08-Jan-2022 10:30:55 tetrahedron_felippa_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test tetrahedron_felippa_rule(). TETRAHEDRON_UNIT_MONOMIAL_TEST For the unit tetrahedron, TETRAHEDRON_UNIT_MONOMIAL returns the exact value of the integral of X^ALPHA Y^BETA Z^GAMMA Volume = 0.166667 ALPHA BETA GAMMA INTEGRAL 0 0 0 1.666667e-01 0 0 1 4.166667e-02 0 0 2 1.666667e-02 0 0 3 8.333333e-03 0 0 4 4.761905e-03 0 1 0 4.166667e-02 0 1 1 8.333333e-03 0 1 2 2.777778e-03 0 1 3 1.190476e-03 0 2 0 1.666667e-02 0 2 1 2.777778e-03 0 2 2 7.936508e-04 0 3 0 8.333333e-03 0 3 1 1.190476e-03 0 4 0 4.761905e-03 1 0 0 4.166667e-02 1 0 1 8.333333e-03 1 0 2 2.777778e-03 1 0 3 1.190476e-03 1 1 0 8.333333e-03 1 1 1 1.388889e-03 1 1 2 3.968254e-04 1 2 0 2.777778e-03 1 2 1 3.968254e-04 1 3 0 1.190476e-03 2 0 0 1.666667e-02 2 0 1 2.777778e-03 2 0 2 7.936508e-04 2 1 0 2.777778e-03 2 1 1 3.968254e-04 2 2 0 7.936508e-04 3 0 0 8.333333e-03 3 0 1 1.190476e-03 3 1 0 1.190476e-03 4 0 0 4.761905e-03 TETRAHEDRON_UNIT_QUAD_TEST For the unit tetrahedron, we approximate monomial integrals with: TETRAHEDRON_UNIT_O01, TETRAHEDRON_UNIT_O04, TETRAHEDRON_UNIT_O08, TETRAHEDRON_UNIT_O08b, TETRAHEDRON_UNIT_O14, TETRAHEDRON_UNIT_O14b, TETRAHEDRON_UNIT_O15, TETRAHEDRON_UNIT_O15b, TETRAHEDRON_UNIT_O24, Monomial exponents: 0 0 0 1 0.166667 4 0.166667 8 0.166667 8 0.166667 14 0.166667 14 0.166667 15 0.166667 15 0.166667 24 0.166667 Exact 0.166667 Monomial exponents: 1 0 0 1 0.041667 4 0.041667 8 0.041667 8 0.041667 14 0.041667 14 0.041667 15 0.041667 15 0.041667 24 0.041667 Exact 0.041667 Monomial exponents: 0 1 0 1 0.041667 4 0.041667 8 0.041667 8 0.041667 14 0.041667 14 0.041667 15 0.041667 15 0.041667 24 0.041667 Exact 0.041667 Monomial exponents: 0 0 1 1 0.041667 4 0.041667 8 0.041667 8 0.041667 14 0.041667 14 0.041667 15 0.041667 15 0.041667 24 0.041667 Exact 0.041667 Monomial exponents: 2 0 0 1 0.010417 4 0.016667 8 0.016667 8 0.016667 14 0.016667 14 0.016667 15 0.016667 15 0.016667 24 0.016667 Exact 0.016667 Monomial exponents: 1 1 0 1 0.010417 4 0.008333 8 0.008333 8 0.008333 14 0.008333 14 0.008333 15 0.008333 15 0.008333 24 0.008333 Exact 0.008333 Monomial exponents: 0 2 0 1 0.010417 4 0.016667 8 0.016667 8 0.016667 14 0.016667 14 0.016667 15 0.016667 15 0.016667 24 0.016667 Exact 0.016667 Monomial exponents: 1 0 1 1 0.010417 4 0.008333 8 0.008333 8 0.008333 14 0.008333 14 0.008333 15 0.008333 15 0.008333 24 0.008333 Exact 0.008333 Monomial exponents: 0 1 1 1 0.010417 4 0.008333 8 0.008333 8 0.008333 14 0.008333 14 0.008333 15 0.008333 15 0.008333 24 0.008333 Exact 0.008333 Monomial exponents: 0 0 2 1 0.010417 4 0.016667 8 0.016667 8 0.016667 14 0.016667 14 0.016667 15 0.016667 15 0.016667 24 0.016667 Exact 0.016667 Monomial exponents: 3 0 0 1 0.002604 4 0.008689 8 0.008333 8 0.008333 14 0.008333 14 0.008333 15 0.008333 15 0.008333 24 0.008333 Exact 0.008333 Monomial exponents: 2 1 0 1 0.002604 4 0.002659 8 0.002778 8 0.002778 14 0.002778 14 0.002778 15 0.002778 15 0.002778 24 0.002778 Exact 0.002778 Monomial exponents: 1 2 0 1 0.002604 4 0.002659 8 0.002778 8 0.002778 14 0.002778 14 0.002778 15 0.002778 15 0.002778 24 0.002778 Exact 0.002778 Monomial exponents: 0 3 0 1 0.002604 4 0.008689 8 