17 June 2014 3:03:35.643 PM TETRAHEDRON_NCO_RULE_PRB: FORTRAN90 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 1.000000000000000 2 1.000000000000000 3 1.000000000000000 4 1.000000000000000 5 1.000000000000000 6 1.000000000000000 7 0.9999999999999942 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 1.000000000000000 2 1 1.000000000000000 3 2 1.000000000000000 0.9999999999999999 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 0.9999999999999999 1.000000000000000 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 6.00000 * 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 0.700000 0.30000000 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 0.440000 0.56000000 3 1.02778 0.02777778 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 0.266000 0.73400000 3 0.972222 0.02777778 4 0.925656 0.07434402 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 0.156800 0.84320000 3 0.831790 0.16820988 4 0.792170 0.20783007 5 1.01074 0.01074219 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 0.900480E-01 0.90995200 3 0.654630 0.34537037 4 0.638948 0.36105194 5 1.01591 0.01590576 6 0.983727 0.01627293 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 1.20000 0.20000000 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 0.960000 0.04000000 3 0.972222 0.02777778 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 0.672000 0.32800000 3 1.10185 0.10185185 4 1.09913 0.09912536 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 0.448000 0.55200000 3 1.20628 0.20627572 4 1.14813 0.14813272 5 0.982096 0.01790365 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 0.87695313 2 0.290304 0.70969600 3 1.18611 0.18611111 4 1.09861 0.09861367 5 1.00042 0.00041504 6 1.03255 0.03254585 7 1.00000 0.00000000 Integrate 60.0000 * X ** 0 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.625000 0.37500000 2 0.700000 0.30000000 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 0.960000 0.04000000 3 0.972222 0.02777778 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 0.820313 0.17968750 2 0.840000 0.16000000 3 0.712963 0.28703704 4 0.844023 0.15597668 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 0.627200 0.37280000 3 0.684156 0.31584362 4 0.846869 0.15313064 5 1.00716 0.00716146 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 0.443520 0.55648000 3 0.799383 0.20061728 4 0.906587 0.09341346 5 0.907288 0.09271240 6 0.936798 0.06320175 7 1.00000 0.00000000 Integrate 120.000 * X ** 0 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.312500 0.68750000 2 0.440000 0.56000000 3 1.02778 0.02777778 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 0.672000 0.32800000 3 1.10185 0.10185185 4 1.09913 0.09912536 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 0.627200 0.37280000 3 0.684156 0.31584362 4 0.846869 0.15313064 5 1.00716 0.00716146 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 0.483840 0.51616000 3 0.410494 0.58950617 4 0.700422 0.29957756 5 1.12134 0.12133789 6 1.07016 0.07016207 7 1.00000 0.00000000 Integrate 210.000 * X ** 0 * Y ** 4 * Z ** 0 Rule QUAD ERROR 1 0.136719 0.86328125 2 0.266000 0.73400000 3 0.972222 0.02777778 4 0.925656 0.07434402 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 0.448000 0.55200000 3 1.20628 0.20627572 4 1.14813 0.14813272 5 0.982096 0.01790365 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 0.443520 0.55648000 3 0.799383 0.20061728 4 0.906587 0.09341346 5 0.907288 0.09271240 6 0.936798 0.06320175 7 1.00000 0.00000000 Integrate 336.000 * X ** 0 * Y ** 5 * Z ** 0 Rule QUAD ERROR 1 0.546875E-01 0.94531250 2 0.156800 0.84320000 3 0.831790 0.16820988 4 0.792170 0.20783007 5 1.01074 0.01074219 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 