09 April 2023 7:03:25.125 AM tetrahedron_ncc_rule_test(): FORTRAN90 version Test 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 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 1.000000000000000 2 1.000000000000000 3 1.000000000000000 4 1.000000000000000 5 0.9999999999999997 6 1.000000000000000 7 1.000000000000000 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 1.000000000000000 2 1 1.000000000000000 3 2 1.000000000000000 1.000000000000000 4 3 1.000000000000000 1.000000000000000 1.000000000000000 5 5 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 6 6 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 7 9 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999999 1.000000000000000 1.000000000000000 0.9999999999999999 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 6.00000 * X ** 0 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 24.0000 * X ** 0 * Y ** 0 * Z ** 1 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 60.0000 * X ** 0 * Y ** 0 * Z ** 2 Rule QUAD ERROR 1 0.625000 0.37500000 2 2.50000 1.50000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 120.000 * X ** 0 * Y ** 0 * Z ** 3 Rule QUAD ERROR 1 0.312500 0.68750000 2 5.00000 4.00000000 3 0.500000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 210.000 * X ** 0 * Y ** 0 * Z ** 4 Rule QUAD ERROR 1 0.136719 0.86328125 2 8.75000 7.75000000 3 -0.437500 1.43750000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 336.000 * X ** 0 * Y ** 0 * Z ** 5 Rule QUAD ERROR 1 0.546875E-01 0.94531250 2 14.0000 13.00000000 3 -1.75000 2.75000000 4 1.55556 0.55555556 5 0.937500 0.06250000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 504.000 * X ** 0 * Y ** 0 * Z ** 6 Rule QUAD ERROR 1 0.205078E-01 0.97949219 2 21.0000 20.00000000 3 -3.41250 4.41250000 4 2.17778 1.17777778 5 0.759375 0.24062500 6 1.02384 0.02384000 7 1.00000 0.00000000 Integrate 24.0000 * X ** 0 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 120.000 * X ** 0 * Y ** 1 * Z ** 1 Rule QUAD ERROR 1 1.25000 0.25000000 2 0.00000 1.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 360.000 * X ** 0 * Y ** 1 * Z ** 2 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.00000 1.00000000 3 1.50000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 840.000 * X ** 0 * Y ** 1 * Z ** 3 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.777778 0.22222222 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 1680.00 * X ** 0 * Y ** 1 * Z ** 4 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.518519 0.48148148 5 1.10417 0.10416667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3024.00 * X ** 0 * Y ** 1 * Z ** 5 Rule QUAD ERROR 1 0.123047 0.87695312 2 0.00000 1.00000000 3 1.57500 0.57500000 4 0.311111 0.68888889 5 1.29375 0.29375000 6 0.952320 0.04768000 7 1.00000 0.00000000 Integrate 60.0000 * X ** 0 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.625000 0.37500000 2 2.50000 1.50000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 360.000 * X ** 0 * Y ** 2 * Z ** 1 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.00000 1.00000000 3 1.50000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 1260.00 * X ** 0 * Y ** 2 * Z ** 2 Rule QUAD ERROR 1 0.820312 0.17968750 2 0.00000 1.00000000 3 2.62500 1.62500000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3360.00 * X ** 0 * Y ** 2 * Z ** 3 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 3.50000 2.50000000 4 1.03704 0.03703704 5 0.958333 0.04166667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 7560.00 * X ** 0 * Y ** 2 * Z ** 4 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.00000 1.00000000 3 3.93750 2.93750000 4 0.777778 0.22222222 5 1.07812 0.07812500 6 1.05120 0.05120000 7 1.00000 0.00000000 Integrate 120.000 * X ** 0 