23 March 2023 8:15:01.410 AM TRIANGLE_WANDZURA_RULE_TEST FORTRAN90 version Test the TRIANGLE_WANDZURA_RULE library. TEST01 WANDZURA_RULE_NUM returns the number of rules; WANDZURA_DEGREE returns the degree of a rule; WANDZURA_ORDER_NUM returns the order of a rule. Number of available rules = 6 Rule Degree Order 1 5 7 2 10 25 3 15 54 4 20 85 5 25 126 6 30 175 TEST02 WANDZURA_RULE returns the points and weights of a Wandzura rule for the triangle. In this test, we simply check that the weights sum to 1. Number of available rules = 6 Rule Sum of weights 1 0.4999999999999999 2 0.5000000000000002 3 0.4999999999999998 4 0.5000000000000000 5 0.5000000000000003 6 0.4999999999999998 TEST03 WANDZURA_RULE returns the points and weights of a Wandzura rule for the triangle. In this test, we simply check that, for each quadrature point, the barycentric coordinates sum to 1. Rule Suborder Sum of coordinates 1 3 0.9999999999999900 1.000000000000010 1.000000000000010 2 7 0.9999999999999900 0.9999999999999900 1.000000000000010 0.9999999999999899 0.9999999999999999 0.9999999999999900 1.000000000000000 3 12 1.000000000000000 1.000000000000000 1.000000000000010 0.9999999999999899 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 4 19 0.9999999999999900 1.000000000000010 0.9999999999999900 1.000000000000010 1.000000000000010 1.000000000000010 0.9999999999999999 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000000 0.9999999999999900 1.000000000000000 5 26 0.9999999999999900 0.9999999999999900 0.9999999999999900 0.9999999999999900 0.9999999999999999 1.000000000000000 0.9999999999999900 1.000000000000010 1.000000000000010 0.9999999999999899 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000000 1.000000000000000 6 36 0.9999999999999900 1.000000000000010 1.000000000000000 0.9999999999999900 1.000000000000010 1.000000000000010 0.9999999999999900 1.000000000000000 1.000000000000010 1.000000000000010 1.000000000000000 1.000000000000000 1.000000000000010 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000010 0.9999999999999900 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 0.9999999999999900 1.000000000000000 TEST04 WANDZURA_RULE returns the points and weights of a Wandzura rule for the unit triangle. This routine uses those rules to estimate the integral of monomomials in the unit triangle. Integrate 2.00000 * X ** 0 * Y ** 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 Integrate 6.00000 * X ** 0 * Y ** 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 Integrate 12.0000 * X ** 0 * Y ** 2 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 Integrate 20.0000 * X ** 0 * Y ** 3 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 Integrate 30.0000 * X ** 0 * Y ** 4 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 Integrate 42.0000 * X ** 0 * Y ** 5 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 Integrate 56.0000 * X ** 0 * Y ** 6 Rule QUAD ERROR 1 0.995414 0.00458554 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 Integrate 72.0000 * X ** 0 * Y ** 7 Rule QUAD ERROR 1 0.981708 0.01829176 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 Integrate 90.0000 * X ** 0 * Y ** 8 Rule QUAD ERROR 1 0.956602 0.04339756 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 Integrate 110.000 * X ** 0 * Y ** 9 Rule QUAD ERROR 1 0.920084 0.07991597 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 Integrate 132.000 * X ** 0 * Y ** 10 Rule QUAD ERROR 1 0.873671 0.12632881 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 Integrate 6.00000 * X ** 1 * Y ** 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 Integrate 24.0000 * X ** 1 * Y ** 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 Integrate 60.0000 * X ** 1 * Y ** 2 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 Integrate 120.000 * X ** 1 * Y ** 3 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 Integrate 210.000 * X ** 1 * Y ** 4 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 Integrate 336.000 * X ** 1 * Y ** 5 Rule QUAD ERROR 1 1.01376 0.01375661 