14 June 2014 02:34:00 PM
TETRAHEDRON_NCC_RULE_PRB:
C++ version
Test the TETRAHEDRON_NCC_RULE library.
TEST01
TETRAHEDRON_NCC_RULE_NUM returns the number of rules;
TETRAHEDRON_NCC_DEGREE returns the degree of a rule;
TETRAHEDRON_NCC_ORDER_NUM returns the order of a rule.
Number of available rules = 7
Rule Degree Order
1 0 1
2 1 4
3 2 10
4 3 20
5 4 35
6 5 56
7 6 84
TEST02
TETRAHEDRON_NCC_RULE returns the points and weights
of an NCC rule for the tetrahedron.
In this test, we simply check that the weights
sum to 1.
Number of available rules = 7
Rule Sum of weights
1 1
2 1
3 1
4 1
5 1
6 1
7 1
TEST03
TETRAHEDRON_NCC_RULE returns the points and weights
of an NCC rule for the tetrahedron.
In this test, we simply check that, for each
quadrature point, the barycentric coordinates
add up to 1.
Rule Suborder Sum of coordinates
1 1
1
2 1
1
3 2
1
1
4 3
1
1
1
5 5
1
1
1
1
1
6 6
1
1
1
1
1
1
7 9
1
1
1
1
1
0.9999999999999999
1
1
0.9999999999999999
TEST04
TETRAHEDRON_NCC_RULE returns the points and weights of
an NCC rule for the unit tetrahedron.
This routine uses those rules to estimate the
integral of monomomials in the unit tetrahedron.
Integrate 6 * X^0 * Y^0 * Z^0
Rule QUAD ERROR
1 1 0
2 1 0
3 1 0
4 1 0
5 1 2.220446049250313e-16
6 0.9999999999999997 3.33066907387547e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 24 * X^0 * Y^0 * Z^1
Rule QUAD ERROR
1 1 0
2 1 0
3 1 0
4 1 0
5 1 0
6 0.9999999999999997 3.33066907387547e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 60 * X^0 * Y^0 * Z^2
Rule QUAD ERROR
1 0.625 0.375
2 2.5 1.5
3 1 0
4 1 0
5 1 4.440892098500626e-16
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 120 * X^0 * Y^0 * Z^3
Rule QUAD ERROR
1 0.3125 0.6875
2 5 4
3 0.5 0.5
4 1 0
5 1 0
6 0.9999999999999993 6.661338147750939e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 210 * X^0 * Y^0 * Z^4
Rule QUAD ERROR
1 0.13671875 0.86328125
2 8.75 7.75
3 -0.4375 1.4375
4 1.166666666666667 0.1666666666666665
5 1 2.220446049250313e-16
6 0.9999999999999998 2.220446049250313e-16
7 1 4.440892098500626e-16
Integrate 336 * X^0 * Y^0 * Z^5
Rule QUAD ERROR
1 0.0546875 0.9453125
2 14 13
3 -1.75 2.75
4 1.555555555555556 0.5555555555555558
5 0.9375000000000004 0.06249999999999956
6 0.9999999999999998 2.220446049250313e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 504 * X^0 * Y^0 * Z^6
Rule QUAD ERROR
1 0.0205078125 0.9794921875
2 21 20
3 -3.412500000000001 4.412500000000001
4 2.177777777777778 1.177777777777778
5 0.7593750000000001 0.2406249999999999
6 1.023839999999999 0.0238399999999992
7 1.000000000000001 1.332267629550188e-15
Integrate 24 * X^0 * Y^1 * Z^0
Rule QUAD ERROR
1 1 0
2 1 0
3 1 0
4 1 0
5 1 0
6 0.9999999999999996 4.440892098500626e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 120 * X^0 * Y^1 * Z^1
Rule QUAD ERROR
1 1.25 0.25
2 0 1
3 1 0
4 1 0
5 1 0
6 0.9999999999999998 2.220446049250313e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 360 * X^0 * Y^1 * Z^2
Rule QUAD ERROR
1 0.9375 0.0625
2 0 1
3 1.5 0.5
4 1 0
5 1 0
6 1 0
7 0.9999999999999998 2.220446049250313e-16