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.312500 0.68750000 2 5.00000 4.00000000 3 0.500000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 840.000 * X ** 0 * Y ** 3 * Z ** 1 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.777778 0.22222222 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3360.00 * X ** 0 * Y ** 3 * Z ** 2 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 3.50000 2.50000000 4 1.03704 0.03703704 5 0.958333 0.04166667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 10080.0 * X ** 0 * Y ** 3 * Z ** 3 Rule QUAD ERROR 1 0.410156 0.58984375 2 0.00000 1.00000000 3 5.25000 4.25000000 4 1.03704 0.03703704 5 0.750000 0.25000000 6 0.950400 0.04960000 7 1.00000 0.00000000 Integrate 210.000 * X ** 0 * Y ** 4 * Z ** 0 Rule QUAD ERROR 1 0.136719 0.86328125 2 8.75000 7.75000000 3 -0.437500 1.43750000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 1680.00 * X ** 0 * Y ** 4 * Z ** 1 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.518519 0.48148148 5 1.10417 0.10416667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 7560.00 * X ** 0 * Y ** 4 * Z ** 2 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.00000 1.00000000 3 3.93750 2.93750000 4 0.777778 0.22222222 5 1.07812 0.07812500 6 1.05120 0.05120000 7 1.00000 0.00000000 Integrate 336.000 * X ** 0 * Y ** 5 * Z ** 0 Rule QUAD ERROR 1 0.546875E-01 0.94531250 2 14.0000 13.00000000 3 -1.75000 2.75000000 4 1.55556 0.55555556 5 0.937500 0.06250000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3024.00 * X ** 0 * Y ** 5 * Z ** 1 Rule QUAD ERROR 1 0.123047 0.87695312 2 0.00000 1.00000000 3 1.57500 0.57500000 4 0.311111 0.68888889 5 1.29375 0.29375000 6 0.952320 0.04768000 7 1.00000 0.00000000 Integrate 504.000 * X ** 0 * Y ** 6 * Z ** 0 Rule QUAD ERROR 1 0.205078E-01 0.97949219 2 21.0000 20.00000000 3 -3.41250 4.41250000 4 2.17778 1.17777778 5 0.759375 0.24062500 6 1.02384 0.02384000 7 1.00000 0.00000000 Integrate 24.0000 * X ** 1 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 1.00000 0.00000000 2 1.00000 0.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 120.000 * X ** 1 * Y ** 0 * Z ** 1 Rule QUAD ERROR 1 1.25000 0.25000000 2 0.00000 1.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 360.000 * X ** 1 * Y ** 0 * Z ** 2 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.00000 1.00000000 3 1.50000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 840.000 * X ** 1 * Y ** 0 * Z ** 3 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.777778 0.22222222 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 1680.00 * X ** 1 * Y ** 0 * Z ** 4 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.518519 0.48148148 5 1.10417 0.10416667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3024.00 * X ** 1 * Y ** 0 * Z ** 5 Rule QUAD ERROR 1 0.123047 0.87695312 2 0.00000 1.00000000 3 1.57500 0.57500000 4 0.311111 0.68888889 5 1.29375 0.29375000 6 0.952320 0.04768000 7 1.00000 0.00000000 Integrate 120.000 * X ** 1 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 1.25000 0.25000000 2 0.00000 1.00000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 720.000 * X ** 1 * Y ** 1 * Z ** 1 Rule QUAD ERROR 1 1.87500 0.87500000 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 2520.00 * X ** 1 * Y ** 1 * Z ** 2 Rule QUAD ERROR 1 1.64062 0.64062500 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 6720.00 * X ** 1 * Y ** 1 * Z ** 3 Rule QUAD ERROR 1 1.09375 0.09375000 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.03704 0.03703704 5 0.833333 0.16666667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 15120.0 * X ** 1 * Y ** 1 * Z ** 4 Rule QUAD ERROR 1 0.615234 0.38476562 2 0.00000 1.00000000 3 0.00000 1.00000000 4 0.777778 0.22222222 5 0.656250 0.34375000 6 1.06800 0.06800000 7 1.00000 0.00000000 