21 January 2020 11:07:18 AM TETRAHEDRON_NCO_RULE_TEST: C version Test the TETRAHEDRON_NCO_RULE library. TEST01 TETRAHEDRON_NCO_RULE_NUM returns the number of rules; TETRAHEDRON_NCO_DEGREE returns the degree of a rule; TETRAHEDRON_NCO_ORDER_NUM returns the order of a rule. Number of available rules = 7 Rule Degree Order 1 0 1 2 1 4 3 2 10 4 3 20 5 4 35 6 5 56 7 6 84 TEST02 TETRAHEDRON_NCO_RULE returns the points and weights of an NCO rule for the tetrahedron. In this test, we simply check that the weights sum to 1. Number of available rules = 7 Rule Sum of weights 1 1 2 1 3 1 4 1 5 1 6 1 7 1 TEST03 TETRAHEDRON_NCO_RULE returns the points and weights of an NCO rule for the tetrahedron. In this test, we simply check that, for each quadrature point, the barycentric coordinates add up to 1. Rule Suborder Sum of coordinates 1 1 1 2 1 1 3 2 1 0.9999999999999999 4 3 1 1 1 5 5 1 1 1 1 1 6 6 1 1 1 1 1 1 7 9 1 1 1 1 1 0.9999999999999999 1 0.9999999999999999 1 TEST04 TETRAHEDRON_NCO_RULE returns the points and weights of an NCO rule for the unit tetrahedron. This routine uses those rules to estimate the integral of monomomials in the unit tetrahedron. Integrate 6 * X^0 * Y^0 * Z^0 Rule QUAD ERROR 1 1 0 2 1 0 3 1 2.22045e-16 4 1 8.88178e-16 5 1 7.77156e-16 6 1 7.77156e-16 7 1 3.77476e-15 Integrate 24 * X^0 * Y^0 * Z^1 Rule QUAD ERROR 1 1 0 2 1 0 3 1 3.33067e-16 4 1 0 5 1 6.66134e-16 6 1 1.11022e-15 7 1 0 Integrate 60 * X^0 * Y^0 * Z^2 Rule QUAD ERROR 1 0.625 0.375 2 0.7 0.3 3 1 4.44089e-16 4 1 0 5 1 6.66134e-16 6 1 4.44089e-16 7 1 3.10862e-15 Integrate 120 * X^0 * Y^0 * Z^3 Rule QUAD ERROR 1 0.3125 0.6875 2 0.44 0.56 3 1.02778 0.0277778 4 1 0 5 1 4.44089e-16 6 1 4.44089e-16 7 1 1.77636e-15 Integrate 210 * X^0 * Y^0 * Z^4 Rule QUAD ERROR 1 0.136719 0.863281 2 0.266 0.734 3 0.972222 0.0277778 4 0.925656 0.074344 5 1 0 6 1 1.66533e-15 7 1 2.22045e-15 Integrate 336 * X^0 * Y^0 * Z^5 Rule QUAD ERROR 1 0.0546875 0.945312 2 0.1568 0.8432 3 0.83179 0.16821 4 0.79217 0.20783 5 1.01074 0.0107422 6 1 4.44089e-16 7 1 1.33227e-15 Integrate 504 * X^0 * Y^0 * Z^6 Rule QUAD ERROR 1 0.0205078 0.979492 2 0.090048 0.909952 3 0.65463 0.34537 4 0.638948 0.361052 5 1.01591 0.0159058 6 0.983727 0.0162729 7 1 2.22045e-16 Integrate 24 * X^0 * Y^1 * Z^0 Rule QUAD ERROR 1 1 0 2 1 0 3 1 2.22045e-16 4 1 2.22045e-16 5 1 2.22045e-16 6 1 8.88178e-16 7 1 3.77476e-15 Integrate 120 * X^0 * Y^1 * Z^1 Rule QUAD ERROR 1 1.25 0.25 2 1.2 0.2 3 1 0 4 1 4.44089e-16 5 1 2.22045e-16 6 1 0 7 1 