Integrate 840 * X^0 * Y^1 * Z^3
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 1.75 0.75
4 0.7777777777777778 0.2222222222222222
5 1 0
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 1680 * X^0 * Y^1 * Z^4
Rule QUAD ERROR
1 0.2734375 0.7265625
2 0 1
3 1.75 0.75
4 0.5185185185185185 0.4814814814814815
5 1.104166666666667 0.1041666666666667
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 3024 * X^0 * Y^1 * Z^5
Rule QUAD ERROR
1 0.123046875 0.876953125
2 0 1
3 1.575 0.5750000000000002
4 0.3111111111111111 0.6888888888888889
5 1.29375 0.2937500000000002
6 0.9523199999999996 0.04768000000000039
7 1 4.440892098500626e-16
Integrate 60 * X^0 * Y^2 * Z^0
Rule QUAD ERROR
1 0.625 0.375
2 2.5 1.5
3 1 0
4 1 0
5 1 4.440892098500626e-16
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 360 * X^0 * Y^2 * Z^1
Rule QUAD ERROR
1 0.9375 0.0625
2 0 1
3 1.5 0.5
4 1 0
5 1 2.220446049250313e-16
6 1 0
7 1 0
Integrate 1260 * X^0 * Y^2 * Z^2
Rule QUAD ERROR
1 0.8203125 0.1796875
2 0 1
3 2.625 1.625
4 1.166666666666667 0.1666666666666665
5 1 0
6 0.9999999999999997 3.33066907387547e-16
7 1 0
Integrate 3360 * X^0 * Y^2 * Z^3
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 3.5 2.5
4 1.037037037037037 0.03703703703703698
5 0.9583333333333333 0.04166666666666674
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 7560 * X^0 * Y^2 * Z^4
Rule QUAD ERROR
1 0.3076171875 0.6923828125
2 0 1
3 3.9375 2.9375
4 0.7777777777777778 0.2222222222222222
5 1.078125 0.078125
6 1.0512 0.05119999999999969
7 1 0
Integrate 120 * X^0 * Y^3 * Z^0
Rule QUAD ERROR
1 0.3125 0.6875
2 5 4
3 0.5 0.5
4 1 0
5 1 0
6 0.9999999999999993 6.661338147750939e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 840 * X^0 * Y^3 * Z^1
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 1.75 0.75
4 0.7777777777777778 0.2222222222222222
5 1 0
6 1 0
7 1 0
Integrate 3360 * X^0 * Y^3 * Z^2
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 3.5 2.5
4 1.037037037037037 0.03703703703703698
5 0.9583333333333333 0.04166666666666674
6 0.9999999999999997 3.33066907387547e-16
7 1 0
Integrate 10080 * X^0 * Y^3 * Z^3
Rule QUAD ERROR
1 0.41015625 0.58984375
2 0 1
3 5.25 4.25
4 1.037037037037037 0.03703703703703698
5 0.7500000000000001 0.2499999999999999
6 0.9503999999999998 0.0496000000000002
7 1 0
Integrate 210 * X^0 * Y^4 * Z^0
Rule QUAD ERROR
1 0.13671875 0.86328125
2 8.75 7.75
3 -0.4375 1.4375
4 1.166666666666667 0.1666666666666665
5 1 2.220446049250313e-16
6 1 0
7 1 2.220446049250313e-16
Integrate 1680 * X^0 * Y^4 * Z^1
Rule QUAD ERROR
1 0.2734375 0.7265625
2 0 1
3 1.75 0.75
4 0.5185185185185185 0.4814814814814815
5 1.104166666666667 0.1041666666666667
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 7560 * X^0 * Y^4 * Z^2
Rule QUAD ERROR
1 0.3076171875 0.6923828125
2 0 1
3 3.9375 2.9375
4 0.7777777777777777 0.2222222222222223
5 1.078125 0.078125
6 1.0512 0.05120000000000013
7 1 2.220446049250313e-16
Integrate 336 * X^0 * Y^5 * Z^0
Rule QUAD ERROR
1 0.0546875 0.9453125
2 14 13
3 -1.75 2.75
4 1.555555555555556 0.5555555555555558
