tetrahedron_nco_rule_test 18-Jun-2014 15:52:58 NCO_TETRAHEDRON_TEST: MATLAB version Test the NCO_TETRAHEDRON 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 1.000000 2 1.000000 3 1.000000 4 1.000000 5 1.000000 6 1.000000 7 1.000000 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 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 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 6.000000 * 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 0.700000 0.300000 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 0.440000 0.560000 3 1.027778 0.027778 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 0.266000 0.734000 3 0.972222 0.027778 4 0.925656 0.074344 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 0.156800 0.843200 3 0.831790 0.168210 4 0.792170 0.207830 5 1.010742 0.010742 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 0.090048 0.909952 3 0.654630 0.345370 4 0.638948 0.361052 5 1.015906 0.015906 6 0.983727 0.016273 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 1.200000 0.200000 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 0.960000 0.040000 3 0.972222 0.027778 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 0.672000 0.328000 3 1.101852 0.101852 4 1.099125 0.099125 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 0.448000 0.552000 3 1.206276 0.206276 4 1.148133 0.148133 5 0.982096 0.017904 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 0.290304 0.709696 3 1.186111 0.186111 4 1.098614 0.098614 5 1.000415 0.000415 6 1.032546 0.032546 7 1.000000 0.000000 Integrate 60.000000 * X^0 * Y^2 * Z^0 Rule QUAD ERROR 1 0.625000 0.375000 2 0.700000 0.300000 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 0.960000 0.040000 3 0.972222 0.027778 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 0.840000 0.160000 3 0.712963 0.287037 4 0.844023 0.155977 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 0.627200 0.372800 3 0.684156 0.315844 4 0.846869 0.153131 5 1.007161 0.007161 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 0.443520 0.556480 3 0.799383 0.200617 4 0.906587 0.093413 5 0.907288 0.092712 6 0.936798 0.063202 7 1.000000 0.000000 Integrate 120.000000 * X^0 * Y^3 * Z^0 Rule QUAD ERROR 1 0.312500 0.687500 2 0.440000 0.560000 3 1.027778 0.027778 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 0.672000 0.328000 3 1.101852 0.101852 4 1.099125 0.099125 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 0.627200 0.372800 3 0.684156 0.315844 4 0.846869 0.153131 5 1.007161 0.007161 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 0.483840 0.516160 3 0.410494 0.589506 4 0.700422 0.299578 5 1.121338 0.121338 6 1.070162 0.070162 7 1.000000 0.000000 Integrate 210.000000 * X^0 * Y^4 * Z^0 Rule QUAD ERROR 1 0.136719 0.863281 2 0.266000 0.734000 3 0.972222 0.027778 4 0.925656 0.074344 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 0.448000 0.552000 3 1.206276 0.206276 4 1.148133 0.148133 5 0.982096 0.017904 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 0.443520 0.556480 3 0.799383 0.200617 4 0.906587 0.093413 5 0.907288 0.092712 6 0.936798 0.063202 7 1.000000 0.000000 Integrate 336.000000 * X^0 * Y^5 * Z^0 Rule QUAD ERROR 1 0.054688 0.945312 2 0.156800 0.843200 3 0.831790 0.168210 4 0.792170 0.207830 5 1.010742 0.010742 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 0.290304 0.709696 3 1.186111 0.186111 4 1.098614 0.098614 5 1.000415 0.000415 6 1.032546 0.032546 7 1.000000 0.000000 Integrate 504.000000 * X^0 * Y^6 * Z^0 Rule QUAD ERROR 1 0.020508 0.979492 2 0.090048 0.909952 3 0.654630 0.345370 4 0.638948 0.361052 5 1.015906 0.015906 6 0.983727 0.016273 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 1.200000 0.200000 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 0.960000 0.040000 3 0.972222 0.027778 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 0.672000 0.328000 3 1.101852 0.101852 4 1.099125 0.099125 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 0.448000 0.552000 3 1.206276 0.206276 4 1.148133 0.148133 5 0.982096 0.017904 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 0.290304 0.709696 3 1.186111 0.186111 4 1.098614 0.098614 5 1.000415 0.000415 6 1.032546 0.032546 7 1.000000 0.000000 