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 Integrate 504.000 * X ** 1 * Y ** 6 Rule QUAD ERROR 1 1.04339 0.04338624 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 Integrate 720.000 * X ** 1 * Y ** 7 Rule QUAD ERROR 1 1.08213 0.08213142 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 Integrate 990.000 * X ** 1 * Y ** 8 Rule QUAD ERROR 1 1.12094 0.12093530 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 Integrate 1320.00 * X ** 1 * Y ** 9 Rule QUAD ERROR 1 1.15215 0.15214823 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 Integrate 12.0000 * X ** 2 * Y ** 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 Integrate 60.0000 * X ** 2 * Y ** 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 Integrate 180.000 * X ** 2 * Y ** 2 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 Integrate 420.000 * X ** 2 * Y ** 3 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 Integrate 840.000 * X ** 2 * Y ** 4 Rule QUAD ERROR 1 0.962963 0.03703704 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 Integrate 1512.00 * X ** 2 * Y ** 5 Rule QUAD ERROR 1 0.909751 0.09024943 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 Integrate 2520.00 * X ** 2 * Y ** 6 Rule QUAD ERROR 1 0.866501 0.13349890 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 Integrate 3960.00 * X ** 2 * Y ** 7 Rule QUAD ERROR 1 0.846090 0.15390976 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 Integrate 5940.00 * X ** 2 * Y ** 8 Rule QUAD ERROR 1 0.849523 0.15047725 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 Integrate 20.0000 * X ** 3 * Y ** 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 Integrate 120.000 * X ** 3 * Y ** 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 Integrate 420.000 * X ** 3 * Y ** 2 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 Integrate 1120.00 * X ** 3 * Y ** 3 Rule QUAD ERROR 1 1.05115 0.05114638 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 Integrate 2520.00 * X ** 3 * Y ** 4 Rule QUAD ERROR 1 1.05367 0.05366591 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 Integrate 5040.00 * X ** 3 * Y ** 5 Rule QUAD ERROR 1 0.992477 0.00752259 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 Integrate 9240.00 * X ** 3 * Y ** 6 Rule QUAD ERROR 1 0.896388 0.10361195 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 Integrate 15840.0 * X ** 3 * Y ** 7 Rule QUAD ERROR 1 0.797080 0.20291962 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 Integrate 30.0000 * X ** 4 * Y ** 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 Integrate 210.000 * X ** 4 * Y ** 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 Integrate 840.000 * X ** 4 * Y ** 2 Rule QUAD ERROR 1 0.962963 0.03703704 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 Integrate 2520.00 * X ** 4 * Y ** 3 Rule QUAD ERROR 1 1.05367 0.05366591 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 Integrate 6300.00 * X ** 4 * Y ** 4 Rule QUAD ERROR 1 1.13775 0.13774610 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 Integrate 13860.0 * X ** 4 * Y ** 5 Rule QUAD ERROR 1 1.14249 0.14249035 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 Integrate 27720.0 * X ** 4 * Y ** 6 Rule QUAD ERROR 1 1.06917 0.06917320 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 Integrate 42.0000 * X ** 5 * Y ** 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 Integrate 336.000 * X ** 5 * Y ** 1 Rule QUAD ERROR 1 1.01376 0.01375661 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 Integrate 1512.00 * X ** 5 * Y ** 2 Rule QUAD ERROR 1 0.909751 0.09024943 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 Integrate 5040.00 * X ** 5 * Y ** 3 Rule QUAD ERROR 1 0.992477 0.00752259 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 Integrate 13860.0 * X ** 5 * Y ** 4 Rule QUAD ERROR 1 1.14249 0.14249035 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 Integrate 33264.0 * X ** 5 * Y ** 5 Rule QUAD ERROR 1 1.23958 0.23957884 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 Integrate 56.0000 * X ** 6 * Y ** 0 Rule QUAD