Integrate 360.000 * X ** 1 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.00000 1.00000000 3 1.50000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 2520.00 * X ** 1 * Y ** 2 * Z ** 1 Rule QUAD ERROR 1 1.64062 0.64062500 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 10080.0 * X ** 1 * Y ** 2 * Z ** 2 Rule QUAD ERROR 1 1.64062 0.64062500 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.12500 0.12500000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 30240.0 * X ** 1 * Y ** 2 * Z ** 3 Rule QUAD ERROR 1 1.23047 0.23046875 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.03125 0.03125000 6 0.972000 0.02800000 7 1.00000 0.00000000 Integrate 840.000 * X ** 1 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.777778 0.22222222 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 6720.00 * X ** 1 * Y ** 3 * Z ** 1 Rule QUAD ERROR 1 1.09375 0.09375000 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.03704 0.03703704 5 0.833333 0.16666667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 30240.0 * X ** 1 * Y ** 3 * Z ** 2 Rule QUAD ERROR 1 1.23047 0.23046875 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.03125 0.03125000 6 0.972000 0.02800000 7 1.00000 0.00000000 Integrate 1680.00 * X ** 1 * Y ** 4 * Z ** 0 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.518519 0.48148148 5 1.10417 0.10416667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 15120.0 * X ** 1 * Y ** 4 * Z ** 1 Rule QUAD ERROR 1 0.615234 0.38476562 2 0.00000 1.00000000 3 0.00000 1.00000000 4 0.777778 0.22222222 5 0.656250 0.34375000 6 1.06800 0.06800000 7 1.00000 0.00000000 Integrate 3024.00 * X ** 1 * Y ** 5 * Z ** 0 Rule QUAD ERROR 1 0.123047 0.87695312 2 0.00000 1.00000000 3 1.57500 0.57500000 4 0.311111 0.68888889 5 1.29375 0.29375000 6 0.952320 0.04768000 7 1.00000 0.00000000 Integrate 60.0000 * X ** 2 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.625000 0.37500000 2 2.50000 1.50000000 3 1.00000 0.00000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 360.000 * X ** 2 * Y ** 0 * Z ** 1 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.00000 1.00000000 3 1.50000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 1260.00 * X ** 2 * Y ** 0 * Z ** 2 Rule QUAD ERROR 1 0.820312 0.17968750 2 0.00000 1.00000000 3 2.62500 1.62500000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3360.00 * X ** 2 * Y ** 0 * Z ** 3 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 3.50000 2.50000000 4 1.03704 0.03703704 5 0.958333 0.04166667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 7560.00 * X ** 2 * Y ** 0 * Z ** 4 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.00000 1.00000000 3 3.93750 2.93750000 4 0.777778 0.22222222 5 1.07812 0.07812500 6 1.05120 0.05120000 7 1.00000 0.00000000 Integrate 360.000 * X ** 2 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.00000 1.00000000 3 1.50000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 2520.00 * X ** 2 * Y ** 1 * Z ** 1 Rule QUAD ERROR 1 1.64062 0.64062500 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 10080.0 * X ** 2 * Y ** 1 * Z ** 2 Rule QUAD ERROR 1 1.64062 0.64062500 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.12500 0.12500000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 30240.0 * X ** 2 * Y ** 1 * Z ** 3 Rule QUAD ERROR 1 1.23047 0.23046875 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.03125 0.03125000 6 0.972000 0.02800000 7 1.00000 0.00000000 Integrate 1260.00 * X ** 2 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.820312 0.17968750 2 0.00000 1.00000000 3 2.62500 1.62500000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 10080.0 * X ** 2 * Y ** 2 * Z ** 1 Rule QUAD ERROR 1 1.64062 0.64062500 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.12500 