Integrate 120.000000 * X^1 * Y^1 * Z^0 Rule QUAD ERROR 1 1.250000 0.250000 2 1.200000 0.200000 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 1.680000 0.680000 3 1.055556 0.055556 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 1.512000 0.512000 3 1.037037 0.037037 4 1.007289 0.007289 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 1.164800 0.164800 3 1.310700 0.310700 4 1.253367 0.253367 5 1.028646 0.028646 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 0.846720 0.153280 3 1.663580 0.663580 4 1.513477 0.513477 5 1.011108 0.011108 6 0.981837 0.018163 7 1.000000 0.000000 Integrate 360.000000 * X^1 * Y^2 * Z^0 Rule QUAD ERROR 1 0.937500 0.062500 2 0.960000 0.040000 3 0.972222 0.027778 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 1.512000 0.512000 3 1.037037 0.037037 4 1.007289 0.007289 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 1.478400 0.478400 3 0.799383 0.200617 4 0.835485 0.164515 5 0.978516 0.021484 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 1.209600 0.209600 3 0.864198 0.135802 4 0.947105 0.052895 5 1.035645 0.035645 6 1.021160 0.021160 7 1.000000 0.000000 Integrate 840.000000 * X^1 * Y^3 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672000 0.328000 3 1.101852 0.101852 4 1.099125 0.099125 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 1.164800 0.164800 3 1.310700 0.310700 4 1.253367 0.253367 5 1.028646 0.028646 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 1.209600 0.209600 3 0.864198 0.135802 4 0.947105 0.052895 5 1.035645 0.035645 6 1.021160 0.021160 7 1.000000 0.000000 Integrate 1680.000000 * X^1 * Y^4 * Z^0 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448000 0.552000 3 1.206276 0.206276 4 1.148133 0.148133 5 0.982096 0.017904 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 0.846720 0.153280 3 1.663580 0.663580 4 1.513477 0.513477 5 1.011108 0.011108 6 0.981837 0.018163 7 1.000000 0.000000 Integrate 3024.000000 * X^1 * Y^5 * Z^0 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.186111 0.186111 4 1.098614 0.098614 5 1.000415 0.000415 6 1.032546 0.032546 7 1.000000 0.000000 Integrate 60.000000 * X^2 * Y^0 * Z^0 Rule QUAD ERROR 1 0.625000 0.375000 2 0.700000 0.300000 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 0.960000 0.040000 3 0.972222 0.027778 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 0.840000 0.160000 3 0.712963 0.287037 4 0.844023 0.155977 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 0.627200 0.372800 3 0.684156 0.315844 4 0.846869 0.153131 5 1.007161 0.007161 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 0.443520 0.556480 3 0.799383 0.200617 4 0.906587 0.093413 5 0.907288 0.092712 6 0.936798 0.063202 7 1.000000 0.000000 Integrate 360.000000 * X^2 * Y^1 * Z^0 Rule QUAD ERROR 1 0.937500 0.062500 2 0.960000 0.040000 3 0.972222 0.027778 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 1.512000 0.512000 3 1.037037 0.037037 4 1.007289 0.007289 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 1.478400 0.478400 3 0.799383 0.200617 4 0.835485 0.164515 5 0.978516 0.021484 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 1.209600 0.209600 3 0.864198 0.135802 4 0.947105 0.052895 5 1.035645 0.035645 6 1.021160 0.021160 7 1.000000 0.000000 Integrate 1260.000000 * X^2 * Y^2 * Z^0 Rule QUAD ERROR 1 0.820312 0.179688 2 0.840000 0.160000 3 0.712963 0.287037 4 0.844023 0.155977 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 1.478400 0.478400 3 0.799383 0.200617 4 0.835485 0.164515 5 0.978516 0.021484 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 1.572480 0.572480 3 0.550926 0.449074 4 0.560659 0.439341 5 0.814087 0.185913 6 0.933521 0.066479 7 1.000000 0.000000 Integrate 3360.000000 * X^2 * Y^3 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.627200 0.372800 3 0.684156 0.315844 4 0.846869 0.153131 5 1.007161 0.007161 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 1.209600 0.209600 3 0.864198 0.135802 4 0.947105 0.052895 5 1.035645 0.035645 6 1.021160 0.021160 7 1.000000 0.000000 Integrate 7560.000000 * X^2 * Y^4 * Z^0 Rule QUAD ERROR 1 0.307617 0.692383 2 0.443520 0.556480 3 0.799383 0.200617 4 0.906587 0.093413 5 0.907288 0.092712 6 0.936798 0.063202 7 