5 0.9375000000000004 0.06249999999999956
6 0.9999999999999997 3.33066907387547e-16
7 0.9999999999999997 3.33066907387547e-16
Integrate 3024 * X^0 * Y^5 * Z^1
Rule QUAD ERROR
1 0.123046875 0.876953125
2 0 1
3 1.575 0.5750000000000002
4 0.311111111111111 0.688888888888889
5 1.29375 0.2937500000000002
6 0.9523199999999995 0.0476800000000005
7 1.000000000000001 6.661338147750939e-16
Integrate 504 * X^0 * Y^6 * Z^0
Rule QUAD ERROR
1 0.0205078125 0.9794921875
2 21 20
3 -3.412500000000001 4.412500000000001
4 2.177777777777778 1.177777777777778
5 0.7593750000000001 0.2406249999999999
6 1.023839999999999 0.0238399999999992
7 1.000000000000001 1.332267629550188e-15
Integrate 24 * X^1 * Y^0 * Z^0
Rule QUAD ERROR
1 1 0
2 1 0
3 1 0
4 1 0
5 1 0
6 0.9999999999999993 6.661338147750939e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 120 * X^1 * Y^0 * Z^1
Rule QUAD ERROR
1 1.25 0.25
2 0 1
3 1 0
4 1 0
5 1 0
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 360 * X^1 * Y^0 * Z^2
Rule QUAD ERROR
1 0.9375 0.0625
2 0 1
3 1.5 0.5
4 1 0
5 1 0
6 1 0
7 1 0
Integrate 840 * X^1 * Y^0 * Z^3
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 1.75 0.75
4 0.7777777777777778 0.2222222222222222
5 1 0
6 1 0
7 1 0
Integrate 1680 * X^1 * Y^0 * Z^4
Rule QUAD ERROR
1 0.2734375 0.7265625
2 0 1
3 1.75 0.75
4 0.5185185185185185 0.4814814814814815
5 1.104166666666667 0.1041666666666667
6 1 0
7 1 0
Integrate 3024 * X^1 * Y^0 * Z^5
Rule QUAD ERROR
1 0.123046875 0.876953125
2 0 1
3 1.575 0.5750000000000002
4 0.3111111111111111 0.6888888888888889
5 1.29375 0.2937500000000002
6 0.9523199999999996 0.04768000000000039
7 1 4.440892098500626e-16
Integrate 120 * X^1 * Y^1 * Z^0
Rule QUAD ERROR
1 1.25 0.25
2 0 1
3 1 0
4 1 0
5 1 2.220446049250313e-16
6 0.9999999999999998 2.220446049250313e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 720 * X^1 * Y^1 * Z^1
Rule QUAD ERROR
1 1.875 0.875
2 0 1
3 0 1
4 1 0
5 1 0
6 1 0
7 1 0
Integrate 2520 * X^1 * Y^1 * Z^2
Rule QUAD ERROR
1 1.640625 0.640625
2 0 1
3 0 1
4 1.166666666666667 0.1666666666666665
5 1 0
6 1 0
7 1 0
Integrate 6720 * X^1 * Y^1 * Z^3
Rule QUAD ERROR
1 1.09375 0.09375
2 0 1
3 0 1
4 1.037037037037037 0.03703703703703698
5 0.8333333333333333 0.1666666666666667
6 1 0
7 0.9999999999999998 2.220446049250313e-16
Integrate 15120 * X^1 * Y^1 * Z^4
Rule QUAD ERROR
1 0.615234375 0.384765625
2 0 1
3 0 1
4 0.7777777777777778 0.2222222222222222
5 0.65625 0.34375
6 1.068 0.06799999999999984
7 0.9999999999999998 2.220446049250313e-16
Integrate 360 * X^1 * Y^2 * Z^0
Rule QUAD ERROR
1 0.9375 0.0625
2 0 1
3 1.5 0.5
4 1 0
5 1 0
6 1 0
7 1 0
Integrate 2520 * X^1 * Y^2 * Z^1
Rule QUAD ERROR
1 1.640625 0.640625
2 0 1
3 0 1
4 1.166666666666667 0.1666666666666665
5 1 0
6 1 0
7 1 0
Integrate 10080 * X^1 * Y^2 * Z^2
Rule QUAD ERROR
1 1.640625 0.640625
2 0 1
3 0 1
4 1.555555555555555 0.5555555555555554
5 1.125 0.125
6 1 0
7 1 0
Integrate 30240 * X^1 * Y^2 * Z^3
Rule QUAD ERROR
1 1.23046875 0.23046875
2 0 1
3 0 1
4 1.555555555555556 0.5555555555555556
5 1.03125 0.03125
6 0.972 0.02800000000000002
7 1 0
