08-Jan-2022 10:03:41 square_felippa_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test square_felippa_rule(). SQUARE_MONOMIAL_TEST For the unit quadrilateral, SQUARE_MONOMIAL returns the exact value of the integral of X^ALPHA Y^BETA Volume = 4.000000 ALPHA BETA INTEGRAL 0 0 4.000000e+00 0 1 0.000000e+00 0 2 1.333333e+00 0 3 0.000000e+00 0 4 8.000000e-01 1 0 0.000000e+00 1 1 0.000000e+00 1 2 0.000000e+00 1 3 0.000000e+00 2 0 1.333333e+00 2 1 0.000000e+00 2 2 4.444444e-01 3 0 0.000000e+00 3 1 0.000000e+00 4 0 8.000000e-01 square_quad_test(): For the unit quadrilateral, we approximate monomial integrals with SQUARE_RULE, which returns M by N point rules.. Monomial exponents: 0 0 1 1 4.000000 2 2 4.000000 3 3 4.000000 4 4 4.000000 5 5 4.000000 3 5 4.000000 Exact 4.000000 Monomial exponents: 1 0 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 0 1 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 -0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 2 0 1 1 0.000000 2 2 1.333333 3 3 1.333333 4 4 1.333333 5 5 1.333333 3 5 1.333333 Exact 1.333333 Monomial exponents: 1 1 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 -0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 0 2 1 1 0.000000 2 2 1.333333 3 3 1.333333 4 4 1.333333 5 5 1.333333 3 5 1.333333 Exact 1.333333 Monomial exponents: 3 0 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 2 1 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 -0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 1 2 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 0 3 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 -0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 4 0 1 1 0.000000 2 2 0.444444 3 3 0.800000 4 4 0.800000 5 5 0.800000 3 5 0.800000 Exact 0.800000 Monomial exponents: 3 1 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 2 2 1 1 0.000000 2 2 0.444444 3 3 0.444444 4 4 0.444444 5 5 0.444444 3 5 0.444444 Exact 0.444444 Monomial exponents: 1 3 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 0 4 1 1 0.000000 2 2 0.444444 3 3 0.800000 4 4 0.800000 5 5 0.800000 3 5 0.800000 Exact 0.800000 Monomial exponents: 5 0 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 4 1 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 -0.000000 Exact 0.000000 Monomial exponents: 3 2 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 2 3 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 -0.000000 3 5 -0.000000 Exact 0.000000 Monomial exponents: 1 4 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 Monomial exponents: 0 5 1 1 0.000000 2 2 0.000000 3 3 0.000000 4 4 0.000000 5 5 0.000000 3 5 0.000000 Exact 0.000000 square_felippa_rule_test(): Normal end of execution. 08-Jan-2022 10:03:41