0.87695313 2 0.290304 0.70969600 3 1.18611 0.18611111 4 1.09861 0.09861367 5 1.00042 0.00041504 6 1.03255 0.03254585 7 1.00000 0.00000000 Integrate 504.000 * X ** 0 * Y ** 6 * Z ** 0 Rule QUAD ERROR 1 0.205078E-01 0.97949219 2 0.900480E-01 0.90995200 3 0.654630 0.34537037 4 0.638948 0.36105194 5 1.01591 0.01590576 6 0.983727 0.01627293 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 1.20000 0.20000000 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 0.960000 0.04000000 3 0.972222 0.02777778 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 0.672000 0.32800000 3 1.10185 0.10185185 4 1.09913 0.09912536 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 0.448000 0.55200000 3 1.20628 0.20627572 4 1.14813 0.14813272 5 0.982096 0.01790365 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 0.87695313 2 0.290304 0.70969600 3 1.18611 0.18611111 4 1.09861 0.09861367 5 1.00042 0.00041504 6 1.03255 0.03254585 7 1.00000 0.00000000 Integrate 120.000 * X ** 1 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 1.25000 0.25000000 2 1.20000 0.20000000 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 1.68000 0.68000000 3 1.05556 0.05555556 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 1.64063 0.64062500 2 1.51200 0.51200000 3 1.03704 0.03703704 4 1.00729 0.00728863 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 1.16480 0.16480000 3 1.31070 0.31069959 4 1.25337 0.25336665 5 1.02865 0.02864583 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 0.38476563 2 0.846720 0.15328000 3 1.66358 0.66358025 4 1.51348 0.51347653 5 1.01111 0.01110840 6 0.981837 0.01816288 7 1.00000 0.00000000 Integrate 360.000 * X ** 1 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.960000 0.04000000 3 0.972222 0.02777778 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 1.64063 0.64062500 2 1.51200 0.51200000 3 1.03704 0.03703704 4 1.00729 0.00728863 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 1.64063 0.64062500 2 1.47840 0.47840000 3 0.799383 0.20061728 4 0.835485 0.16451479 5 0.978516 0.02148438 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 1.20960 0.20960000 3 0.864198 0.13580247 4 0.947105 0.05289463 5 1.03564 0.03564453 6 1.02116 0.02116039 7 1.00000 0.00000000 Integrate 840.000 * X ** 1 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.672000 0.32800000 3 1.10185 0.10185185 4 1.09913 0.09912536 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 1.16480 0.16480000 3 1.31070 0.31069959 4 1.25337 0.25336665 5 1.02865 0.02864583 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 1.20960 0.20960000 3 0.864198 0.13580247 4 0.947105 0.05289463 5 1.03564 0.03564453 6 1.02116 0.02116039 7 1.00000 0.00000000 Integrate 1680.00 * X ** 1 * Y ** 4 * Z ** 0 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.448000 0.55200000 3 1.20628 0.20627572 4 1.14813 0.14813272 5 0.982096 0.01790365 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 0.38476563 2 0.846720 0.15328000 3 1.66358 0.66358025 4 1.51348 0.51347653 5 1.01111 0.01110840 6 0.981837 0.01816288 7 1.00000 0.00000000 Integrate 3024.00 * X ** 1 * Y ** 5 * Z ** 0 Rule QUAD ERROR 1 0.123047 0.87695313 2 0.290304 0.70969600 3 1.18611 0.18611111 4 1.09861 0.09861367 5 1.00042 0.00041504 6 1.03255 0.03254585 7 1.00000 0.00000000 Integrate 60.0000 * X ** 2 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.625000 0.37500000 2 0.700000 0.30000000 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 0.960000 0.04000000 3 0.972222 0.02777778 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 0.820313 0.17968750 2 0.840000 0.16000000 3 0.712963 0.28703704 4 0.844023 0.15597668 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 