0.12500000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 45360.0 * X ** 2 * Y ** 2 * Z ** 2 Rule QUAD ERROR 1 1.84570 0.84570312 2 0.00000 1.00000000 3 0.00000 1.00000000 4 2.33333 1.33333333 5 1.40625 0.40625000 6 1.04400 0.04400000 7 1.00000 0.00000000 Integrate 3360.00 * X ** 2 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 3.50000 2.50000000 4 1.03704 0.03703704 5 0.958333 0.04166667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 30240.0 * X ** 2 * Y ** 3 * Z ** 1 Rule QUAD ERROR 1 1.23047 0.23046875 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.03125 0.03125000 6 0.972000 0.02800000 7 1.00000 0.00000000 Integrate 7560.00 * X ** 2 * Y ** 4 * Z ** 0 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.00000 1.00000000 3 3.93750 2.93750000 4 0.777778 0.22222222 5 1.07812 0.07812500 6 1.05120 0.05120000 7 1.00000 0.00000000 Integrate 120.000 * X ** 3 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.312500 0.68750000 2 5.00000 4.00000000 3 0.500000 0.50000000 4 1.00000 0.00000000 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 840.000 * X ** 3 * Y ** 0 * Z ** 1 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.777778 0.22222222 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3360.00 * X ** 3 * Y ** 0 * Z ** 2 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 3.50000 2.50000000 4 1.03704 0.03703704 5 0.958333 0.04166667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 10080.0 * X ** 3 * Y ** 0 * Z ** 3 Rule QUAD ERROR 1 0.410156 0.58984375 2 0.00000 1.00000000 3 5.25000 4.25000000 4 1.03704 0.03703704 5 0.750000 0.25000000 6 0.950400 0.04960000 7 1.00000 0.00000000 Integrate 840.000 * X ** 3 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.777778 0.22222222 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 6720.00 * X ** 3 * Y ** 1 * Z ** 1 Rule QUAD ERROR 1 1.09375 0.09375000 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.03704 0.03703704 5 0.833333 0.16666667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 30240.0 * X ** 3 * Y ** 1 * Z ** 2 Rule QUAD ERROR 1 1.23047 0.23046875 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.03125 0.03125000 6 0.972000 0.02800000 7 1.00000 0.00000000 Integrate 3360.00 * X ** 3 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.00000 1.00000000 3 3.50000 2.50000000 4 1.03704 0.03703704 5 0.958333 0.04166667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 30240.0 * X ** 3 * Y ** 2 * Z ** 1 Rule QUAD ERROR 1 1.23047 0.23046875 2 0.00000 1.00000000 3 0.00000 1.00000000 4 1.55556 0.55555556 5 1.03125 0.03125000 6 0.972000 0.02800000 7 1.00000 0.00000000 Integrate 10080.0 * X ** 3 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.410156 0.58984375 2 0.00000 1.00000000 3 5.25000 4.25000000 4 1.03704 0.03703704 5 0.750000 0.25000000 6 0.950400 0.04960000 7 1.00000 0.00000000 Integrate 210.000 * X ** 4 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.136719 0.86328125 2 8.75000 7.75000000 3 -0.437500 1.43750000 4 1.16667 0.16666667 5 1.00000 0.00000000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 1680.00 * X ** 4 * Y ** 0 * Z ** 1 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.518519 0.48148148 5 1.10417 0.10416667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 7560.00 * X ** 4 * Y ** 0 * Z ** 2 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.00000 1.00000000 3 3.93750 2.93750000 4 0.777778 0.22222222 5 1.07812 0.07812500 6 1.05120 0.05120000 7 1.00000 0.00000000 Integrate 1680.00 * X ** 4 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.00000 1.00000000 3 1.75000 0.75000000 4 0.518519 0.48148148 5 1.10417 0.10416667 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 15120.0 * X ** 4 * Y ** 1 * Z ** 1 Rule QUAD ERROR 1 0.615234 0.38476562 