08-Jan-2022 10:31:19 tetrahedron_ncc_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test tetrahedron_ncc_rule(). tetrahedron_ncc_rule_test01(): TETRAHEDRON_NCC_RULE_NUM returns the number of rules; TETRAHEDRON_NCC_DEGREE returns the degree of a rule; TETRAHEDRON_NCC_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 tetrahedron_ncc_rule_test02() TETRAHEDRON_NCC_RULE returns the points and weights of an NCC 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 1.000000 2 1.000000 3 1.000000 4 1.000000 5 1.000000 6 1.000000 7 1.000000 tetrahedron_ncc_rule_test03 TETRAHEDRON_NCC_RULE returns the points and weights of an NCC rule for the tetrahedron. In this test, we simply check that, for each quadrature point, the barycentric coordinates sum to 1. Rule Suborder Sum of coordinates 1 1 1.000000e+00 2 1 1.000000e+00 3 2 1.000000e+00 1.000000e+00 4 3 1.000000e+00 1.000000e+00 1.000000e+00 5 5 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 6 6 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 7 9 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 tetrahedron_ncc_rule_test04 TETRAHEDRON_NCC_RULE returns the points and weights of an NCC rule for the unit tetrahedron. This routine uses those rules to estimate the integral of monomomials in the unit tetrahedron. Integrate 6.000000 * X^0 * Y^0 * Z^0 Rule QUAD ERROR 1 1.000000 0.000000 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 24.000000 * X^0 * Y^0 * Z^1 Rule QUAD ERROR 1 1.000000 0.000000 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 60.000000 * X^0 * Y^0 * Z^2 Rule QUAD ERROR 1 0.625000 0.375000 2 2.500000 1.500000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 120.000000 * X^0 * Y^0 * Z^3 Rule QUAD ERROR 1 0.312500 0.687500 2 5.000000 4.000000 3 0.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 210.000000 * X^0 * Y^0 * Z^4 Rule QUAD ERROR 1 0.136719 0.863281 2 8.750000 7.750000 3 -0.437500 1.437500 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 336.000000 * X^0 * Y^0 * Z^5 Rule QUAD ERROR 1 0.054688 0.945312 2 14.000000 13.000000 3 -1.750000 2.750000 4 1.555556 0.555556 5 0.937500 0.062500 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 504.000000 * X^0 * Y^0 * Z^6 Rule QUAD ERROR 1 0.020508 0.979492 2 21.000000 20.000000 3 -3.412500 4.412500 4 2.177778 1.177778 5 0.759375 0.240625 6 1.023840 0.023840 7 1.000000 0.000000 Integrate 24.000000 * X^0 * Y^1 * Z^0 Rule QUAD ERROR 1 1.000000 0.000000 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 120.000000 * X^0 * Y^1 * Z^1 Rule QUAD ERROR 1 1.250000 0.250000 2 0.000000 1.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 360.000000 * X^0 * Y^1 * Z^2 Rule QUAD ERROR 1 0.937500 0.062500 2 0.000000 1.000000 3 1.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 840.000000 * X^0 * Y^1 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 1.750000 0.750000 4 0.777778 0.222222 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 1680.000000 * X^0 * Y^1 * Z^4 Rule QUAD ERROR 1 0.273438 0.726562 2 0.000000 1.000000 3 1.750000 0.750000 4 0.518519 0.481481 5 1.104167 0.104167 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3024.000000 * X^0 * Y^1 * Z^5 Rule QUAD ERROR 1 0.123047 0.876953 2 0.000000 1.000000 3 1.575000 0.575000 4 0.311111 0.688889 5 1.293750 0.293750 6 0.952320 0.047680 7 1.000000 0.000000 Integrate 60.000000 * X^0 * Y^2 * Z^0 Rule QUAD ERROR 1 0.625000 0.375000 2 2.500000 1.500000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 360.000000 * X^0 * Y^2 * Z^1 Rule QUAD ERROR 1 0.937500 0.062500 2 0.000000 1.000000 3 1.