Tue Jul 11 09:48:08 2023 tetrahedron_jaskowiec_rule_test(): Python version: 3.8.10 tetrahedron_jaskowiec_rule() returns Jaskowiec quadrature rules for a tetrahedron. tetrahedron_jaskowiec_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 0.310886 0.067342 1 0.112688 0.067342 0.310886 0.310886 0.310886 2 0.112688 0.310886 0.067342 0.310886 0.310886 3 0.112688 0.310886 0.310886 0.067342 0.310886 4 0.073493 0.092735 0.092735 0.092735 0.721794 5 0.073493 0.721794 0.092735 0.092735 0.092735 6 0.073493 0.092735 0.721794 0.092735 0.092735 7 0.073493 0.092735 0.092735 0.721794 0.092735 8 0.042546 0.045504 0.454496 0.454496 0.045504 9 0.042546 0.454496 0.045504 0.454496 0.045504 10 0.042546 0.045504 0.045504 0.454496 0.454496 11 0.042546 0.454496 0.454496 0.045504 0.045504 12 0.042546 0.045504 0.454496 0.045504 0.454496 13 0.042546 0.454496 0.045504 0.045504 0.454496 Weight Sum 1.0 tetrahedron_jaskowiec_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 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000136183321160 7 0.0000376250658163 tetrahedron_jaskowiec_rule_test02(): 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 2.775557561562891e-17 4.098284211995207e-16 8 8.326672684688674e-17 1.024571052998801e-15 9 5.551115123125783e-17 6.14742631799281e-16 10 6.938893903907228e-18 5.869938324472299e-16 11 2.081668171172169e-17 9.861496385113466e-16 12 8.326672684688674e-17 7.04392598936676e-16 13 2.775557561562891e-17 9.15710378617679e-16 14 6.938893903907228e-18 1.095454310358063e-15 15 2.775557561562891e-17 8.584784799540739e-16 16 6.938893903907228e-18 8.107852310677369e-16 17 2.775557561562891e-17 1.137316314361032e-15 18 8.326672684688674e-17 8.844929793466222e-16 19 2.775557561562891e-17 1.077267090229859e-15 20 2.775557561562891e-17 9.082734454966572e-16 tetrahedron_jaskowiec_rule_test04(): Integrate 1/sqrt(r) over the reference tetrahedron. 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 0.2421415445769921 0.002082634414989182 4 14 0.2410193813886114 0.0009604712266084448 5 14 0.241442689571049 0.001383779409046021 6 24 0.2403540555991646 0.0002951454371616646 7 35 0.2396527439280942 0.0004061662339087391 8 46 0.2404603979555744 0.0004014877935714922 9 59 0.2402098487285089 0.0001509385665059149 10 81 0.2399908438432392 6.806631876371538e-05 11 110 0.2401675962446256 0.0001086860826226554 12 168 0.2400320171196073 2.689304239561485e-05 13 172 0.2400773798220387 1.846966003576922e-05 14 204 0.2401064662715017 4.755610949877531e-05 15 264 0.2400749490947743 1.603893277138391e-05 16 304 0.2400527172492863 6.192912716612708e-06 17 364 0.2400730008057124 1.409064370941349e-05 18 436 0.2400708087778067 1.189861580377927e-05 19 487 0.2400533785020641 5.531659938856626e-06 20 552 0.2400588444706486 6.569135438394547e-08 tetrahedron_jaskowiec_rule_test(): Normal end of execution. Tue Jul 11 09:48:08 2023