11 July 2023   9:08:01.692 PM

tetrahedron_witherden_rule_test():
  Fortran90 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

     1    0.112688    0.310886    0.310886    0.067342    0.310886
     2    0.112688    0.310886    0.067342    0.310886    0.310886
     3    0.112688    0.067342    0.310886    0.310886    0.310886
     4    0.112688    0.310886    0.310886    0.310886    0.067342
     5    0.073493    0.092735    0.092735    0.721794    0.092735
     6    0.073493    0.092735    0.721794    0.092735    0.092735
     7    0.073493    0.721794    0.092735    0.092735    0.092735
     8    0.073493    0.092735    0.092735    0.092735    0.721794
     9    0.042546    0.045504    0.454496    0.454496    0.045504
    10    0.042546    0.454496    0.045504    0.454496    0.045504
    11    0.042546    0.045504    0.045504    0.454496    0.454496
    12    0.042546    0.045504    0.454496    0.045504    0.454496
    13    0.042546    0.454496    0.045504    0.045504    0.454496
    14    0.042546    0.454496    0.454496    0.045504    0.045504

  Weight Sum =    1.00000    

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     0.000000000000000    
   1    0.6938893903907228E-17
   2    0.3469446951953614E-17
   3    0.1734723475976807E-17
   4    0.1734723475976807E-17
   5    0.8673617379884035E-18
   6    0.1361833211602648E-04
   7    0.3762506581633752E-04

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     0.000000000000000         0.000000000000000    
   1     0.000000000000000         0.000000000000000    
   2    0.3469446951953614E-17    0.2081668171172169E-15
   3    0.1734723475976807E-17    0.2081668171172169E-15
   4    0.6938893903907228E-17    0.5464378949326943E-15
   5    0.6938893903907228E-17    0.5464378949326943E-15
   6    0.8326672684688674E-16    0.6245004513516506E-15
   7    0.1387778780781446E-15    0.9221139476989215E-15
   8    0.8326672684688674E-16    0.9367506770274760E-15
   9    0.2775557561562891E-16    0.8326672684688674E-15
  10    0.1110223024625157E-15    0.1502704211064909E-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   0.2400589101620030    
  Volume of tetrahedron is   0.1666666666666667    

   P    N     Q     |Q-Exact]

   0    1    0.2532785618838642        0.1321965172186121E-01
   1    1    0.2532785618838642        0.1321965172186121E-01
   2    4    0.2442781387638714        0.4219228601868463E-02
   3    8    0.2422436873187426        0.2184777156739648E-02
   4   14    0.2414426895710490        0.1383779409046021E-02
   5   14    0.2414426895710490        0.1383779409046021E-02
   6   24    0.2403540555991645        0.2951454371615259E-03
   7   35    0.2396527439280942        0.4061662339087946E-03
   8   46    0.2404524584761409        0.3935483141379037E-03
   9   59    0.5672984490527836        0.3272395388907806    
  10   81    0.2399650072174329        0.9390294457004011E-04

tetrahedron_witherden_rule_test()
  Normal end of execution.

11 July 2023   9:08:01.694 PM