Warning: X does not support locale en_US.UTF-8 11-Jul-2023 13:52:33 tetrahedron_jaskowiec_rule_test(): MATLAB/Octave version 9.14.0.2206163 (R2023a) Test tetrahedron_jaskowiec_rule(). tetrahedron_jaskowiec_rule_test01(): Quadrature rule for the tetrahedron, given in barycentric coordinates. Precision p = 5 I W A B C D 1 0.112688 0.310886 0.310886 0.310886 0.0673422 2 0.112688 0.0673422 0.310886 0.310886 0.310886 3 0.112688 0.310886 0.0673422 0.310886 0.310886 4 0.112688 0.310886 0.310886 0.0673422 0.310886 5 0.073493 0.0927353 0.0927353 0.0927353 0.721794 6 0.073493 0.721794 0.0927353 0.0927353 0.0927353 7 0.073493 0.0927353 0.721794 0.0927353 0.0927353 8 0.073493 0.0927353 0.0927353 0.721794 0.0927353 9 0.042546 0.0455037 0.454496 0.454496 0.0455037 10 0.042546 0.454496 0.0455037 0.454496 0.0455037 11 0.042546 0.0455037 0.0455037 0.454496 0.454496 12 0.042546 0.454496 0.454496 0.0455037 0.0455037 13 0.042546 0.0455037 0.454496 0.0455037 0.454496 14 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, 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 3.469446951953614e-18 2.081668171172169e-16 3 3.469446951953614e-18 3.122502256758253e-16 4 6.938893903907228e-18 3.122502256758253e-16 5 3.469446951953614e-18 5.828670879282072e-16 6 6.938893903907228e-18 4.098284211995207e-16 7 2.775557561562891e-17 4.098284211995207e-16 8 6.938893903907228e-18 1.056588898405014e-15 9 6.938893903907228e-18 5.282944492025069e-16 10 3.469446951953614e-18 5.869938324472299e-16 11 6.938893903907228e-18 8.54663020043167e-16 12 6.938893903907228e-18 7.043925989366759e-16 13 6.938893903907228e-18 6.65971184449221e-16 14 6.938893903907228e-18 9.434591779697297e-16 15 3.469446951953614e-18 6.384933694658424e-16 16 8.673617379884035e-19 7.601111541260032e-16 17 1.734723475976807e-18 8.844929793466222e-16 18 8.673617379884035e-19 8.424565291563196e-16 19 2.775557561562891e-17 9.479950394022763e-16 20 3.469446951953614e-18 8.325839917052691e-16 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 0.2404603979555744 0.0004014877935714367 9 59 0.2402098487285088 0.0001509385665058871 10 81 0.2399908438432392 6.806631876371538e-05 11 110 0.2401675962446256 0.0001086860826226277 12 168 0.2400320171196074 2.689304239550383e-05 13 172 0.2400773798220387 1.846966003574146e-05 14 204 0.2401064662715018 4.755610949883082e-05 15 264 0.2400749490947744 1.603893277143942e-05 16 304 0.2400527172492863 6.19291271666822e-06 17 364 0.2400730008057123 1.409064370933022e-05 18 436 0.2400708087778068 1.189861580383478e-05 19 487 0.2400533785020641 5.53165993882887e-06 20 552 0.2400588444706487 6.569135430067874e-08 tetrahedron_jaskowiec_rule_test(): Normal end of execution. 11-Jul-2023 13:52:34