1.33227e-15 Integrate 360 * X^0 * Y^1 * Z^2 Rule QUAD ERROR 1 0.9375 0.0625 2 0.96 0.04 3 0.972222 0.0277778 4 1 3.33067e-16 5 1 8.88178e-16 6 1 3.33067e-16 7 1 1.9984e-15 Integrate 840 * X^0 * Y^1 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672 0.328 3 1.10185 0.101852 4 1.09913 0.0991254 5 1 0 6 1 0 7 1 6.66134e-16 Integrate 1680 * X^0 * Y^1 * Z^4 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448 0.552 3 1.20628 0.206276 4 1.14813 0.148133 5 0.982096 0.0179036 6 1 8.88178e-16 7 1 1.33227e-15 Integrate 3024 * X^0 * Y^1 * Z^5 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.18611 0.186111 4 1.09861 0.0986137 5 1.00042 0.000415039 6 1.03255 0.0325459 7 1 2.66454e-15 Integrate 60 * X^0 * Y^2 * Z^0 Rule QUAD ERROR 1 0.625 0.375 2 0.7 0.3 3 1 2.22045e-16 4 1 0 5 1 0 6 1 0 7 1 1.66533e-15 Integrate 360 * X^0 * Y^2 * Z^1 Rule QUAD ERROR 1 0.9375 0.0625 2 0.96 0.04 3 0.972222 0.0277778 4 1 2.22045e-16 5 1 4.44089e-16 6 1 0 7 1 3.55271e-15 Integrate 1260 * X^0 * Y^2 * Z^2 Rule QUAD ERROR 1 0.820312 0.179688 2 0.84 0.16 3 0.712963 0.287037 4 0.844023 0.155977 5 1 0 6 1 2.22045e-16 7 1 7.77156e-16 Integrate 3360 * X^0 * Y^2 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.6272 0.3728 3 0.684156 0.315844 4 0.846869 0.153131 5 1.00716 0.00716146 6 1 2.22045e-16 7 1 8.77076e-15 Integrate 7560 * X^0 * Y^2 * Z^4 Rule QUAD ERROR 1 0.307617 0.692383 2 0.44352 0.55648 3 0.799383 0.200617 4 0.906587 0.0934135 5 0.907288 0.0927124 6 0.936798 0.0632017 7 1 1.77636e-15 Integrate 120 * X^0 * Y^3 * Z^0 Rule QUAD ERROR 1 0.3125 0.6875 2 0.44 0.56 3 1.02778 0.0277778 4 1 0 5 1 4.44089e-16 6 1 6.66134e-16 7 1 4.44089e-16 Integrate 840 * X^0 * Y^3 * Z^1 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672 0.328 3 1.10185 0.101852 4 1.09913 0.0991254 5 1 0 6 1 6.66134e-16 7 1 7.77156e-16 Integrate 3360 * X^0 * Y^3 * Z^2 Rule QUAD ERROR 1 0.546875 0.453125 2 0.6272 0.3728 3 0.684156 0.315844 4 0.846869 0.153131 5 1.00716 0.00716146 6 1 4.44089e-16 7 1 5.66214e-15 Integrate 10080 * X^0 * Y^3 * Z^3 Rule QUAD ERROR 1 0.410156 0.589844 2 0.48384 0.51616 3 0.410494 0.589506 4 0.700422 0.299578 5 1.12134 0.121338 6 1.07016 0.0701621 7 1 1.66533e-15 Integrate 210 * X^0 * Y^4 * Z^0 Rule QUAD ERROR 1 0.136719 0.863281 2 0.266 0.734 3 0.972222 0.0277778 4 0.925656 0.074344 5 1 0 6 1 1.55431e-15 7 1 2.44249e-15 Integrate 1680 * X^0 * Y^4 * Z^1 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448 0.552 3 1.20628 0.206276 4 1.14813 0.148133 5 0.982096 