Integrate 840 * X^1 * Y^3 * Z^0
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 1.75 0.75
4 0.7777777777777778 0.2222222222222222
5 1 0
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 6720 * X^1 * Y^3 * Z^1
Rule QUAD ERROR
1 1.09375 0.09375
2 0 1
3 0 1
4 1.037037037037037 0.03703703703703698
5 0.8333333333333333 0.1666666666666667
6 1 0
7 1 0
Integrate 30240 * X^1 * Y^3 * Z^2
Rule QUAD ERROR
1 1.23046875 0.23046875
2 0 1
3 0 1
4 1.555555555555555 0.5555555555555554
5 1.03125 0.03125
6 0.9720000000000001 0.02799999999999991
7 1 0
Integrate 1680 * X^1 * Y^4 * Z^0
Rule QUAD ERROR
1 0.2734375 0.7265625
2 0 1
3 1.75 0.75
4 0.5185185185185185 0.4814814814814815
5 1.104166666666667 0.1041666666666667
6 1 0
7 1 0
Integrate 15120 * X^1 * Y^4 * Z^1
Rule QUAD ERROR
1 0.615234375 0.384765625
2 0 1
3 0 1
4 0.7777777777777778 0.2222222222222222
5 0.65625 0.34375
6 1.068 0.06799999999999962
7 0.9999999999999998 2.220446049250313e-16
Integrate 3024 * X^1 * Y^5 * Z^0
Rule QUAD ERROR
1 0.123046875 0.876953125
2 0 1
3 1.575 0.5750000000000002
4 0.3111111111111111 0.6888888888888889
5 1.29375 0.2937500000000002
6 0.9523199999999996 0.04768000000000039
7 1 4.440892098500626e-16
Integrate 60 * X^2 * Y^0 * Z^0
Rule QUAD ERROR
1 0.625 0.375
2 2.5 1.5
3 1 0
4 1 0
5 1 0
6 0.9999999999999998 2.220446049250313e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 360 * X^2 * Y^0 * Z^1
Rule QUAD ERROR
1 0.9375 0.0625
2 0 1
3 1.5 0.5
4 1 0
5 1 0
6 1 0
7 1 0
Integrate 1260 * X^2 * Y^0 * Z^2
Rule QUAD ERROR
1 0.8203125 0.1796875
2 0 1
3 2.625 1.625
4 1.166666666666667 0.1666666666666665
5 1 0
6 0.9999999999999997 3.33066907387547e-16
7 1 0
Integrate 3360 * X^2 * Y^0 * Z^3
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 3.5 2.5
4 1.037037037037037 0.03703703703703698
5 0.9583333333333333 0.04166666666666674
6 0.9999999999999998 2.220446049250313e-16
7 1 0
Integrate 7560 * X^2 * Y^0 * Z^4
Rule QUAD ERROR
1 0.3076171875 0.6923828125
2 0 1
3 3.9375 2.9375
4 0.7777777777777778 0.2222222222222222
5 1.078125 0.078125
6 1.0512 0.05119999999999969
7 1 0
Integrate 360 * X^2 * Y^1 * Z^0
Rule QUAD ERROR
1 0.9375 0.0625
2 0 1
3 1.5 0.5
4 1 0
5 1 0
6 1 0
7 1 2.220446049250313e-16
Integrate 2520 * X^2 * Y^1 * Z^1
Rule QUAD ERROR
1 1.640625 0.640625
2 0 1
3 0 1
4 1.166666666666667 0.1666666666666665
5 1 0
6 1 0
7 1 0
Integrate 10080 * X^2 * Y^1 * Z^2
Rule QUAD ERROR
1 1.640625 0.640625
2 0 1
3 0 1
4 1.555555555555555 0.5555555555555554
5 1.125 0.1250000000000002
6 1 2.220446049250313e-16
7 1 0
Integrate 30240 * X^2 * Y^1 * Z^3
Rule QUAD ERROR
1 1.23046875 0.23046875
2 0 1
3 0 1
4 1.555555555555556 0.5555555555555556
5 1.03125 0.03125
6 0.9720000000000001 0.02799999999999991
7 1 0
Integrate 1260 * X^2 * Y^2 * Z^0
Rule QUAD ERROR
1 0.8203125 0.1796875
2 0 1
3 2.625 1.625
4 1.166666666666667 0.1666666666666665
5 1 0
6 0.9999999999999997 3.33066907387547e-16
7 1 0
Integrate 10080 * X^2 * Y^2 * Z^1
Rule QUAD ERROR
1 1.640625 0.640625
2 0 1
3 0 1
4 1.555555555555556 0.5555555555555556
5 1.125 0.1250000000000002
6 1 2.220446049250313e-16