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 1260.000000 * X^0 * Y^2 * Z^2 Rule QUAD ERROR 1 0.820312 0.179688 2 0.000000 1.000000 3 2.625000 1.625000 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3360.000000 * X^0 * Y^2 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 3.500000 2.500000 4 1.037037 0.037037 5 0.958333 0.041667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 7560.000000 * X^0 * Y^2 * Z^4 Rule QUAD ERROR 1 0.307617 0.692383 2 0.000000 1.000000 3 3.937500 2.937500 4 0.777778 0.222222 5 1.078125 0.078125 6 1.051200 0.051200 7 1.000000 0.000000 Integrate 120.000000 * X^0 * Y^3 * Z^0 Rule QUAD ERROR 1 0.312500 0.687500 2 5.000000 4.000000 3 0.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 840.000000 * X^0 * Y^3 * Z^1 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 1.750000 0.750000 4 0.777778 0.222222 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3360.000000 * X^0 * Y^3 * Z^2 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 3.500000 2.500000 4 1.037037 0.037037 5 0.958333 0.041667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 10080.000000 * X^0 * Y^3 * Z^3 Rule QUAD ERROR 1 0.410156 0.589844 2 0.000000 1.000000 3 5.250000 4.250000 4 1.037037 0.037037 5 0.750000 0.250000 6 0.950400 0.049600 7 1.000000 0.000000 Integrate 210.000000 * X^0 * Y^4 * Z^0 Rule QUAD ERROR 1 0.136719 0.863281 2 8.750000 7.750000 3 -0.437500 1.437500 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 1680.000000 * X^0 * Y^4 * Z^1 Rule QUAD ERROR 1 0.273438 0.726562 2 0.000000 1.000000 3 1.750000 0.750000 4 0.518519 0.481481 5 1.104167 0.104167 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 7560.000000 * X^0 * Y^4 * Z^2 Rule QUAD ERROR 1 0.307617 0.692383 2 0.000000 1.000000 3 3.937500 2.937500 4 0.777778 0.222222 5 1.078125 0.078125 6 1.051200 0.051200 7 1.000000 0.000000 Integrate 336.000000 * X^0 * Y^5 * Z^0 Rule QUAD ERROR 1 0.054688 0.945312 2 14.000000 13.000000 3 -1.750000 2.750000 4 1.555556 0.555556 5 0.937500 0.062500 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3024.000000 * X^0 * Y^5 * Z^1 Rule QUAD ERROR 1 0.123047 0.876953 2 0.000000 1.000000 3 1.575000 0.575000 4 0.311111 0.688889 5 1.293750 0.293750 6 0.952320 0.047680 7 1.000000 0.000000 Integrate 504.000000 * X^0 * Y^6 * Z^0 Rule QUAD ERROR 1 0.020508 0.979492 2 21.000000 20.000000 3 -3.412500 4.412500 4 2.177778 1.177778 5 0.759375 0.240625 6 1.023840 0.023840 7 1.000000 0.000000 Integrate 24.000000 * X^1 * Y^0 * Z^0 Rule QUAD ERROR 1 1.000000 0.000000 2 1.000000 0.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 120.000000 * X^1 * Y^0 * Z^1 Rule QUAD ERROR 1 1.250000 0.250000 2 0.000000 1.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 360.000000 * X^1 * Y^0 * Z^2 Rule QUAD ERROR 1 0.937500 0.062500 2 0.000000 1.000000 3 1.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 840.000000 * X^1 * Y^0 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 1.750000 0.750000 4 0.777778 0.222222 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 1680.000000 * X^1 * Y^0 * Z^4 Rule QUAD ERROR 1 0.273438 0.726562 2 0.000000 1.000000 3 1.750000 0.750000 4 0.518519 0.481481 5 1.104167 0.104167 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3024.000000 * X^1 * Y^0 * Z^5 Rule QUAD ERROR 1 0.123047 0.876953 2 0.000000 1.000000 3 1.575000 0.575000 4 0.311111 0.688889 5 1.293750 0.293750 6 0.952320 0.047680 7 1.000000 0.000000 Integrate 120.000000 * X^1 * Y^1 * Z^0 Rule QUAD ERROR 1 1.250000 0.250000 2 0.000000 1.000000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 720.000000 * X^1 * Y^1 * Z^1 Rule QUAD ERROR 1 1.875000 0.875000 2 0.000000 1.000000 3 0.000000 1.