15 January 2017 08:57:26 AM CUBE_FELIPPA_RULE_PRB C version Test the CUBE_FELIPPA_RULE library. CUBE_MONOMIAL_TEST For the unit hexahedron, CUBE_MONOMIAL returns the exact value of the integral of X^ALPHA Y^BETA Z^GAMMA Volume = 8 ALPHA BETA GAMMA INTEGRAL 0 0 0 8 0 0 1 0 0 0 2 3 0 0 3 0 0 0 4 2 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 2 0 3 0 2 1 0 0 2 2 0.9 0 3 0 0 0 3 1 0 0 4 0 2 1 0 0 0 1 0 1 0 1 0 2 0 1 0 3 0 1 1 0 0 1 1 1 0 1 1 2 0 1 2 0 0 1 2 1 0 1 3 0 0 2 0 0 3 2 0 1 0 2 0 2 0.9 2 1 0 0 2 1 1 0 2 2 0 0.9 3 0 0 0 3 0 1 0 3 1 0 0 4 0 0 2 CUBE_QUAD_TEST For the unit hexahedron, we approximate monomial integrals with: CUBE_RULE, which returns N1 by N2 by N3 point rules.. Monomial exponents: 0 0 0 1 1 1 8 2 2 2 8 3 3 3 8 4 4 4 8 5 5 5 8 3 5 2 8 Exact 8 Monomial exponents: 1 0 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 3.81639e-17 3 5 2 0 Exact 0 Monomial exponents: 0 1 0 1 1 1 0 2 2 2 0 3 3 3 2.77556e-17 4 4 4 2.77556e-17 5 5 5 -8.67362e-17 3 5 2 -3.33067e-16 Exact 0 Monomial exponents: 0 0 1 1 1 1 0 2 2 2 0 3 3 3 2.77556e-17 4 4 4 5.55112e-17 5 5 5 -3.46945e-18 3 5 2 -1.11022e-16 Exact 0 Monomial exponents: 2 0 0 1 1 1 0 2 2 2 2.66667 3 3 3 2.66667 4 4 4 2.66667 5 5 5 2.66667 3 5 2 2.66667 Exact 2.66667 Monomial exponents: 1 1 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 1.73472e-18 3 5 2 0 Exact 0 Monomial exponents: 0 2 0 1 1 1 0 2 2 2 2.66667 3 3 3 2.66667 4 4 4 2.66667 5 5 5 2.66667 3 5 2 2.66667 Exact 2.66667 Monomial exponents: 1 0 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -2.08167e-17 5 5 5 1.73472e-18 3 5 2 0 Exact 0 Monomial exponents: 0 1 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -4.16334e-17 5 5 5 -1.73472e-18 3 5 2 -4.16334e-17 Exact 0 Monomial exponents: 0 0 2 1 1 1 0 2 2 2 2.66667 3 3 3 2.66667 4 4 4 2.66667 5 5 5 2.66667 3 5 2 2.66667 Exact 2.66667 Monomial exponents: 3 0 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 6.93889e-18 5 5 5 4.51028e-17 3 5 2 0 Exact 0 Monomial exponents: 2 1 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 3.1225e-17 5 5 5 -8.67362e-18 3 5 2 0 Exact 0 Monomial exponents: 1 2 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 3.46945e-18 5 5 5 5.20417e-18 3 5 2 0 Exact 0 Monomial exponents: 0 3 0 1 1 1 0 2 2 2 0 3 3 3 1.38778e-17 4 4 4 0 5 5 5 -1.56125e-17 3 5 2 -1.38778e-17 Exact 0 Monomial exponents: 2 0 1 1 1 1 0 2 2 2 -5.55112e-17 3 3 3 0 4 4 4 -2.42861e-17 5 5 5 -1.73472e-18 3 5 2 0 Exact 0 Monomial exponents: 1 1 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 3.46945e-18 5 5 5 -8.67362e-18 3 5 2 0 Exact 0 Monomial exponents: 0 2 1 1 1 1 0 2 2 2 -5.55112e-17 3 3 3 -1.38778e-17 4 4 4 0 5 5 5 9.54098e-17 3 5 2 -4.85723e-17 Exact 0 Monomial exponents: 1 0 2 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 3.46945e-18 5 5 5 -1.73472e-18 3 5 2 0 Exact 0 Monomial exponents: 0 1 2 1 1 1 0 2 2 2 0 3 3 3 -1.38778e-17 4 4 4 -5.55112e-17 5 5 5 5.37764e-17 3 5 2 -2.77556e-17 Exact 0 Monomial exponents: 0 0 3 1 1 1 0 2 2 2 -5.55112e-17 3 3 3 -9.71445e-17 4 4 4 -2.77556e-17 5 5 5 1.78677e-16 3 5 2 3.1225e-17 Exact 0 Monomial exponents: 4 0 0 1 1 1 0 2 2 2 0.888889 3 3 3 1.6 4 4 4 1.6 5 5 5 1.6 3 5 2 1.6 Exact 1.6 Monomial exponents: 3 1 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 3.46945e-18 5 5 5 3.46945e-18 3 5 2 0 Exact 0 Monomial exponents: 2 2 0 1 1 1 0 2 2 2 0.888889 3 3 3 0.888889 4 4 4 0.888889 5 5 5 0.888889 3 5 2 0.888889 Exact 0.888889 Monomial exponents: 1 3 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -6.93889e-18 