ERROR 1 0.995414 0.00458554 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 Integrate 504.000 * X ** 6 * Y ** 1 Rule QUAD ERROR 1 1.04339 0.04338624 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 Integrate 2520.00 * X ** 6 * Y ** 2 Rule QUAD ERROR 1 0.866501 0.13349890 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 Integrate 9240.00 * X ** 6 * Y ** 3 Rule QUAD ERROR 1 0.896388 0.10361195 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 Integrate 27720.0 * X ** 6 * Y ** 4 Rule QUAD ERROR 1 1.06917 0.06917320 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 Integrate 72.0000 * X ** 7 * Y ** 0 Rule QUAD ERROR 1 0.981708 0.01829176 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 Integrate 720.000 * X ** 7 * Y ** 1 Rule QUAD ERROR 1 1.08213 0.08213142 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 Integrate 3960.00 * X ** 7 * Y ** 2 Rule QUAD ERROR 1 0.846090 0.15390976 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 Integrate 15840.0 * X ** 7 * Y ** 3 Rule QUAD ERROR 1 0.797080 0.20291962 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 Integrate 90.0000 * X ** 8 * Y ** 0 Rule QUAD ERROR 1 0.956602 0.04339756 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 Integrate 990.000 * X ** 8 * Y ** 1 Rule QUAD ERROR 1 1.12094 0.12093530 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 Integrate 5940.00 * X ** 8 * Y ** 2 Rule QUAD ERROR 1 0.849523 0.15047725 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 Integrate 110.000 * X ** 9 * Y ** 0 Rule QUAD ERROR 1 0.920084 0.07991597 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 Integrate 1320.00 * X ** 9 * Y ** 1 Rule QUAD ERROR 1 1.15215 0.15214823 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 Integrate 132.000 * X ** 10 * Y ** 0 Rule QUAD ERROR 1 0.873671 0.12632881 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 TEST05 REFERENCE_TO_PHYSICAL_T3 transforms a rule on the unit (reference) triangle to a rule on an arbitrary (physical) triangle. The reference triangle: 1 0.00000 0.00000 2 1.00000 0.00000 3 0.00000 1.00000 Rule 2 for reference triangle with area = 0.500000 X Y W 1 0.333333 0.333333 0.417617E-01 2 0.426913E-02 0.497865 0.361493E-02 3 0.497865 0.497865 0.361493E-02 4 0.497865 0.426913E-02 0.361493E-02 5 0.143975 0.428012 0.372461E-01 6 0.428012 0.428012 0.372461E-01 7 0.428012 0.143975 0.372461E-01 8 0.630487 0.184756 0.393232E-01 9 0.184756 0.184756 0.393232E-01 10 0.184756 0.630487 0.393232E-01 11 0.959038 0.204812E-01 0.346416E-02 12 0.204812E-01 0.204812E-01 0.346416E-02 13 0.204812E-01 0.959038 0.346416E-02 14 0.350030E-01 0.136574 0.147592E-01 15 0.136574 0.828423 0.147592E-01 16 0.828423 0.350030E-01 0.147592E-01 17 0.136574 0.350030E-01 0.147592E-01 18 0.828423 0.136574 0.147592E-01 19 0.350030E-01 0.828423 0.147592E-01 20 0.375491E-01 0.332744 0.197897E-01 21 0.332744 0.629707 0.197897E-01 22 0.629707 0.375491E-01 0.197897E-01 23 0.332744 0.375491E-01 0.197897E-01 24 0.629707 0.332744 0.197897E-01 25 0.375491E-01 0.629707 0.197897E-01 The physical triangle: 1 1.00000 2.00000 2 1.00000 1.00000 3 3.00000 2.00000 Rule 2 for physical triangle with area = 1.00000 X Y W 1 1.66667 1.66667 0.417617E-01 2 1.99573 1.99573 0.361493E-02 3 1.99573 1.50213 0.361493E-02 4 1.00854 1.50213 0.361493E-02 5 1.85602 1.85602 0.372461E-01 6 1.85602 1.57199 0.372461E-01 7 1.28795 1.57199 0.372461E-01 8 1.36951 1.36951 0.393232E-01 9 1.36951 1.81524 0.393232E-01 10 2.26097 1.81524 0.393232E-01 11 1.04096 1.04096 0.346416E-02 12 1.04096 1.97952 0.346416E-02 13 2.91808 1.97952 0.346416E-02 14 1.27315 1.96500 0.147592E-01 15 2.65685 1.86343 0.147592E-01 16 1.07001 1.17158 0.147592E-01 17 1.07001 1.86343 0.147592E-01 18 1.27315 1.17158 0.147592E-01 19 2.65685 1.96500 0.147592E-01 20 1.66549 1.96245 0.197897E-01 21 2.25941 1.66726 0.197897E-01 22 1.07510 1.37029 0.197897E-01 23 1.07510 1.66726 0.197897E-01 24 1.66549 1.37029 0.197897E-01 25 2.25941 1.96245 0.197897E-01 TRIANGLE_WANDZURA_RULEA_TEST Normal end of execution. 23 March 2023 8:15:01.413 AM