0.627200 0.37280000 3 0.684156 0.31584362 4 0.846869 0.15313064 5 1.00716 0.00716146 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 0.443520 0.55648000 3 0.799383 0.20061728 4 0.906587 0.09341346 5 0.907288 0.09271240 6 0.936798 0.06320175 7 1.00000 0.00000000 Integrate 360.000 * X ** 2 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.937500 0.06250000 2 0.960000 0.04000000 3 0.972222 0.02777778 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 1.64063 0.64062500 2 1.51200 0.51200000 3 1.03704 0.03703704 4 1.00729 0.00728863 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 1.64063 0.64062500 2 1.47840 0.47840000 3 0.799383 0.20061728 4 0.835485 0.16451479 5 0.978516 0.02148438 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 1.20960 0.20960000 3 0.864198 0.13580247 4 0.947105 0.05289463 5 1.03564 0.03564453 6 1.02116 0.02116039 7 1.00000 0.00000000 Integrate 1260.00 * X ** 2 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.820313 0.17968750 2 0.840000 0.16000000 3 0.712963 0.28703704 4 0.844023 0.15597668 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 1.64063 0.64062500 2 1.47840 0.47840000 3 0.799383 0.20061728 4 0.835485 0.16451479 5 0.978516 0.02148438 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 0.84570313 2 1.57248 0.57248000 3 0.550926 0.44907407 4 0.560659 0.43934075 5 0.814087 0.18591309 6 0.933521 0.06647869 7 1.00000 0.00000000 Integrate 3360.00 * X ** 2 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.627200 0.37280000 3 0.684156 0.31584362 4 0.846869 0.15313064 5 1.00716 0.00716146 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 1.20960 0.20960000 3 0.864198 0.13580247 4 0.947105 0.05289463 5 1.03564 0.03564453 6 1.02116 0.02116039 7 1.00000 0.00000000 Integrate 7560.00 * X ** 2 * Y ** 4 * Z ** 0 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.443520 0.55648000 3 0.799383 0.20061728 4 0.906587 0.09341346 5 0.907288 0.09271240 6 0.936798 0.06320175 7 1.00000 0.00000000 Integrate 120.000 * X ** 3 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.312500 0.68750000 2 0.440000 0.56000000 3 1.02778 0.02777778 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 0.672000 0.32800000 3 1.10185 0.10185185 4 1.09913 0.09912536 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 0.627200 0.37280000 3 0.684156 0.31584362 4 0.846869 0.15313064 5 1.00716 0.00716146 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 0.483840 0.51616000 3 0.410494 0.58950617 4 0.700422 0.29957756 5 1.12134 0.12133789 6 1.07016 0.07016207 7 1.00000 0.00000000 Integrate 840.000 * X ** 3 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.672000 0.32800000 3 1.10185 0.10185185 4 1.09913 0.09912536 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 1.16480 0.16480000 3 1.31070 0.31069959 4 1.25337 0.25336665 5 1.02865 0.02864583 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 1.20960 0.20960000 3 0.864198 0.13580247 4 0.947105 0.05289463 5 1.03564 0.03564453 6 1.02116 0.02116039 7 1.00000 0.00000000 Integrate 3360.00 * X ** 3 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.546875 0.45312500 2 0.627200 0.37280000 3 0.684156 0.31584362 4 0.846869 0.15313064 5 1.00716 0.00716146 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 1.20960 0.20960000 3 0.864198 0.13580247 4 0.947105 0.05289463 5 1.03564 0.03564453 6 1.02116 0.02116039 7 1.00000 0.00000000 Integrate 10080.0 * X ** 3 * Y ** 3 * Z ** 0 Rule QUAD ERROR 1 0.410156 0.58984375 2 0.483840 0.51616000 3 0.410494 0.58950617 4 0.700422 0.29957756 5 1.12134 0.12133789 6 1.07016 0.07016207 7 1.00000 0.00000000 Integrate 210.000 * X ** 4 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.136719 