08-Jan-2022 11:06:37 wedge_felippa_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2. Test wedge_felippa_rule() WEDGE_FELIPPA_RULE_TEST01 For the unit wedge, WEDGE_INTEGRAL returns the exact value of the integral of X^ALPHA Y^BETA Z^GAMMA Volume = 1.000000 ALPHA BETA GAMMA INTEGRAL 0 0 0 1.000000e+00 0 0 1 0.000000e+00 0 0 2 3.333333e-01 0 0 3 0.000000e+00 0 0 4 2.000000e-01 0 1 0 3.333333e-01 0 1 1 0.000000e+00 0 1 2 1.111111e-01 0 1 3 0.000000e+00 0 2 0 1.666667e-01 0 2 1 0.000000e+00 0 2 2 5.555556e-02 0 3 0 1.000000e-01 0 3 1 0.000000e+00 0 4 0 6.666667e-02 1 0 0 3.333333e-01 1 0 1 0.000000e+00 1 0 2 1.111111e-01 1 0 3 0.000000e+00 1 1 0 8.333333e-02 1 1 1 0.000000e+00 1 1 2 2.777778e-02 1 2 0 3.333333e-02 1 2 1 0.000000e+00 1 3 0 1.666667e-02 2 0 0 1.666667e-01 2 0 1 0.000000e+00 2 0 2 5.555556e-02 2 1 0 3.333333e-02 2 1 1 0.000000e+00 2 2 0 1.111111e-02 3 0 0 1.000000e-01 3 0 1 0.000000e+00 3 1 0 1.666667e-02 4 0 0 6.666667e-02 WEDGE_FELIPPA_RULE_TEST02 For the unit wedge, we approximate monomial integrals with WEDGE_RULE. Monomial exponents: 0 0 0 1 1 1 1.000000 3 2 6 1.000000 -3 2 6 1.000000 6 3 18 1.000000 -6 2 12 1.000000 7 3 21 1.000000 12 4 48 1.000000 Exact 1.000000 Monomial exponents: 1 0 0 1 1 1 0.333333 3 2 6 0.333333 -3 2 6 0.333333 6 3 18 0.333333 -6 2 12 0.333333 7 3 21 0.333333 12 4 48 0.333333 Exact 0.333333 Monomial exponents: 0 1 0 1 1 1 0.333333 3 2 6 0.333333 -3 2 6 0.333333 6 3 18 0.333333 -6 2 12 0.333333 7 3 21 0.333333 12 4 48 0.333333 Exact 0.333333 Monomial exponents: 2 0 0 1 1 1 0.111111 3 2 6 0.166667 -3 2 6 0.166667 6 3 18 0.166667 -6 2 12 0.166667 7 3 21 0.166667 12 4 48 0.166667 Exact 0.166667 Monomial exponents: 1 1 0 1 1 1 0.111111 3 2 6 0.083333 -3 2 6 0.083333 6 3 18 0.083333 -6 2 12 0.083333 7 3 21 0.083333 12 4 48 0.083333 Exact 0.083333 Monomial exponents: 0 2 0 1 1 1 0.111111 3 2 6 0.166667 -3 2 6 0.166667 6 3 18 0.166667 -6 2 12 0.166667 7 3 21 0.166667 12 4 48 0.166667 Exact 0.166667 Monomial exponents: 0 0 2 1 1 1 0.000000 3 2 6 0.333333 -3 2 6 0.333333 6 3 18 0.333333 -6 2 12 0.333333 7 3 21 0.333333 12 4 48 0.333333 Exact 0.333333 Monomial exponents: 3 0 0 1 1 1 0.037037 3 2 6 0.101852 -3 2 6 0.083333 6 3 18 0.100000 -6 2 12 0.100000 7 3 21 0.100000 12 4 48 0.100000 Exact 0.100000 Monomial exponents: 2 1 0 1 1 1 0.037037 3 2 6 0.032407 -3 2 6 0.041667 6 3 18 0.033333 -6 2 12 0.033333 7 3 21 0.033333 12 4 48 0.033333 Exact 0.033333 Monomial exponents: 1 2 0 1 1 1 0.037037 3 2 6 0.032407 -3 2 6 0.041667 6 3 18 