0.0179036 6 1 7.77156e-16 7 1 1.55431e-15 Integrate 7560 * X^0 * Y^4 * Z^2 Rule QUAD ERROR 1 0.307617 0.692383 2 0.44352 0.55648 3 0.799383 0.200617 4 0.906587 0.0934135 5 0.907288 0.0927124 6 0.936798 0.0632017 7 1 1.9984e-15 Integrate 336 * X^0 * Y^5 * Z^0 Rule QUAD ERROR 1 0.0546875 0.945312 2 0.1568 0.8432 3 0.83179 0.16821 4 0.79217 0.20783 5 1.01074 0.0107422 6 1 3.33067e-16 7 1 1.55431e-15 Integrate 3024 * X^0 * Y^5 * Z^1 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.18611 0.186111 4 1.09861 0.0986137 5 1.00042 0.000415039 6 1.03255 0.0325459 7 1 2.44249e-15 Integrate 504 * X^0 * Y^6 * Z^0 Rule QUAD ERROR 1 0.0205078 0.979492 2 0.090048 0.909952 3 0.65463 0.34537 4 0.638948 0.361052 5 1.01591 0.0159058 6 0.983727 0.0162729 7 1 2.22045e-16 Integrate 24 * X^1 * Y^0 * Z^0 Rule QUAD ERROR 1 1 0 2 1 0 3 1 4.44089e-16 4 1 4.44089e-16 5 1 8.88178e-16 6 1 0 7 1 1.33227e-15 Integrate 120 * X^1 * Y^0 * Z^1 Rule QUAD ERROR 1 1.25 0.25 2 1.2 0.2 3 1 2.22045e-16 4 1 4.44089e-16 5 1 4.44089e-16 6 1 0 7 1 1.77636e-15 Integrate 360 * X^1 * Y^0 * Z^2 Rule QUAD ERROR 1 0.9375 0.0625 2 0.96 0.04 3 0.972222 0.0277778 4 1 4.44089e-16 5 1 0 6 1 0 7 1 1.33227e-15 Integrate 840 * X^1 * Y^0 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672 0.328 3 1.10185 0.101852 4 1.09913 0.0991254 5 1 0 6 1 2.22045e-16 7 1 1.33227e-15 Integrate 1680 * X^1 * Y^0 * Z^4 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448 0.552 3 1.20628 0.206276 4 1.14813 0.148133 5 0.982096 0.0179036 6 1 7.77156e-16 7 1 4.44089e-16 Integrate 3024 * X^1 * Y^0 * Z^5 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.18611 0.186111 4 1.09861 0.0986137 5 1.00042 0.000415039 6 1.03255 0.0325459 7 1 2.55351e-15 Integrate 120 * X^1 * Y^1 * Z^0 Rule QUAD ERROR 1 1.25 0.25 2 1.2 0.2 3 1 2.22045e-16 4 1 2.22045e-16 5 1 2.22045e-16 6 1 4.44089e-16 7 1 1.77636e-15 Integrate 720 * X^1 * Y^1 * Z^1 Rule QUAD ERROR 1 1.875 0.875 2 1.68 0.68 3 1.05556 0.0555556 4 1 2.22045e-16 5 1 4.44089e-16 6 1 8.88178e-16 7 1 1.11022e-15 Integrate 2520 * X^1 * Y^1 * Z^2 Rule QUAD ERROR 1 1.64062 0.640625 2 1.512 0.512 3 1.03704 0.037037 4 1.00729 0.00728863 5 1 0 6 1 6.66134e-16 7 1 1.66533e-15 Integrate 6720 * X^1 * Y^1 * Z^3 Rule QUAD ERROR 1 1.09375 0.09375 2 1.1648 0.1648 3 1.3107 0.3107 4 1.25337 0.253367 5 1.02865 0.0286458 6 1 0 7 1 5.66214e-15 Integrate 15120 * X^1 * Y^1 * Z^4 Rule QUAD ERROR 1 0.615234 0.384766 2 0.84672 0.15328 3 1.66358 0.66358 4 1.51348 0.513477 5 1.01111 0.0111084 6 0.981837 