0.008333 8 0.008333 14 0.008333 14 0.008333 15 0.008333 15 0.008333 24 0.008333 Exact 0.008333 Monomial exponents: 2 0 1 1 0.002604 4 0.002659 8 0.002778 8 0.002778 14 0.002778 14 0.002778 15 0.002778 15 0.002778 24 0.002778 Exact 0.002778 Monomial exponents: 1 1 1 1 0.002604 4 0.001508 8 0.001389 8 0.001389 14 0.001389 14 0.001389 15 0.001389 15 0.001389 24 0.001389 Exact 0.001389 Monomial exponents: 0 2 1 1 0.002604 4 0.002659 8 0.002778 8 0.002778 14 0.002778 14 0.002778 15 0.002778 15 0.002778 24 0.002778 Exact 0.002778 Monomial exponents: 1 0 2 1 0.002604 4 0.002659 8 0.002778 8 0.002778 14 0.002778 14 0.002778 15 0.002778 15 0.002778 24 0.002778 Exact 0.002778 Monomial exponents: 0 1 2 1 0.002604 4 0.002659 8 0.002778 8 0.002778 14 0.002778 14 0.002778 15 0.002778 15 0.002778 24 0.002778 Exact 0.002778 Monomial exponents: 0 0 3 1 0.002604 4 0.008689 8 0.008333 8 0.008333 14 0.008333 14 0.008333 15 0.008333 15 0.008333 24 0.008333 Exact 0.008333 Monomial exponents: 4 0 0 1 0.000651 4 0.004939 8 0.004762 8 0.005556 14 0.004762 14 0.004762 15 0.004762 15 0.004762 24 0.004762 Exact 0.004762 Monomial exponents: 3 1 0 1 0.000651 4 0.001250 8 0.001190 8 0.000926 14 0.001190 14 0.001190 15 0.001190 15 0.001190 24 0.001190 Exact 0.001190 Monomial exponents: 2 2 0 1 0.000651 4 0.000576 8 0.000737 8 0.000926 14 0.000794 14 0.000794 15 0.000794 15 0.000794 24 0.000794 Exact 0.000794 Monomial exponents: 1 3 0 1 0.000651 4 0.001250 8 0.001190 8 0.000926 14 0.001190 14 0.001190 15 0.001190 15 0.001190 24 0.001190 Exact 0.001190 Monomial exponents: 0 4 0 1 0.000651 4 0.004939 8 0.004762 8 0.005556 14 0.004762 14 0.004762 15 0.004762 15 0.004762 24 0.004762 Exact 0.004762 Monomial exponents: 3 0 1 1 0.000651 4 0.001250 8 0.001190 8 0.000926 14 0.001190 14 0.001190 15 0.001190 15 0.001190 24 0.001190 Exact 0.001190 Monomial exponents: 2 1 1 1 0.000651 4 0.000417 8 0.000425 8 0.000463 14 0.000397 14 0.000397 15 0.000397 15 0.000397 24 0.000397 Exact 0.000397 Monomial exponents: 1 2 1 1 0.000651 4 0.000417 8 0.000425 8 0.000463 14 0.000397 14 0.000397 15 0.000397 15 0.000397 24 0.000397 Exact 0.000397 Monomial exponents: 0 3 1 1 0.000651 4 0.001250 8 0.001190 8 0.000926 14 0.001190 14 0.001190 15 0.001190 15 0.001190 24 0.001190 Exact 0.001190 Monomial exponents: 2 0 2 1 0.000651 4 0.000576 8 0.000737 8 0.000926 14 0.000794 14 0.000794 15 0.000794 15 0.000794 24 0.000794 Exact 0.000794 Monomial exponents: 1 1 2 1 0.000651 4 0.000417 8 0.000425 8 0.000463 14 0.000397 14 0.000397 15 0.000397 15 0.000397 24 0.000397 Exact 0.000397 Monomial exponents: 0 2 2 1 0.000651 4 0.000576 8 0.000737 8 0.000926 14 0.000794 14 0.000794 15 0.000794 15 0.000794 24 0.000794 Exact 0.000794 Monomial exponents: 1 0 3 1 0.000651 4 0.001250 8 0.001190 8 0.000926 14 0.001190 14 0.001190 15 0.001190 15 0.001190 24 0.001190 Exact 0.001190 Monomial exponents: 0 1 3 1 0.000651 4 0.001250 8 0.001190 8 0.000926 14 0.001190 14 0.001190 15 0.001190 15 0.001190 24 0.001190 Exact 0.001190 Monomial exponents: 0 0 4 1 0.000651 4 0.004939 8 0.004762 8 0.005556 14 0.004762 14 0.004762 15 0.004762 15 0.004762 24 0.004762 Exact 0.004762 tetrahedron_felippa_rule_test(): Normal end of execution. 08-Jan-2022 10:30:55