7 1 0
Integrate 45360 * X^2 * Y^2 * Z^2
Rule QUAD ERROR
1 1.845703125 0.845703125
2 0 1
3 0 1
4 2.333333333333333 1.333333333333333
5 1.40625 0.4062500000000002
6 1.044 0.04400000000000048
7 1 0
Integrate 3360 * X^2 * Y^3 * Z^0
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 3.5 2.5
4 1.037037037037037 0.03703703703703698
5 0.9583333333333333 0.04166666666666674
6 1 0
7 1 0
Integrate 30240 * X^2 * Y^3 * Z^1
Rule QUAD ERROR
1 1.23046875 0.23046875
2 0 1
3 0 1
4 1.555555555555556 0.5555555555555556
5 1.03125 0.03125
6 0.9720000000000004 0.02799999999999958
7 1 0
Integrate 7560 * X^2 * Y^4 * Z^0
Rule QUAD ERROR
1 0.3076171875 0.6923828125
2 0 1
3 3.9375 2.9375
4 0.7777777777777778 0.2222222222222222
5 1.078125 0.078125
6 1.0512 0.05119999999999969
7 1 2.220446049250313e-16
Integrate 120 * X^3 * Y^0 * Z^0
Rule QUAD ERROR
1 0.3125 0.6875
2 5 4
3 0.5 0.5
4 1 0
5 1 0
6 0.9999999999999992 7.771561172376096e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 840 * X^3 * Y^0 * Z^1
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 1.75 0.75
4 0.7777777777777778 0.2222222222222222
5 1 0
6 1 0
7 1 0
Integrate 3360 * X^3 * Y^0 * Z^2
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 3.5 2.5
4 1.037037037037037 0.03703703703703698
5 0.9583333333333333 0.04166666666666674
6 0.9999999999999997 3.33066907387547e-16
7 1 0
Integrate 10080 * X^3 * Y^0 * Z^3
Rule QUAD ERROR
1 0.41015625 0.58984375
2 0 1
3 5.25 4.25
4 1.037037037037037 0.03703703703703698
5 0.7500000000000001 0.2499999999999999
6 0.9503999999999998 0.0496000000000002
7 1 0
Integrate 840 * X^3 * Y^1 * Z^0
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 1.75 0.75
4 0.7777777777777778 0.2222222222222222
5 1 0
6 1 0
7 1 0
Integrate 6720 * X^3 * Y^1 * Z^1
Rule QUAD ERROR
1 1.09375 0.09375
2 0 1
3 0 1
4 1.037037037037037 0.03703703703703698
5 0.8333333333333333 0.1666666666666667
6 1 0
7 1 0
Integrate 30240 * X^3 * Y^1 * Z^2
Rule QUAD ERROR
1 1.23046875 0.23046875
2 0 1
3 0 1
4 1.555555555555555 0.5555555555555554
5 1.03125 0.03125
6 0.9720000000000002 0.0279999999999998
7 1 0
Integrate 3360 * X^3 * Y^2 * Z^0
Rule QUAD ERROR
1 0.546875 0.453125
2 0 1
3 3.5 2.5
4 1.037037037037037 0.03703703703703698
5 0.9583333333333333 0.04166666666666674
6 0.9999999999999997 3.33066907387547e-16
7 1 0
Integrate 30240 * X^3 * Y^2 * Z^1
Rule QUAD ERROR
1 1.23046875 0.23046875
2 0 1
3 0 1
4 1.555555555555556 0.5555555555555556
5 1.03125 0.03125
6 0.9720000000000001 0.02799999999999991
7 1 0
Integrate 10080 * X^3 * Y^3 * Z^0
Rule QUAD ERROR
1 0.41015625 0.58984375
2 0 1
3 5.25 4.25
4 1.037037037037037 0.03703703703703698
5 0.7500000000000001 0.2499999999999999
6 0.9504000000000001 0.04959999999999987
7 1 0
Integrate 210 * X^4 * Y^0 * Z^0
Rule QUAD ERROR
1 0.13671875 0.86328125
2 8.75 7.75
3 -0.4375 1.4375
4 1.166666666666667 0.1666666666666665
5 1 2.220446049250313e-16
6 1 2.220446049250313e-16
7 1 4.440892098500626e-16
Integrate 1680 * X^4 * Y^0 * Z^1
Rule QUAD ERROR
1 0.2734375 0.7265625
2 0 1
3 1.75 0.75
4 0.5185185185185185 0.4814814814814815