0.0181629 7 1 4.66294e-15 Integrate 360 * X^1 * Y^2 * Z^0 Rule QUAD ERROR 1 0.9375 0.0625 2 0.96 0.04 3 0.972222 0.0277778 4 1 3.33067e-16 5 1 0 6 1 0 7 1 1.9984e-15 Integrate 2520 * X^1 * Y^2 * Z^1 Rule QUAD ERROR 1 1.64062 0.640625 2 1.512 0.512 3 1.03704 0.037037 4 1.00729 0.00728863 5 1 0 6 1 4.44089e-16 7 1 4.44089e-16 Integrate 10080 * X^1 * Y^2 * Z^2 Rule QUAD ERROR 1 1.64062 0.640625 2 1.4784 0.4784 3 0.799383 0.200617 4 0.835485 0.164515 5 0.978516 0.0214844 6 1 1.33227e-15 7 1 3.88578e-15 Integrate 30240 * X^1 * Y^2 * Z^3 Rule QUAD ERROR 1 1.23047 0.230469 2 1.2096 0.2096 3 0.864198 0.135802 4 0.947105 0.0528946 5 1.03564 0.0356445 6 1.02116 0.0211604 7 1 6.88338e-15 Integrate 840 * X^1 * Y^3 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672 0.328 3 1.10185 0.101852 4 1.09913 0.0991254 5 1 0 6 1 0 7 1 0 Integrate 6720 * X^1 * Y^3 * Z^1 Rule QUAD ERROR 1 1.09375 0.09375 2 1.1648 0.1648 3 1.3107 0.3107 4 1.25337 0.253367 5 1.02865 0.0286458 6 1 4.44089e-16 7 1 2.66454e-15 Integrate 30240 * X^1 * Y^3 * Z^2 Rule QUAD ERROR 1 1.23047 0.230469 2 1.2096 0.2096 3 0.864198 0.135802 4 0.947105 0.0528946 5 1.03564 0.0356445 6 1.02116 0.0211604 7 1 6.88338e-15 Integrate 1680 * X^1 * Y^4 * Z^0 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448 0.552 3 1.20628 0.206276 4 1.14813 0.148133 5 0.982096 0.0179036 6 1 6.66134e-16 7 1 4.44089e-16 Integrate 15120 * X^1 * Y^4 * Z^1 Rule QUAD ERROR 1 0.615234 0.384766 2 0.84672 0.15328 3 1.66358 0.66358 4 1.51348 0.513477 5 1.01111 0.0111084 6 0.981837 0.0181629 7 1 4.77396e-15 Integrate 3024 * X^1 * Y^5 * Z^0 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.18611 0.186111 4 1.09861 0.0986137 5 1.00042 0.000415039 6 1.03255 0.0325459 7 1 1.55431e-15 Integrate 60 * X^2 * Y^0 * Z^0 Rule QUAD ERROR 1 0.625 0.375 2 0.7 0.3 3 1 0 4 1 0 5 1 2.22045e-16 6 1 0 7 1 1.33227e-15 Integrate 360 * X^2 * Y^0 * Z^1 Rule QUAD ERROR 1 0.9375 0.0625 2 0.96 0.04 3 0.972222 0.0277778 4 1 0 5 1 3.33067e-16 6 1 2.22045e-16 7 1 0 Integrate 1260 * X^2 * Y^0 * Z^2 Rule QUAD ERROR 1 0.820312 0.179688 2 0.84 0.16 3 0.712963 0.287037 4 0.844023 0.155977 5 1 0 6 1 6.66134e-16 7 1 1.9984e-15 Integrate 3360 * X^2 * Y^0 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.6272 0.3728 3 0.684156 0.315844 4 0.846869 0.153131 5 1.00716 0.00716146 6 1 3.33067e-16 7 1 9.10383e-15 Integrate 7560 * X^2 * Y^0 * Z^4 Rule QUAD ERROR 1 0.307617 0.692383 2 0.44352 0.55648 3 0.799383 0.200617 4 0.906587 0.0934135 5 0.907288 