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 0 4 0 1 1 1 0 2 2 2 0.888889 3 3 3 1.6 4 4 4 1.6 5 5 5 1.6 3 5 2 1.6 Exact 1.6 Monomial exponents: 3 0 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -3.46945e-18 5 5 5 -3.46945e-18 3 5 2 0 Exact 0 Monomial exponents: 2 1 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -1.04083e-17 5 5 5 6.93889e-18 3 5 2 0 Exact 0 Monomial exponents: 1 2 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -3.46945e-18 5 5 5 -5.20417e-18 3 5 2 0 Exact 0 Monomial exponents: 0 3 1 1 1 1 0 2 2 2 0 3 3 3 -2.08167e-17 4 4 4 3.46945e-18 5 5 5 1.73472e-17 3 5 2 -3.46945e-17 Exact 0 Monomial exponents: 2 0 2 1 1 1 0 2 2 2 0.888889 3 3 3 0.888889 4 4 4 0.888889 5 5 5 0.888889 3 5 2 0.888889 Exact 0.888889 Monomial exponents: 1 1 2 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 3.46945e-18 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 0 2 2 1 1 1 0 2 2 2 0.888889 3 3 3 0.888889 4 4 4 0.888889 5 5 5 0.888889 3 5 2 0.888889 Exact 0.888889 Monomial exponents: 1 0 3 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -6.93889e-18 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 0 1 3 1 1 1 0 2 2 2 0 3 3 3 -2.08167e-17 4 4 4 -2.42861e-17 5 5 5 3.46945e-18 3 5 2 0 Exact 0 Monomial exponents: 0 0 4 1 1 1 0 2 2 2 0.888889 3 3 3 1.6 4 4 4 1.6 5 5 5 1.6 3 5 2 0.888889 Exact 1.6 Monomial exponents: 5 0 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 4 1 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -1.38778e-17 5 5 5 3.46945e-18 3 5 2 -2.77556e-17 Exact 0 Monomial exponents: 3 2 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 -1.73472e-18 3 5 2 0 Exact 0 Monomial exponents: 2 3 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 1.56125e-17 3 5 2 -1.38778e-17 Exact 0 Monomial exponents: 1 4 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -6.93889e-18 5 5 5 -3.46945e-18 3 5 2 0 Exact 0 Monomial exponents: 0 5 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 4.68375e-17 3 5 2 2.77556e-17 Exact 0 Monomial exponents: 4 0 1 1 1 1 0 2 2 2 -2.77556e-17 3 3 3 -2.77556e-17 4 4 4 6.93889e-18 5 5 5 -1.38778e-17 3 5 2 -5.55112e-17 Exact 0 Monomial exponents: 3 1 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 1.73472e-18 3 5 2 0 Exact 0 Monomial exponents: 2 2 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 4.51028e-17 5 5 5 -5.20417e-18 3 5 2 -2.77556e-17 Exact 0 Monomial exponents: 1 3 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -3.46945e-18 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 0 4 1 1 1 1 0 2 2 2 -2.77556e-17 3 3 3 -2.77556e-17 4 4 4 -1.73472e-17 5 5 5 -8.67362e-18 3 5 2 -6.93889e-18 Exact 0 Monomial exponents: 3 0 2 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 2 1 2 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 6.93889e-18 5 5 5 8.67362e-18 3 5 2 -6.93889e-18 Exact 0 Monomial exponents: 1 2 2 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -3.46945e-18 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 0 3 2 1 1 1 0 2 2 2 0 3 3 3 1.38778e-17 4 4 4 1.38778e-17 5 5 5 5.20417e-18 3 5 2 6.93889e-18 Exact 0 Monomial exponents: 2 0 3 1 1 1 0 2 2 2 0 3 3 3 6.93889e-17 4 4 4 0 5 5 5 8.67362e-18 3 5 2 6.93889e-18 Exact 0 Monomial exponents: 1 1 3 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 0 3 5 2 0 Exact 0 Monomial exponents: 0 2 3 1 1 1 0 2 2 2 0 3 3 3 4.16334e-17 4 4 4 4.16334e-17 5 5 5 -2.25514e-17 3 5 2 -3.46945e-18 Exact 0 Monomial exponents: 1 0 4 