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 2520.000000 * X^1 * Y^1 * Z^2 Rule QUAD ERROR 1 1.640625 0.640625 2 0.000000 1.000000 3 0.000000 1.000000 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 6720.000000 * X^1 * Y^1 * Z^3 Rule QUAD ERROR 1 1.093750 0.093750 2 0.000000 1.000000 3 0.000000 1.000000 4 1.037037 0.037037 5 0.833333 0.166667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 15120.000000 * X^1 * Y^1 * Z^4 Rule QUAD ERROR 1 0.615234 0.384766 2 0.000000 1.000000 3 0.000000 1.000000 4 0.777778 0.222222 5 0.656250 0.343750 6 1.068000 0.068000 7 1.000000 0.000000 Integrate 360.000000 * X^1 * Y^2 * Z^0 Rule QUAD ERROR 1 0.937500 0.062500 2 0.000000 1.000000 3 1.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 2520.000000 * X^1 * Y^2 * Z^1 Rule QUAD ERROR 1 1.640625 0.640625 2 0.000000 1.000000 3 0.000000 1.000000 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 10080.000000 * X^1 * Y^2 * Z^2 Rule QUAD ERROR 1 1.640625 0.640625 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.125000 0.125000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 30240.000000 * X^1 * Y^2 * Z^3 Rule QUAD ERROR 1 1.230469 0.230469 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.031250 0.031250 6 0.972000 0.028000 7 1.000000 0.000000 Integrate 840.000000 * X^1 * Y^3 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 1.750000 0.750000 4 0.777778 0.222222 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 6720.000000 * X^1 * Y^3 * Z^1 Rule QUAD ERROR 1 1.093750 0.093750 2 0.000000 1.000000 3 0.000000 1.000000 4 1.037037 0.037037 5 0.833333 0.166667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 30240.000000 * X^1 * Y^3 * Z^2 Rule QUAD ERROR 1 1.230469 0.230469 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.031250 0.031250 6 0.972000 0.028000 7 1.000000 0.000000 Integrate 1680.000000 * X^1 * Y^4 * Z^0 Rule QUAD ERROR 1 0.273438 0.726562 2 0.000000 1.000000 3 1.750000 0.750000 4 0.518519 0.481481 5 1.104167 0.104167 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 15120.000000 * X^1 * Y^4 * Z^1 Rule QUAD ERROR 1 0.615234 0.384766 2 0.000000 1.000000 3 0.000000 1.000000 4 0.777778 0.222222 5 0.656250 0.343750 6 1.068000 0.068000 7 1.000000 0.000000 Integrate 3024.000000 * X^1 * Y^5 * Z^0 Rule QUAD ERROR 1 0.123047 0.876953 2 0.000000 1.000000 3 1.575000 0.575000 4 0.311111 0.688889 5 1.293750 0.293750 6 0.952320 0.047680 7 1.000000 0.000000 Integrate 60.000000 * X^2 * Y^0 * Z^0 Rule QUAD ERROR 1 0.625000 0.375000 2 2.500000 1.500000 3 1.000000 0.000000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 360.000000 * X^2 * Y^0 * Z^1 Rule QUAD ERROR 1 0.937500 0.062500 2 0.000000 1.000000 3 1.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 1260.000000 * X^2 * Y^0 * Z^2 Rule QUAD ERROR 1 0.820312 0.179688 2 0.000000 1.000000 3 2.625000 1.625000 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3360.000000 * X^2 * Y^0 * Z^3 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 3.500000 2.500000 4 1.037037 0.037037 5 0.958333 0.041667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 7560.000000 * X^2 * Y^0 * Z^4 Rule QUAD ERROR 1 0.307617 0.692383 2 0.000000 1.000000 3 3.937500 2.937500 4 0.777778 0.222222 5 1.078125 0.078125 6 1.051200 0.051200 7 1.000000 0.000000 Integrate 360.000000 * X^2 * Y^1 * Z^0 Rule QUAD ERROR 1 0.937500 0.062500 2 0.000000 1.000000 3 1.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 2520.000000 * X^2 * Y^1 * Z^1 Rule QUAD ERROR 1 1.640625 0.640625 2 0.000000 1.000000 3 0.000000 1.000000 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 10080.000000 * X^2 * Y^1 * Z^2 Rule QUAD ERROR 1 1.640625 0.640625 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.125000 0.125000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 30240.000000 * X^2 * Y^1 * Z^3 Rule QUAD ERROR 1 1.230469 0.230469 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.031250 0.031250 6 0.972000 0.028000 7 1.000000 0.000000 Integrate 1260.000000 * X^2 * Y^2 * Z^0 Rule QUAD ERROR 1 0.820312 0.179688 2 0.000000 1.000000 3 2.625000 1.625000 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 10080.000000 * X^2 * Y^2 * Z^1 Rule QUAD ERROR 1 1.640625 0.640625 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.125000 0.125000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 45360.000000 * X^2 * Y^2 * Z^2 Rule QUAD ERROR 1 1.845703 0.845703 2 0.000000 1.000000 3 0.000000 1.000000 4 2.333333 1.333333 5 1.406250 0.406250 6 1.044000 0.044000 7 1.000000 0.000000 Integrate 3360.000000 * X^2 * Y^3 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 3.500000 2.500000 4 1.037037 0.037037 5 0.958333 0.041667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 30240.000000 * X^2 * Y^3 * Z^1 Rule QUAD ERROR 1 1.230469 0.230469 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.031250 0.031250 6 0.972000 0.028000 7 1.000000 0.000000 Integrate 7560.000000 * X^2 * Y^4 * Z^0 Rule QUAD ERROR 1 0.307617 0.692383 2 0.000000 1.000000 3 3.937500 2.937500 4 0.777778 0.222222 5 1.078125 0.078125 6 1.051200 0.051200 7 1.000000 0.000000 Integrate 120.000000 * X^3 * Y^0 * Z^0 Rule QUAD ERROR 1 0.312500 0.687500 2 5.000000 4.000000 3 0.500000 0.500000 4 1.000000 0.000000 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 840.000000 * X^3 * Y^0 * Z^1 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 1.750000 0.750000 4 0.777778 0.222222 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3360.000000 * X^3 * Y^0 * Z^2 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 3.500000 2.500000 4 1.037037 0.037037 5 0.958333 0.041667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 10080.000000 * X^3 * Y^0 * Z^3 Rule QUAD ERROR 1 0.410156 0.589844 2 0.000000 1.000000 3 5.250000 4.250000 4 1.037037 0.037037 5 0.750000 0.250000 6 0.950400 0.049600 7 1.000000 0.000000 Integrate 840.000000 * X^3 * Y^1 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 1.750000 0.750000 4 0.777778 0.222222 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 6720.000000 * X^3 * Y^1 * Z^1 Rule QUAD ERROR 1 1.093750 0.093750 2 0.000000 1.000000 3 0.000000 1.000000 4 1.037037 0.037037 5 0.833333 0.166667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 30240.000000 * X^3 * Y^1 * Z^2 Rule QUAD ERROR 1 1.230469 0.230469 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.031250 0.031250 6 0.972000 0.028000 7 1.000000 0.000000 Integrate 3360.000000 * X^3 * Y^2 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.000000 1.000000 3 3.500000 2.500000 4 1.037037 0.037037 5 0.958333 0.041667 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 30240.000000 * X^3 * Y^2 * Z^1 Rule QUAD ERROR 1 1.230469 0.230469 2 0.000000 1.000000 3 0.000000 1.000000 4 1.555556 0.555556 5 1.031250 0.031250 6 0.972000 0.028000 7 1.000000 0.000000 Integrate 10080.000000 * X^3 * Y^3 * Z^0 Rule QUAD ERROR 1 0.410156 0.589844 2 0.000000 1.000000 3 5.250000 4.250000 4 1.037037 0.037037 5 0.750000 0.250000 6 0.950400 0.049600 7 1.000000 0.000000 Integrate 210.000000 * X^4 * Y^0 * Z^0 Rule QUAD ERROR 1 0.136719 0.863281 2 8.750000 7.750000 3 -0.437500 1.437500 4 1.166667 0.166667 5 1.000000 0.000000 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 1680.000000 * X^4 * Y^0 * Z^1 Rule QUAD ERROR 1 0.273438 0.726562 2 0.000000 1.000000 3 1.750000 0.750000 4 0.518519 0.481481 5 1.104167 0.104167 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 7560.000000 * X^4 * Y^0 * Z^2 Rule QUAD ERROR 1 0.307617 0.692383 2 0.000000 1.000000 3 3.937500 2.937500 4 0.777778 0.222222 5 1.078125 0.078125 6 1.051200 0.051200 7 1.000000 0.000000 Integrate 1680.000000 * X^4 * Y^1 * Z^0 Rule QUAD ERROR 1 0.273438 0.726562 2 0.000000 1.000000 3 1.750000 0.750000 4 0.518519 0.481481 5 1.104167 0.104167 