0.0927124 6 0.936798 0.0632017 7 1 2.44249e-15 Integrate 360 * X^2 * Y^1 * Z^0 Rule QUAD ERROR 1 0.9375 0.0625 2 0.96 0.04 3 0.972222 0.0277778 4 1 0 5 1 0 6 1 4.44089e-16 7 1 0 Integrate 2520 * X^2 * Y^1 * Z^1 Rule QUAD ERROR 1 1.64062 0.640625 2 1.512 0.512 3 1.03704 0.037037 4 1.00729 0.00728863 5 1 0 6 1 4.44089e-16 7 1 2.9976e-15 Integrate 10080 * X^2 * Y^1 * Z^2 Rule QUAD ERROR 1 1.64062 0.640625 2 1.4784 0.4784 3 0.799383 0.200617 4 0.835485 0.164515 5 0.978516 0.0214844 6 1 8.88178e-16 7 1 7.43849e-15 Integrate 30240 * X^2 * Y^1 * Z^3 Rule QUAD ERROR 1 1.23047 0.230469 2 1.2096 0.2096 3 0.864198 0.135802 4 0.947105 0.0528946 5 1.03564 0.0356445 6 1.02116 0.0211604 7 1 5.21805e-15 Integrate 1260 * X^2 * Y^2 * Z^0 Rule QUAD ERROR 1 0.820312 0.179688 2 0.84 0.16 3 0.712963 0.287037 4 0.844023 0.155977 5 1 0 6 1 0 7 1 8.88178e-16 Integrate 10080 * X^2 * Y^2 * Z^1 Rule QUAD ERROR 1 1.64062 0.640625 2 1.4784 0.4784 3 0.799383 0.200617 4 0.835485 0.164515 5 0.978516 0.0214844 6 1 4.44089e-16 7 1 5.55112e-15 Integrate 45360 * X^2 * Y^2 * Z^2 Rule QUAD ERROR 1 1.8457 0.845703 2 1.57248 0.57248 3 0.550926 0.449074 4 0.560659 0.439341 5 0.814087 0.185913 6 0.933521 0.0664787 7 1 1.08802e-14 Integrate 3360 * X^2 * Y^3 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.6272 0.3728 3 0.684156 0.315844 4 0.846869 0.153131 5 1.00716 0.00716146 6 1 0 7 1 8.32667e-15 Integrate 30240 * X^2 * Y^3 * Z^1 Rule QUAD ERROR 1 1.23047 0.230469 2 1.2096 0.2096 3 0.864198 0.135802 4 0.947105 0.0528946 5 1.03564 0.0356445 6 1.02116 0.0211604 7 1 5.21805e-15 Integrate 7560 * X^2 * Y^4 * Z^0 Rule QUAD ERROR 1 0.307617 0.692383 2 0.44352 0.55648 3 0.799383 0.200617 4 0.906587 0.0934135 5 0.907288 0.0927124 6 0.936798 0.0632017 7 1 1.22125e-15 Integrate 120 * X^3 * Y^0 * Z^0 Rule QUAD ERROR 1 0.3125 0.6875 2 0.44 0.56 3 1.02778 0.0277778 4 1 2.22045e-16 5 1 0 6 1 0 7 1 2.22045e-15 Integrate 840 * X^3 * Y^0 * Z^1 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672 0.328 3 1.10185 0.101852 4 1.09913 0.0991254 5 1 0 6 1 0 7 1 3.33067e-16 Integrate 3360 * X^3 * Y^0 * Z^2 Rule QUAD ERROR 1 0.546875 0.453125 2 0.6272 0.3728 3 0.684156 0.315844 4 0.846869 0.153131 5 1.00716 0.00716146 6 1 0 7 1 6.88338e-15 Integrate 10080 * X^3 * Y^0 * Z^3 Rule QUAD ERROR 1 0.410156 0.589844 2 0.48384 0.51616 3 0.410494 0.589506 4 0.700422 0.299578 5 1.12134 0.121338 6 1.07016 0.0701621 7 1 2.9976e-15 Integrate 840 * X^3 * Y^1 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672 0.328 