0.033333 -6 2 12 0.033333 7 3 21 0.033333 12 4 48 0.033333 Exact 0.033333 Monomial exponents: 0 3 0 1 1 1 0.037037 3 2 6 0.101852 -3 2 6 0.083333 6 3 18 0.100000 -6 2 12 0.100000 7 3 21 0.100000 12 4 48 0.100000 Exact 0.100000 Monomial exponents: 1 0 2 1 1 1 0.000000 3 2 6 0.111111 -3 2 6 0.111111 6 3 18 0.111111 -6 2 12 0.111111 7 3 21 0.111111 12 4 48 0.111111 Exact 0.111111 Monomial exponents: 0 1 2 1 1 1 0.000000 3 2 6 0.111111 -3 2 6 0.111111 6 3 18 0.111111 -6 2 12 0.111111 7 3 21 0.111111 12 4 48 0.111111 Exact 0.111111 Monomial exponents: 4 0 0 1 1 1 0.012346 3 2 6 0.066358 -3 2 6 0.041667 6 3 18 0.066667 -6 2 12 0.063889 7 3 21 0.066667 12 4 48 0.066667 Exact 0.066667 Monomial exponents: 3 1 0 1 1 1 0.012346 3 2 6 0.017747 -3 2 6 0.020833 6 3 18 0.016667 -6 2 12 0.018056 7 3 21 0.016667 12 4 48 0.016667 Exact 0.016667 Monomial exponents: 2 2 0 1 1 1 0.012346 3 2 6 0.008488 -3 2 6 0.020833 6 3 18 0.011111 -6 2 12 0.009722 7 3 21 0.011111 12 4 48 0.011111 Exact 0.011111 Monomial exponents: 1 3 0 1 1 1 0.012346 3 2 6 0.017747 -3 2 6 0.020833 6 3 18 0.016667 -6 2 12 0.018056 7 3 21 0.016667 12 4 48 0.016667 Exact 0.016667 Monomial exponents: 0 4 0 1 1 1 0.012346 3 2 6 0.066358 -3 2 6 0.041667 6 3 18 0.066667 -6 2 12 0.063889 7 3 21 0.066667 12 4 48 0.066667 Exact 0.066667 Monomial exponents: 2 0 2 1 1 1 0.000000 3 2 6 0.055556 -3 2 6 0.055556 6 3 18 0.055556 -6 2 12 0.055556 7 3 21 0.055556 12 4 48 0.055556 Exact 0.055556 Monomial exponents: 1 1 2 1 1 1 0.000000 3 2 6 0.027778 -3 2 6 0.027778 6 3 18 0.027778 -6 2 12 0.027778 7 3 21 0.027778 12 4 48 0.027778 Exact 0.027778 Monomial exponents: 0 2 2 1 1 1 0.000000 3 2 6 0.055556 -3 2 6 0.055556 6 3 18 0.055556 -6 2 12 0.055556 7 3 21 0.055556 12 4 48 0.055556 Exact 0.055556 Monomial exponents: 0 0 4 1 1 1 0.000000 3 2 6 0.111111 -3 2 6 0.111111 6 3 18 0.200000 -6 2 12 0.111111 7 3 21 0.200000 12 4 48 0.200000 Exact 0.200000 WEDGE_FELIPPA_RULE_TEST03 For the unit wedge, write some rules to a file Rule Trig Line Total W_File X_File Order Order Order 1 1 1 1 wedge_felippa_1x1_w.txt wedge_felippa_1x1_x.txt 2 3 2 6 wedge_felippa_3x2_w.txt wedge_felippa_3x2_x.txt 3 -3 2 6 wedge_felippa_3bx2_w.txt wedge_felippa_3bx2_x.txt 4 6 3 18 wedge_felippa_6x3_w.txt wedge_felippa_6x3_x.txt 5 -6 2 12 wedge_felippa_6bx2_w.txt wedge_felippa_6bx2_x.txt 6 7 3 21 wedge_felippa_7x3_w.txt wedge_felippa_7x3_x.txt 7 12 4 48 wedge_felippa_12x4_w.txt wedge_felippa_12x4_x.txt wedge_felippa_rule_test(): Normal end of execution. 08-Jan-2022 11:06:37