0.86328125 2 0.266000 0.73400000 3 0.972222 0.02777778 4 0.925656 0.07434402 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 0.448000 0.55200000 3 1.20628 0.20627572 4 1.14813 0.14813272 5 0.982096 0.01790365 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 0.443520 0.55648000 3 0.799383 0.20061728 4 0.906587 0.09341346 5 0.907288 0.09271240 6 0.936798 0.06320175 7 1.00000 0.00000000 Integrate 1680.00 * X ** 4 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.273438 0.72656250 2 0.448000 0.55200000 3 1.20628 0.20627572 4 1.14813 0.14813272 5 0.982096 0.01790365 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 0.38476563 2 0.846720 0.15328000 3 1.66358 0.66358025 4 1.51348 0.51347653 5 1.01111 0.01110840 6 0.981837 0.01816288 7 1.00000 0.00000000 Integrate 7560.00 * X ** 4 * Y ** 2 * Z ** 0 Rule QUAD ERROR 1 0.307617 0.69238281 2 0.443520 0.55648000 3 0.799383 0.20061728 4 0.906587 0.09341346 5 0.907288 0.09271240 6 0.936798 0.06320175 7 1.00000 0.00000000 Integrate 336.000 * X ** 5 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.546875E-01 0.94531250 2 0.156800 0.84320000 3 0.831790 0.16820988 4 0.792170 0.20783007 5 1.01074 0.01074219 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 0.87695313 2 0.290304 0.70969600 3 1.18611 0.18611111 4 1.09861 0.09861367 5 1.00042 0.00041504 6 1.03255 0.03254585 7 1.00000 0.00000000 Integrate 3024.00 * X ** 5 * Y ** 1 * Z ** 0 Rule QUAD ERROR 1 0.123047 0.87695313 2 0.290304 0.70969600 3 1.18611 0.18611111 4 1.09861 0.09861367 5 1.00042 0.00041504 6 1.03255 0.03254585 7 1.00000 0.00000000 Integrate 504.000 * X ** 6 * Y ** 0 * Z ** 0 Rule QUAD ERROR 1 0.205078E-01 0.97949219 2 0.900480E-01 0.90995200 3 0.654630 0.34537037 4 0.638948 0.36105194 5 1.01591 0.01590576 6 0.983727 0.01627293 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 0.166667 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 4.00000 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 4.33333 5.50000 1.66667 0.550000 2 4.33333 5.50000 3.00000 0.550000 3 4.33333 6.50000 1.66667 0.550000 4 5.00000 5.50000 1.66667 0.550000 5 4.66667 6.00000 1.66667 -0.200000 6 4.66667 5.50000 2.33333 -0.200000 7 4.66667 5.50000 1.66667 -0.200000 8 4.33333 6.00000 2.33333 -0.200000 9 4.33333 6.00000 1.66667 -0.200000 10 4.33333 5.50000 2.33333 -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 0.1667 0.1429 0.1429 0.1429 0.5714 2 12 0.1083 0.1429 0.1429 0.2857 0.4286 3 4 -0.2417 0.2857 0.2857 0.2857 0.1429 The full rule: Order = 20 O Weight X Y Z 1 0.1667 0.1429 0.1429 0.1429 2 0.1667 0.1429 0.1429 0.5714 3 0.1667 0.1429 0.5714 0.1429 4 0.1667 0.5714 0.1429 0.1429 5 0.1083 0.1429 0.1429 0.2857 6 0.1083 0.1429 0.1429 0.4286 7 0.1083 0.1429 0.2857 0.1429 8 0.1083 0.1429 0.2857 0.4286 9 0.1083 0.1429 0.4286 0.1429 10 0.1083 0.1429 0.4286 0.2857 11 0.1083 0.2857 0.1429 0.1429 12 0.1083 0.2857 0.1429 0.4286 13 0.1083 0.2857 0.4286 0.1429 14 0.1083 0.4286 0.1429 0.1429 15 0.1083 0.4286 0.1429 0.2857 16 0.1083 0.4286 0.2857 0.1429 17 -0.2417 0.2857 0.2857 0.2857 18 -0.2417 0.2857 0.2857 0.1429 19 -0.2417 0.2857 0.1429 0.2857 20 -0.2417 0.1429 0.2857 0.2857 TEST07 TETRAHEDRON_NCO_RULE returns the points and weights of an NCO rule for the tetrahedron. In this test, we write each rule to a file. Wrote rule 1 to "nco0_w.txt" and "nco0_x.txt". Wrote rule 2 to "nco1_w.txt" and "nco1_x.txt". Wrote rule 3 to "nco2_w.txt" and "nco2_x.txt". Wrote rule 4 to "nco3_w.txt" and "nco3_x.txt". Wrote rule 5 to "nco4_w.txt" and "nco4_x.txt". Wrote rule 6 to "nco5_w.txt" and "nco5_x.txt". Wrote rule 7 to "nco6_w.txt" and "nco6_x.txt". TETRAHEDRON_NCO_RULE_PRB: Normal end of execution. 17 June 2014 3:03:35.728 PM