   5     4.336808689942018e-19
   6     1.361833211602735e-05
   7     3.762506581633795e-05

tetrahedron_jaskowiec_rule_test03():
  Test the precision of quadrature rules for the unit tetrahedron.
  Check rules of precision p = 0 through 20
  for error in approximating integrals of monomials.

              maximum                   maximum
   p          absolute                  relative
              error                     error

   0                         0                         0
   1                         0                         0
   2     6.938893903907228e-18     2.081668171172169e-16
   3     2.775557561562891e-17     3.122502256758253e-16
   4     5.551115123125783e-17     3.642919299551295e-16
   5     6.938893903907228e-18     3.642919299551295e-16
   6     8.326672684688674e-17      7.28583859910259e-16
   7     8.326672684688674e-17     8.196568423990415e-16
   8     1.110223024625157e-16     1.056588898405014e-15
   9     1.040834085586084e-17     8.586881206085197e-16
  10     1.942890293094024e-16     1.165734175856414e-15
  11     1.942890293094024e-16     1.561251128379127e-15
  12     2.775557561562891e-17     2.185751579730777e-15
  13     1.387778780781446e-16     2.185751579730777e-15
  14      3.05311331771918e-16     1.831867990631508e-15
  15     2.498001805406602e-16     2.604687299179176e-15
  16     4.440892098500626e-16     2.664535259100376e-15
  17     8.326672684688674e-17     3.148523108897904e-15
  18     2.498001805406602e-16     3.329855922246105e-15
  19     5.551115123125783e-17      3.82506526452886e-15
  20     1.942890293094024e-16     4.293440603042597e-15

tetrahedron_jaskowiec_rule_test04():
  Integrate 1/sqrt(r) over the reference tetrahedron.
  Exact integral value is 0.240059.
  Volume of tetrahedron is 0.166667.

   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    0.2421415445769921  0.002082634414989182
   4   14    0.2410193813886114  0.0009604712266084448
   5   14     0.241442689571049  0.001383779409046021
   6   24    0.2403540555991646  0.0002951454371616369
   7   35    0.2396527439280942  0.0004061662339087113
   8   46    0.2404603979555745  0.0004014877935715477
   9   59    0.2402098487285089  0.0001509385665059704
  10   81    0.2399908438432391  6.806631876382641e-05
  11  110    0.2401675962446256  0.0001086860826226554
  12  168    0.2400320171196075  2.689304239547607e-05
  13  172    0.2400773798220388  1.846966003585249e-05
  14  204    0.2401064662715015  4.755610949852551e-05
  15  264    0.2400749490947738  1.60389327708288e-05
  16  304     0.240052717249286  6.192912716945775e-06
  17  364    0.2400730008057125  1.409064370958002e-05
  18  436    0.2400708087778065  1.189861580358498e-05
  19  487     0.240053378502064  5.531659938912137e-06
  20  552    0.2400588444706481  6.569135482803468e-08

tetrahedron_jaskowiec_rule_test()
  Normal end of execution.

11 July 2023 11:55:44 AM