07-Jan-2022 18:16:08 CUBE_FELIPPA_RULE_TEST() MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2. Test CUBE_FELIPPA_RULE(). CUBE_MONOMIAL_TEST For a cube, CUBE_MONOMIAL returns the exact value of the integral of X^ALPHA Y^BETA Z^GAMMA Volume = 8.000000 ALPHA BETA GAMMA INTEGRAL 0 0 0 8.000000e+00 0 0 1 0.000000e+00 0 0 2 2.666667e+00 0 0 3 0.000000e+00 0 0 4 1.600000e+00 0 1 0 0.000000e+00 0 1 1 0.000000e+00 0 1 2 0.000000e+00 0 1 3 0.000000e+00 0 2 0 2.666667e+00 0 2 1 0.000000e+00 0 2 2 8.888889e-01 0 3 0 0.000000e+00 0 3 1 0.000000e+00 0 4 0 1.600000e+00 1 0 0 0.000000e+00 1 0 1 0.000000e+00 1 0 2 0.000000e+00 1 0 3 0.000000e+00 1 1 0 0.000000e+00 1 1 1 0.000000e+00 1 1 2 0.000000e+00 1 2 0 0.000000e+00 1 2 1 0.000000e+00 1 3 0 0.000000e+00 2 0 0 2.666667e+00 2 0 1 0.000000e+00 2 0 2 8.888889e-01 2 1 0 0.000000e+00 2 1 1 0.000000e+00 2 2 0 8.888889e-01 3 0 0 0.000000e+00 3 0 1 0.000000e+00 3 1 0 0.000000e+00 4 0 0 1.600000e+00 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 8.000000 2 2 2 8.000000 3 3 3 8.000000 4 4 4 8.000000 5 5 5 8.000000 3 5 2 8.000000 Exact 8.000000 Monomial exponents: 2 0 0 1 1 1 0.000000 2 2 2 2.666667 3 3 3 2.666667 4 4 4 2.666667 5 5 5 2.666667 3 5 2 2.666667 Exact 2.666667 Monomial exponents: 0 2 0 1 1 1 0.000000 2 2 2 2.666667 3 3 3 2.666667 4 4 4 2.666667 5 5 5 2.666667 3 5 2 2.666667 Exact 2.666667 Monomial exponents: 0 0 2 1 1 1 0.000000 2 2 2 2.666667 3 3 3 2.666667 4 4 4 2.666667 5 5 5 2.666667 3 5 2 2.666667 Exact 2.666667 Monomial exponents: 4 0 0 1 1 1 0.000000 2 2 2 0.888889 3 3 3 1.600000 4 4 4 1.600000 5 5 5 1.600000 3 5 2 1.600000 Exact 1.600000 Monomial exponents: 2 2 0 1 1 1 0.000000 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: 0 4 0 1 1 1 0.000000 2 2 2 0.888889 3 3 3 1.600000 4 4 4 1.600000 5 5 5 1.600000 3 5 2 1.600000 Exact 1.600000 Monomial exponents: 2 0 2 1 1 1 0.000000 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: 0 2 2 1 1 1 0.000000 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: 0 0 4 1 1 1 0.000000 2 2 2 0.888889 3 3 3 1.600000 4 4 4 1.600000 5 5 5 1.600000 3 5 2 0.888889 Exact 1.600000 Monomial exponents: 6 0 0 1 1 1 0.000000 2 2 2 0.296296 3 3 3 0.960000 4 4 4 1.142857 5 5 5 1.142857 3 5 2 0.960000 Exact 1.142857 Monomial exponents: 4 2 0 1 1 1 0.000000 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: 2 4 0 1 1 1 0.000000 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: 0 6 0 1 1 1 0.000000 2 2 2 0.296296 3 3 3 0.960000 4 4 4 1.142857 5 5 5 1.142857 3 5 2 1.142857 Exact 1.142857 Monomial exponents: 4 0 2 1 1 1 0.000000 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: 2 2 2 1 1 1 0.000000 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: 0 4 2 1 1 1 0.000000 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: 2 0 4 1 1 1 0.000000 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: 0 2 4 1 1 1 0.000000 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: 0 0 6 1 1 1 0.000000 2 2 2 0.296296 3 3 3 0.960000 4 4 4 1.142857 5 5 5 1.142857 3 5 2 0.296296 Exact 1.142857 CUBE_FELIPPA_RULE_TEST() Normal end of execution. 07-Jan-2022 18:16:08