1.000000 0.000000 Integrate 120.000000 * X^3 * Y^0 * Z^0 Rule QUAD ERROR 1 0.312500 0.687500 2 0.440000 0.560000 3 1.027778 0.027778 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 0.672000 0.328000 3 1.101852 0.101852 4 1.099125 0.099125 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 0.627200 0.372800 3 0.684156 0.315844 4 0.846869 0.153131 5 1.007161 0.007161 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 0.483840 0.516160 3 0.410494 0.589506 4 0.700422 0.299578 5 1.121338 0.121338 6 1.070162 0.070162 7 1.000000 0.000000 Integrate 840.000000 * X^3 * Y^1 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.672000 0.328000 3 1.101852 0.101852 4 1.099125 0.099125 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 1.164800 0.164800 3 1.310700 0.310700 4 1.253367 0.253367 5 1.028646 0.028646 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 1.209600 0.209600 3 0.864198 0.135802 4 0.947105 0.052895 5 1.035645 0.035645 6 1.021160 0.021160 7 1.000000 0.000000 Integrate 3360.000000 * X^3 * Y^2 * Z^0 Rule QUAD ERROR 1 0.546875 0.453125 2 0.627200 0.372800 3 0.684156 0.315844 4 0.846869 0.153131 5 1.007161 0.007161 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 1.209600 0.209600 3 0.864198 0.135802 4 0.947105 0.052895 5 1.035645 0.035645 6 1.021160 0.021160 7 1.000000 0.000000 Integrate 10080.000000 * X^3 * Y^3 * Z^0 Rule QUAD ERROR 1 0.410156 0.589844 2 0.483840 0.516160 3 0.410494 0.589506 4 0.700422 0.299578 5 1.121338 0.121338 6 1.070162 0.070162 7 1.000000 0.000000 Integrate 210.000000 * X^4 * Y^0 * Z^0 Rule QUAD ERROR 1 0.136719 0.863281 2 0.266000 0.734000 3 0.972222 0.027778 4 0.925656 0.074344 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 0.448000 0.552000 3 1.206276 0.206276 4 1.148133 0.148133 5 0.982096 0.017904 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 0.443520 0.556480 3 0.799383 0.200617 4 0.906587 0.093413 5 0.907288 0.092712 6 0.936798 0.063202 7 1.000000 0.000000 Integrate 1680.000000 * X^4 * Y^1 * Z^0 Rule QUAD ERROR 1 0.273438 0.726562 2 0.448000 0.552000 3 1.206276 0.206276 4 1.148133 0.148133 5 0.982096 0.017904 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 0.846720 0.153280 3 1.663580 0.663580 4 1.513477 0.513477 5 1.011108 0.011108 6 0.981837 0.018163 7 1.000000 0.000000 Integrate 7560.000000 * X^4 * Y^2 * Z^0 Rule QUAD ERROR 1 0.307617 0.692383 2 0.443520 0.556480 3 0.799383 0.200617 4 0.906587 0.093413 5 0.907288 0.092712 6 0.936798 0.063202 7 1.000000 0.000000 Integrate 336.000000 * X^5 * Y^0 * Z^0 Rule QUAD ERROR 1 0.054688 0.945312 2 0.156800 0.843200 3 0.831790 0.168210 4 0.792170 0.207830 5 1.010742 0.010742 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 0.290304 0.709696 3 1.186111 0.186111 4 1.098614 0.098614 5 1.000415 0.000415 6 1.032546 0.032546 7 1.000000 0.000000 Integrate 3024.000000 * X^5 * Y^1 * Z^0 Rule QUAD ERROR 1 0.123047 0.876953 2 0.290304 0.709696 3 1.186111 0.186111 4 1.098614 0.098614 5 1.000415 0.000415 6 1.032546 0.032546 7 1.000000 0.000000 Integrate 504.000000 * X^6 * Y^0 * Z^0 Rule QUAD ERROR 1 0.020508 0.979492 2 0.090048 0.909952 3 0.654630 0.345370 4 0.638948 0.361052 5 1.015906 0.015906 6 0.983727 0.016273 7 1.000000 0.000000 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 0.166667 0.166667 0.166667 0.550000 2 0.166667 0.166667 0.500000 0.550000 3 0.166667 0.500000 0.166667 0.550000 4 0.500000 0.166667 0.166667 0.550000 5 0.333333 0.333333 0.166667 -0.200000 6 0.333333 0.166667 0.333333 -0.200000 7 0.333333 0.166667 0.166667 -0.200000 8 0.166667 0.333333 0.333333 -0.200000 9 0.166667 0.333333 0.166667 -0.200000 10 0.166667 0.166667 0.333333 -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 4.333333 5.500000 1.666667 0.550000 2 4.333333 5.500000 3.000000 0.550000 3 4.333333 6.500000 1.666667 0.550000 4 5.000000 5.500000 1.666667 0.550000 5 4.666667 6.000000 1.666667 -0.200000 6 4.666667 5.500000 2.333333 -0.200000 7 4.666667 5.500000 1.666667 -0.200000 8 4.333333 6.000000 2.333333 -0.200000 9 4.333333 6.000000 1.666667 -0.200000 10 4.333333 5.500000 2.333333 -0.200000 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 NCO_TETRAHEDRON_TEST: Normal end of execution. 18-Jun-2014 15:52:58 diary off