2 0.00000 1.00000000 3 0.00000 1.00000000 4 0.777778 0.22222222 5 0.656250 0.34375000 6 1.06800 0.06800000 7 1.00000 0.00000000 Integrate 7560.00 * X ** 4 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.00000 1.00000000 3 3.93750 2.93750000 4 0.777778 0.22222222 5 1.07812 0.07812500 6 1.05120 0.05120000 7 1.00000 0.00000000 Integrate 336.000 * X ** 5 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.546875E-01 0.94531250 2 14.0000 13.00000000 3 -1.75000 2.75000000 4 1.55556 0.55555556 5 0.937500 0.06250000 6 1.00000 0.00000000 7 1.00000 0.00000000 Integrate 3024.00 * X ** 5 * Y ** 0 * Z ** 1 Rule QUAD ERROR 1 0.123047 0.87695312 2 0.00000 1.00000000 3 1.57500 0.57500000 4 0.311111 0.68888889 5 1.29375 0.29375000 6 0.952320 0.04768000 7 1.00000 0.00000000 Integrate 3024.00 * X ** 5 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.123047 0.87695312 2 0.00000 1.00000000 3 1.57500 0.57500000 4 0.311111 0.68888889 5 1.29375 0.29375000 6 0.952320 0.04768000 7 1.00000 0.00000000 Integrate 504.000 * X ** 6 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.205078E-01 0.97949219 2 21.0000 20.00000000 3 -3.41250 4.41250000 4 2.17778 1.17777778 5 0.759375 0.24062500 6 1.02384 0.02384000 7 1.00000 0.00000000 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 0.00000 0.00000 0.00000 2 1.00000 0.00000 0.00000 3 0.00000 1.00000 0.00000 4 0.00000 0.00000 1.00000 Rule 3 for reference tetrahedron with volume = 0.166667 X Y Z W 1 0.00000 0.00000 0.00000 -0.500000E-01 2 0.00000 0.00000 1.00000 -0.500000E-01 3 0.00000 1.00000 0.00000 -0.500000E-01 4 1.00000 0.00000 0.00000 -0.500000E-01 5 0.500000 0.500000 0.00000 0.200000 6 0.500000 0.00000 0.500000 0.200000 7 0.500000 0.00000 0.00000 0.200000 8 0.00000 0.500000 0.500000 0.200000 9 0.00000 0.500000 0.00000 0.200000 10 0.00000 0.00000 0.500000 0.200000 The physical tetrahedron: 1 4.00000 5.00000 1.00000 2 6.00000 5.00000 1.00000 3 4.00000 8.00000 1.00000 4 4.00000 5.00000 5.00000 Rule 3 for physical tetrahedron with volume = 4.00000 X Y Z W 1 4.00000 5.00000 1.00000 -0.500000E-01 2 4.00000 5.00000 5.00000 -0.500000E-01 3 4.00000 8.00000 1.00000 -0.500000E-01 4 6.00000 5.00000 1.00000 -0.500000E-01 5 5.00000 6.50000 1.00000 0.200000 6 5.00000 5.00000 3.00000 0.200000 7 5.00000 5.00000 1.00000 0.200000 8 4.00000 6.50000 3.00000 0.200000 9 4.00000 6.50000 1.00000 0.200000 10 4.00000 5.00000 3.00000 0.200000 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 0.0250 0.0000 0.0000 0.0000 1.0000 2 12 0.0000 0.0000 0.0000 0.3333 0.6667 3 4 0.2250 0.3333 0.3333 0.3333 0.0000 The full rule: Order = 20 O Weight X Y Z 1 0.0250 0.0000 0.0000 0.0000 2 0.0250 0.0000 0.0000 1.0000 3 0.0250 0.0000 1.0000 0.0000 4 0.0250 1.0000 0.0000 0.0000 5 0.0000 0.0000 0.0000 0.3333 6 0.0000 0.0000 0.0000 0.6667 7 0.0000 0.0000 0.3333 0.0000 8 0.0000 0.0000 0.3333 0.6667 9 0.0000 0.0000 0.6667 0.0000 10 0.0000 0.0000 0.6667 0.3333 11 0.0000 0.3333 0.0000 0.0000 12 0.0000 0.3333 0.0000 0.6667 13 0.0000 0.3333 0.6667 0.0000 14 0.0000 0.6667 0.0000 0.0000 15 0.0000 0.6667 0.0000 0.3333 16 0.0000 0.6667 0.3333 0.0000 17 0.2250 0.3333 0.3333 0.3333 18 0.2250 0.3333 0.3333 0.0000 19 0.2250 0.3333 0.0000 0.3333 20 0.2250 0.0000 0.3333 0.3333 TEST07 TETRAHEDRON_NCC_RULE returns the points and weights of an NCC rule for the tetrahedron. In this test, we write each rule to a file. Wrote rule 1 to "ncc0_w.txt" and "ncc0_x.txt". Wrote rule 2 to "ncc1_w.txt" and "ncc1_x.txt". Wrote rule 3 to "ncc2_w.txt" and "ncc2_x.txt". Wrote rule 4 to "ncc3_w.txt" and "ncc3_x.txt". Wrote rule 5 to "ncc4_w.txt" and "ncc4_x.txt". Wrote rule 6 to "ncc5_w.txt" and "ncc5_x.txt". Wrote rule 7 to "ncc6_w.txt" and "ncc6_x.txt". TETRAHEDRON_NCC_RULE_TEST(): Normal end of execution. 09 April 2023 7:03:25.128 AM