08-Jan-2022 10:38:35 triangle_felippa_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test triangle_felippa_rule(). TRIANGLE_UNIT_MONOMIAL_TEST For the unit triangle, TRIANGLE_UNIT_MONOMIAL returns the exact value of the integral of X^ALPHA Y^BETA Volume = 0.500000 ALPHA BETA INTEGRAL 0 0 5.000000e-01 0 1 1.666667e-01 0 2 8.333333e-02 0 3 5.000000e-02 0 4 3.333333e-02 1 0 1.666667e-01 1 1 4.166667e-02 1 2 1.666667e-02 1 3 8.333333e-03 2 0 8.333333e-02 2 1 1.666667e-02 2 2 5.555556e-03 3 0 5.000000e-02 3 1 8.333333e-03 4 0 3.333333e-02 TRIANGLE_UNIT_QUAD_TEST For the unit triangle, we approximate monomial integrals with: TRIANGLE_UNIT_O01, TRIANGLE_UNIT_O03, TRIANGLE_UNIT_O03b, TRIANGLE_UNIT_O06, TRIANGLE_UNIT_O06b, TRIANGLE_UNIT_O07, TRIANGLE_UNIT_O12, Monomial exponents: 0 0 1 0.500000 3 0.500000 3 0.500000 6 0.500000 6 0.500000 7 0.500000 12 0.500000 Exact 0.500000 Monomial exponents: 1 0 1 0.166667 3 0.166667 3 0.166667 6 0.166667 6 0.166667 7 0.166667 12 0.166667 Exact 0.166667 Monomial exponents: 0 1 1 0.166667 3 0.166667 3 0.166667 6 0.166667 6 0.166667 7 0.166667 12 0.166667 Exact 0.166667 Monomial exponents: 2 0 1 0.055556 3 0.083333 3 0.083333 6 0.083333 6 0.083333 7 0.083333 12 0.083333 Exact 0.083333 Monomial exponents: 1 1 1 0.055556 3 0.041667 3 0.041667 6 0.041667 6 0.041667 7 0.041667 12 0.041667 Exact 0.041667 Monomial exponents: 0 2 1 0.055556 3 0.083333 3 0.083333 6 0.083333 6 0.083333 7 0.083333 12 0.083333 Exact 0.083333 Monomial exponents: 3 0 1 0.018519 3 0.050926 3 0.041667 6 0.050000 6 0.050000 7 0.050000 12 0.050000 Exact 0.050000 Monomial exponents: 2 1 1 0.018519 3 0.016204 3 0.020833 6 0.016667 6 0.016667 7 0.016667 12 0.016667 Exact 0.016667 Monomial exponents: 1 2 1 0.018519 3 0.016204 3 0.020833 6 0.016667 6 0.016667 7 0.016667 12 0.016667 Exact 0.016667 Monomial exponents: 0 3 1 0.018519 3 0.050926 3 0.041667 6 0.050000 6 0.050000 7 0.050000 12 0.050000 Exact 0.050000 Monomial exponents: 4 0 1 0.006173 3 0.033179 3 0.020833 6 0.033333 6 0.031944 7 0.033333 12 0.033333 Exact 0.033333 Monomial exponents: 3 1 1 0.006173 3 0.008873 3 0.010417 6 0.008333 6 0.009028 7 0.008333 12 0.008333 Exact 0.008333 Monomial exponents: 2 2 1 0.006173 3 0.004244 3 0.010417 6 0.005556 6 0.004861 7 0.005556 12 0.005556 Exact 0.005556 Monomial exponents: 1 3 1 0.006173 3 0.008873 3 0.010417 6 0.008333 6 0.009028 7 0.008333 12 0.008333 Exact 0.008333 Monomial exponents: 0 4 1 0.006173 3 0.033179 3 0.020833 6 0.033333 6 0.031944 7 0.033333 12 0.033333 Exact 0.033333 Monomial exponents: 5 0 1 0.002058 3 0.021991 3 0.010417 6 0.023935 6 0.020833 7 0.023810 12 0.023810 Exact 0.023810 Monomial exponents: 4 1 1 0.002058 3 0.005594 3 0.005208 6 0.004699 6 0.005556 7 0.004762 12 0.004762 Exact 0.004762 Monomial exponents: 3 2 1 0.002058 3 0.001736 3 0.005208 6 0.002394 6 0.002083 7 0.002381 12 0.002381 Exact 0.002381 Monomial exponents: 2 3 1 0.002058 3 0.001736 3 0.005208 6 0.002394 6 0.002083 7 0.002381 12 0.002381 Exact 0.002381 Monomial exponents: 1 4 1 0.002058 3 0.005594 3 0.005208 6 0.004699 6 0.005556 7 0.004762 12 0.004762 Exact 0.004762 Monomial exponents: 0 5 1 0.002058 3 0.021991 3 0.010417 6 0.023935 6 0.020833 7 0.023810 12 0.023810 Exact 0.023810 Monomial exponents: 6 0 1 0.000686 3 0.014639 3 0.005208 6 0.018088 6 0.013696 7 0.017775 12 0.017857 Exact 0.017857 Monomial exponents: 5 1 1 0.000686 3 0.003676 3 0.002604 6 0.002923 6 0.003569 7 0.003017 12 0.002976 Exact 0.002976 Monomial exponents: 4 2 1 0.000686 3 0.000975 3 0.002604 6 0.001141 6 0.001138 7 0.001146 12 0.001190 Exact 0.001190 Monomial exponents: 3 3 1 0.000686 3 0.000461 3 0.002604 6 0.000950 6 0.000675 7 0.000939 12 0.000893 Exact 0.000893 Monomial exponents: 2 4 1 0.000686 3 0.000975 3 0.002604 6 0.001141 6 0.001138 7 0.001146 12 0.001190 Exact 0.001190 Monomial exponents: 1 5 1 0.000686 3 0.003676 3 0.002604 6 0.002923 6 0.003569 7 0.003017 12 0.002976 Exact 0.002976 Monomial exponents: 0 6 1 0.000686 3 0.014639 3 0.005208 6 0.018088 6 0.013696 7 0.017775 12 0.017857 Exact 0.017857 Monomial exponents: 7 0 1 0.000229 3 0.009756 3 0.002604 6 0.014124 6 0.009041 7 0.013635 12 0.013892 Exact 0.013889 Monomial exponents: 6 1 1 0.000229 3 0.002442 3 0.001302 6 0.001982 6 0.002328 7 0.002070 12 0.001983 Exact 0.001984 Monomial exponents: 5 2 1 0.000229 3 0.000620 3 0.001302 6 0.000583 6 0.000688 7 0.000602 12 0.000662 Exact 0.000661 Monomial exponents: 4 3 1 0.000229 3 0.000191 3 0.001302 6 0.000420 6 0.000302 7 0.000418 12 0.000397 Exact 0.000397 Monomial exponents: 3 4 1 0.000229 3 0.000191 3 0.001302 6 0.000420 6 0.000302 7 0.000418 12 0.000397 Exact 0.000397 Monomial exponents: 2 5 1 0.000229 3 0.000620 3 0.001302 6 0.000583 6 0.000688 7 0.000602 12 0.000662 Exact 0.000661 Monomial exponents: 1 6 1 0.000229 3 0.002442 3 0.001302 6 0.001982 6 0.002328 7 0.002070 12 0.001983 Exact 0.001984 Monomial exponents: 0 7 1 0.000229 3 0.009756 3 0.002604 6 0.014124 6 0.009041 7 0.013635 12 0.013892 Exact 0.013889 triangle_felippa_rule_test(): Normal end of execution. 08-Jan-2022 10:38:35