3 1.10185 0.101852 4 1.09913 0.0991254 5 1 0 6 1 0 7 1 3.33067e-16 Integrate 6720 * X^3 * Y^1 * Z^1 Rule QUAD ERROR 1 1.09375 0.09375 2 1.1648 0.1648 3 1.3107 0.3107 4 1.25337 0.253367 5 1.02865 0.0286458 6 1 4.44089e-16 7 1 5.77316e-15 Integrate 30240 * X^3 * Y^1 * Z^2 Rule QUAD ERROR 1 1.23047 0.230469 2 1.2096 0.2096 3 0.864198 0.135802 4 0.947105 0.0528946 5 1.03564 0.0356445 6 1.02116 0.0211604 7 1 6.21725e-15 Integrate 3360 * X^3 * Y^2 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.6272 0.3728 3 0.684156 0.315844 4 0.846869 0.153131 5 1.00716 0.00716146 6 1 0 7 1 6.55032e-15 Integrate 30240 * X^3 * Y^2 * Z^1 Rule QUAD ERROR 1 1.23047 0.230469 2 1.2096 0.2096 3 0.864198 0.135802 4 0.947105 0.0528946 5 1.03564 0.0356445 6 1.02116 0.0211604 7 1 5.77316e-15 Integrate 10080 * X^3 * Y^3 * Z^0 Rule QUAD ERROR 1 0.410156 0.589844 2 0.48384 0.51616 3 0.410494 0.589506 4 0.700422 0.299578 5 1.12134 0.121338 6 1.07016 0.0701621 7 1 5.9952e-15 Integrate 210 * X^4 * Y^0 * Z^0 Rule QUAD ERROR 1 0.136719 0.863281 2 0.266 0.734 3 0.972222 0.0277778 4 0.925656 0.074344 5 1 0 6 1 1.55431e-15 7 1 1.11022e-15 Integrate 1680 * X^4 * Y^0 * Z^1 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448 0.552 3 1.20628 0.206276 4 1.14813 0.148133 5 0.982096 0.0179036 6 1 4.44089e-16 7 1 8.88178e-16 Integrate 7560 * X^4 * Y^0 * Z^2 Rule QUAD ERROR 1 0.307617 0.692383 2 0.44352 0.55648 3 0.799383 0.200617 4 0.906587 0.0934135 5 0.907288 0.0927124 6 0.936798 0.0632017 7 1 2.22045e-16 Integrate 1680 * X^4 * Y^1 * Z^0 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448 0.552 3 1.20628 0.206276 4 1.14813 0.148133 5 0.982096 0.0179036 6 1 3.33067e-16 7 1 2.22045e-16 Integrate 15120 * X^4 * Y^1 * Z^1 Rule QUAD ERROR 1 0.615234 0.384766 2 0.84672 0.15328 3 1.66358 0.66358 4 1.51348 0.513477 5 1.01111 0.0111084 6 0.981837 0.0181629 7 1 4.77396e-15 Integrate 7560 * X^4 * Y^2 * Z^0 Rule QUAD ERROR 1 0.307617 0.692383 2 0.44352 0.55648 3 0.799383 0.200617 4 0.906587 0.0934135 5 0.907288 0.0927124 6 0.936798 0.0632017 7 1 1.33227e-15 Integrate 336 * X^5 * Y^0 * Z^0 Rule QUAD ERROR 1 0.0546875 0.945312 2 0.1568 0.8432 3 0.83179 0.16821 4 0.79217 0.20783 5 1.01074 0.0107422 6 1 8.88178e-16 7 1 1.55431e-15 Integrate 3024 * X^5 * Y^0 * Z^1 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.18611 0.186111 4 1.09861 0.0986137 5 1.00042 0.000415039 6 1.03255 0.0325459 7 1 1.9984e-15 Integrate 3024 * X^5 * Y^1 * Z^0 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.18611 