5 1.104166666666667 0.1041666666666667
6 0.9999999999999997 3.33066907387547e-16
7 1 2.220446049250313e-16
Integrate 7560 * X^4 * Y^0 * Z^2
Rule QUAD ERROR
1 0.3076171875 0.6923828125
2 0 1
3 3.9375 2.9375
4 0.7777777777777777 0.2222222222222223
5 1.078125 0.078125
6 1.0512 0.05119999999999991
7 1 2.220446049250313e-16
Integrate 1680 * X^4 * Y^1 * Z^0
Rule QUAD ERROR
1 0.2734375 0.7265625
2 0 1
3 1.75 0.75
4 0.5185185185185185 0.4814814814814815
5 1.104166666666667 0.1041666666666667
6 0.9999999999999997 3.33066907387547e-16
7 1 2.220446049250313e-16
Integrate 15120 * X^4 * Y^1 * Z^1
Rule QUAD ERROR
1 0.615234375 0.384765625
2 0 1
3 0 1
4 0.7777777777777777 0.2222222222222223
5 0.65625 0.34375
6 1.068 0.06799999999999962
7 1 0
Integrate 7560 * X^4 * Y^2 * Z^0
Rule QUAD ERROR
1 0.3076171875 0.6923828125
2 0 1
3 3.9375 2.9375
4 0.7777777777777777 0.2222222222222223
5 1.078125 0.078125
6 1.0512 0.05119999999999991
7 1 2.220446049250313e-16
Integrate 336 * X^5 * Y^0 * Z^0
Rule QUAD ERROR
1 0.0546875 0.9453125
2 14 13
3 -1.75 2.75
4 1.555555555555556 0.5555555555555558
5 0.9375000000000006 0.06249999999999944
6 0.9999999999999997 3.33066907387547e-16
7 0.9999999999999998 2.220446049250313e-16
Integrate 3024 * X^5 * Y^0 * Z^1
Rule QUAD ERROR
1 0.123046875 0.876953125
2 0 1
3 1.575 0.5750000000000002
4 0.311111111111111 0.688888888888889
5 1.29375 0.2937500000000002
6 0.9523199999999994 0.04768000000000061
7 1 4.440892098500626e-16
Integrate 3024 * X^5 * Y^1 * Z^0
Rule QUAD ERROR
1 0.123046875 0.876953125
2 0 1
3 1.575 0.5750000000000002
4 0.311111111111111 0.688888888888889
5 1.29375 0.2937500000000002
6 0.9523199999999994 0.04768000000000061
7 1 4.440892098500626e-16
Integrate 504 * X^6 * Y^0 * Z^0
Rule QUAD ERROR
1 0.0205078125 0.9794921875
2 21 20
3 -3.412500000000001 4.412500000000001
4 2.177777777777778 1.177777777777778
5 0.7593750000000001 0.2406249999999999
6 1.023839999999999 0.02383999999999897
7 1.000000000000002 1.77635683940025e-15
TEST06
REFERENCE_TO_PHYSICAL_T4 transforms a rule
on the unit (reference) tetrahedron to a rule on
an arbitrary (physical) tetrahedron.
The reference tetrahedron:
1 0 0 0
2 1 0 0
3 0 1 0
4 0 0 1
Rule 3 for reference tetrahedron
with volume = 0.1666666666666667
X Y Z W
0 0 0 0 -0.05
1 0 0 1 -0.05
2 0 1 0 -0.05
3 1 0 0 -0.05
4 0.5 0.5 0 0.2
5 0.5 0 0.5 0.2
6 0.5 0 0 0.2
7 0 0.5 0.5 0.2
8 0 0.5 0 0.2
9 0 0 0.5 0.2
The physical tetrahedron:
1 4 5 1
2 6 5 1
3 4 8 1
4 4 5 5
Rule 3 for physical tetrahedron
with volume = 4
X Y Z W
0 4 5 1 -0.05
1 4 5 5 -0.05
2 4 8 1 -0.05
3 6 5 1 -0.05
4 5 6.5 1 0.2
5 5 5 3 0.2
6 5 5 1 0.2
7 4 6.5 3 0.2
8 4 6.5 1 0.2
9 4 5 3 0.2
TEST06
TETRAHEDRON_NCC_RULE returns the points and weights
of an NCC rule for the tetrahedron.
In this test, we simply print rule 4
The compressed rule:
Number of suborders = 3
S Sub Weight Xsi1 Xsi2 Xsi3 Xsi4
1 4 0.025 0 0 0 1
2 12 0 0 0 0.3333 0.6667
3 4 0.225 0.3333 0.3333 0.3333 0
The full rule:
Order = 20
O Weight X Y Z
TETRAHEDRON_NCC_RULE_PRB:
Normal end of execution.
14 June 2014 02:34:00 PM