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 15120.000000 * X^4 * Y^1 * Z^1 Rule QUAD ERROR 1 0.615234 0.384766 2 0.000000 1.000000 3 0.000000 1.000000 4 0.777778 0.222222 5 0.656250 0.343750 6 1.068000 0.068000 7 1.000000 0.000000 Integrate 7560.000000 * X^4 * Y^2 * Z^0 Rule QUAD ERROR 1 0.307617 0.692383 2 0.000000 1.000000 3 3.937500 2.937500 4 0.777778 0.222222 5 1.078125 0.078125 6 1.051200 0.051200 7 1.000000 0.000000 Integrate 336.000000 * X^5 * Y^0 * Z^0 Rule QUAD ERROR 1 0.054688 0.945312 2 14.000000 13.000000 3 -1.750000 2.750000 4 1.555556 0.555556 5 0.937500 0.062500 6 1.000000 0.000000 7 1.000000 0.000000 Integrate 3024.000000 * X^5 * Y^0 * Z^1 Rule QUAD ERROR 1 0.123047 0.876953 2 0.000000 1.000000 3 1.575000 0.575000 4 0.311111 0.688889 5 1.293750 0.293750 6 0.952320 0.047680 7 1.000000 0.000000 Integrate 3024.000000 * X^5 * Y^1 * Z^0 Rule QUAD ERROR 1 0.123047 0.876953 2 0.000000 1.000000 3 1.575000 0.575000 4 0.311111 0.688889 5 1.293750 0.293750 6 0.952320 0.047680 7 1.000000 0.000000 Integrate 504.000000 * X^6 * Y^0 * Z^0 Rule QUAD ERROR 1 0.020508 0.979492 2 21.000000 20.000000 3 -3.412500 4.412500 4 2.177778 1.177778 5 0.759375 0.240625 6 1.023840 0.023840 7 1.000000 0.000000 tetrahedron_ncc_rule_test05 REFERENCE_TO_PHYSICAL_T4 transforms a rule on the unit (reference) tetrahedron to a rule on an arbitrary (physical) tetrahedron. The reference tetrahedron: 1 0.000000 0.000000 0.000000 2 1.000000 0.000000 0.000000 3 0.000000 1.000000 0.000000 4 0.000000 0.000000 1.000000 Rule 3 for reference tetrahedron with volume = 0.166667 X Y Z W 1 0.000000 0.000000 0.000000 -0.050000 2 0.000000 0.000000 1.000000 -0.050000 3 0.000000 1.000000 0.000000 -0.050000 4 1.000000 0.000000 0.000000 -0.050000 5 0.500000 0.500000 0.000000 0.200000 6 0.500000 0.000000 0.500000 0.200000 7 0.500000 0.000000 0.000000 0.200000 8 0.000000 0.500000 0.500000 0.200000 9 0.000000 0.500000 0.000000 0.200000 10 0.000000 0.000000 0.500000 0.200000 The physical tetrahedron: 1 4.000000 5.000000 1.000000 2 6.000000 5.000000 1.000000 3 4.000000 8.000000 1.000000 4 4.000000 5.000000 5.000000 Rule 3 for physical tetrahedron with volume = 4.000000 X Y Z W 1 4.000000 5.000000 1.000000 -0.050000 2 4.000000 5.000000 5.000000 -0.050000 3 4.000000 8.000000 1.000000 -0.050000 4 6.000000 5.000000 1.000000 -0.050000 5 5.000000 6.500000 1.000000 0.200000 6 5.000000 5.000000 3.000000 0.200000 7 5.000000 5.000000 1.000000 0.200000 8 4.000000 6.500000 3.000000 0.200000 9 4.000000 6.500000 1.000000 0.200000 10 4.000000 5.000000 3.000000 0.200000 tetrahedron_ncc_rule_test06() TETRAHEDRON_NCC_RULE returns the points and weights of an NCC 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 0.025000 0.000000 0.000000 0.000000 1.000000 2 12 0.000000 0.000000 0.000000 0.333333 0.666667 3 4 0.225000 0.333333 0.333333 0.333333 0.000000 The full rule: Order = 20 O Weight X Y Z 1 0.025000 0.000000 0.000000 0.000000 2 0.025000 0.000000 0.000000 1.000000 3 0.025000 0.000000 1.000000 0.000000 4 0.025000 1.000000 0.000000 0.000000 5 0.000000 0.000000 0.000000 0.333333 6 0.000000 0.000000 0.000000 0.666667 7 0.000000 0.000000 0.333333 0.000000 8 0.000000 0.000000 0.333333 0.666667 9 0.000000 0.000000 0.666667 0.000000 10 0.000000 0.000000 0.666667 0.333333 11 0.000000 0.333333 0.000000 0.000000 12 0.000000 0.333333 0.000000 0.666667 13 0.000000 0.333333 0.666667 0.000000 14 0.000000 0.666667 0.000000 0.000000 15 0.000000 0.666667 0.000000 0.333333 16 0.000000 0.666667 0.333333 0.000000 17 0.225000 0.333333 0.333333 0.333333 18 0.225000 0.333333 0.333333 0.000000 19 0.225000 0.333333 0.000000 0.333333 20 0.225000 0.000000 0.333333 0.333333 tetrahedron_ncc_rule_test(): Normal end of execution. 08-Jan-2022 10:31:19