0.186111 4 1.09861 0.0986137 5 1.00042 0.000415039 6 1.03255 0.0325459 7 1 2.10942e-15 Integrate 504 * X^6 * Y^0 * Z^0 Rule QUAD ERROR 1 0.0205078 0.979492 2 0.090048 0.909952 3 0.65463 0.34537 4 0.638948 0.361052 5 1.01591 0.0159058 6 0.983727 0.0162729 7 1 1.11022e-15 TEST06 REFERENCE_TO_PHYSICAL_T4 transforms a rule on the unit (reference) tetrahedron to a rule on an arbitrary (physical) tetrahedron. The reference tetrahedron: 1 0 0 0 2 1 0 0 3 0 1 0 4 0 0 1 Rule 3 for reference tetrahedron with volume = 0.166667 X Y Z W 0 0.166667 0.166667 0.166667 0.55 1 0.166667 0.166667 0.5 0.55 2 0.166667 0.5 0.166667 0.55 3 0.5 0.166667 0.166667 0.55 4 0.333333 0.333333 0.166667 -0.2 5 0.333333 0.166667 0.333333 -0.2 6 0.333333 0.166667 0.166667 -0.2 7 0.166667 0.333333 0.333333 -0.2 8 0.166667 0.333333 0.166667 -0.2 9 0.166667 0.166667 0.333333 -0.2 The physical tetrahedron: 1 4 5 1 2 6 5 1 3 4 8 1 4 4 5 5 Rule 3 for physical tetrahedron with volume = 4 X Y Z W 0 4.33333 5.5 1.66667 0.55 1 4.33333 5.5 3 0.55 2 4.33333 6.5 1.66667 0.55 3 5 5.5 1.66667 0.55 4 4.66667 6 1.66667 -0.2 5 4.66667 5.5 2.33333 -0.2 6 4.66667 5.5 1.66667 -0.2 7 4.33333 6 2.33333 -0.2 8 4.33333 6 1.66667 -0.2 9 4.33333 5.5 2.33333 -0.2 TEST06 TETRAHEDRON_NCO_RULE returns the points and weights of an NCO rule for the tetrahedron. In this test, we simply print rule 4 The compressed rule: Number of suborders = 3 S Sub Weight Xsi1 Xsi2 Xsi3 Xsi4 1 4 0.166667 0.142857 0.142857 0.142857 0.571429 2 12 0.108333 0.142857 0.142857 0.285714 0.428571 3 4 -0.241667 0.285714 0.285714 0.285714 0.142857 The full rule: Order = 20 O Weight X Y Z 1 0.166667 0.142857 0.142857 0.142857 2 0.166667 0.142857 0.142857 0.571429 3 0.166667 0.142857 0.571429 0.142857 4 0.166667 0.571429 0.142857 0.142857 5 0.108333 0.142857 0.142857 0.285714 6 0.108333 0.142857 0.142857 0.428571 7 0.108333 0.142857 0.285714 0.142857 8 0.108333 0.142857 0.285714 0.428571 9 0.108333 0.142857 0.428571 0.142857 10 0.108333 0.142857 0.428571 0.285714 11 0.108333 0.285714 0.142857 0.142857 12 0.108333 0.285714 0.142857 0.428571 13 0.108333 0.285714 0.428571 0.142857 14 0.108333 0.428571 0.142857 0.142857 15 0.108333 0.428571 0.142857 0.285714 16 0.108333 0.428571 0.285714 0.142857 17 -0.241667 0.285714 0.285714 0.285714 18 -0.241667 0.285714 0.285714 0.142857 19 -0.241667 0.285714 0.142857 0.285714 20 -0.241667 0.142857 0.285714 0.285714 TETRAHEDRON_NCO_RULE_TEST: Normal end of execution. 21 January 2020 11:07:18 AM