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -6.93889e-18 5 5 5 -3.46945e-18 3 5 2 0 Exact 0 Monomial exponents: 0 1 4 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 2.42861e-17 5 5 5 1.9082e-17 3 5 2 -1.73472e-18 Exact 0 Monomial exponents: 0 0 5 1 1 1 0 2 2 2 -2.77556e-17 3 3 3 -2.77556e-17 4 4 4 -8.32667e-17 5 5 5 -2.25514e-17 3 5 2 -1.56125e-17 Exact 0 Monomial exponents: 6 0 0 1 1 1 0 2 2 2 0.296296 3 3 3 0.96 4 4 4 1.14286 5 5 5 1.14286 3 5 2 0.96 Exact 1.14286 Monomial exponents: 5 1 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 -8.67362e-19 3 5 2 0 Exact 0 Monomial exponents: 4 2 0 1 1 1 0 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 3 3 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 -8.67362e-19 3 5 2 0 Exact 0 Monomial exponents: 2 4 0 1 1 1 0 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 1 5 0 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 -9.54098e-18 3 5 2 0 Exact 0 Monomial exponents: 0 6 0 1 1 1 0 2 2 2 0.296296 3 3 3 0.96 4 4 4 1.14286 5 5 5 1.14286 3 5 2 1.14286 Exact 1.14286 Monomial exponents: 5 0 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 2.60209e-18 3 5 2 0 Exact 0 Monomial exponents: 4 1 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 -5.20417e-18 3 5 2 -2.08167e-17 Exact 0 Monomial exponents: 3 2 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 -8.67362e-19 3 5 2 0 Exact 0 Monomial exponents: 2 3 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 6.93889e-18 5 5 5 -1.73472e-18 3 5 2 -1.38778e-17 Exact 0 Monomial exponents: 1 4 1 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 8.67362e-19 3 5 2 0 Exact 0 Monomial exponents: 0 5 1 1 1 1 0 2 2 2 0 3 3 3 6.93889e-18 4 4 4 0 5 5 5 -6.07153e-18 3 5 2 2.08167e-17 Exact 0 Monomial exponents: 4 0 2 1 1 1 0 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 3 1 2 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -3.46945e-18 5 5 5 8.67362e-19 3 5 2 0 Exact 0 Monomial exponents: 2 2 2 1 1 1 0 2 2 2 0.296296 3 3 3 0.296296 4 4 4 0.296296 5 5 5 0.296296 3 5 2 0.296296 Exact 0.296296 Monomial exponents: 1 3 2 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 -3.46945e-18 5 5 5 -2.60209e-18 3 5 2 0 Exact 0 Monomial exponents: 0 4 2 1 1 1 0 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.533333 Exact 0.533333 Monomial exponents: 3 0 3 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 8.67362e-19 3 5 2 0 Exact 0 Monomial exponents: 2 1 3 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 8.67362e-18 3 5 2 -3.46945e-18 Exact 0 Monomial exponents: 1 2 3 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 -2.60209e-18 3 5 2 0 Exact 0 Monomial exponents: 0 3 3 1 1 1 0 2 2 2 0 3 3 3 6.93889e-18 4 4 4 0 5 5 5 -6.07153e-18 3 5 2 3.46945e-18 Exact 0 Monomial exponents: 2 0 4 1 1 1 0 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.296296 Exact 0.533333 Monomial exponents: 1 1 4 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 3.46945e-18 5 5 5 2.60209e-18 3 5 2 0 Exact 0 Monomial exponents: 0 2 4 1 1 1 0 2 2 2 0.296296 3 3 3 0.533333 4 4 4 0.533333 5 5 5 0.533333 3 5 2 0.296296 Exact 0.533333 Monomial exponents: 1 0 5 1 1 1 0 2 2 2 0 3 3 3 0 4 4 4 0 5 5 5 7.80626e-18 3 5 2 0 Exact 0 Monomial exponents: 0 1 5 1 1 1 0 2 2 2 0 3 3 3 6.93889e-18 4 4 4 1.38778e-17 5 5 5 -6.07153e-18 3 5 2 -1.73472e-18 Exact 0 Monomial exponents: 0 0 6 1 1 1 0 2 2 2 0.296296 3 3 3 0.96 4 4 4 1.14286 5 5 5 1.14286 3 5 2 0.296296 Exact 1.14286 CUBE_FELIPPA_RULE_PRB Normal end of execution. 15 January 2017 08:57:26 AM