28 August 2014 08:12:06 AM
PYRAMID_FELIPPA_RULE_PRB
C++ version
Test the PYRAMID_FELIPPA_RULE library.
PYRAMID__UNIT_MONOMIAL_TEST
For the unit pyramid,
PYRAMID__UNIT_MONOMIAL returns the exact value of the
integral of X^ALPHA Y^BETA Z^GAMMA
Volume = 1.33333
ALPHA BETA GAMMA INTEGRAL
0 0 0 1.33333
0 0 1 0.333333
0 0 2 0.133333
0 0 3 0.0666667
0 0 4 0.0380952
0 1 0 0
0 1 1 0
0 1 2 0
0 1 3 0
0 2 0 0.266667
0 2 1 0.0444444
0 2 2 0.0126984
0 3 0 0
0 3 1 0
0 4 0 0.114286
1 0 0 0
1 0 1 0
1 0 2 0
1 0 3 0
1 1 0 0
1 1 1 0
1 1 2 0
1 2 0 0
1 2 1 0
1 3 0 0
2 0 0 0.266667
2 0 1 0.0444444
2 0 2 0.0126984
2 1 0 0
2 1 1 0
2 2 0 0.0634921
3 0 0 0
3 0 1 0
3 1 0 0
4 0 0 0.114286
PYRAMID__UNIT_QUAD_TEST
For the unit pyramid,
we approximate monomial integrals with:
PYRAMID__UNIT_O01,
PYRAMID__UNIT_O05,
PYRAMID__UNIT_O06,
PYRAMID__UNIT_O08,
PYRAMID__UNIT_O08b,
PYRAMID__UNIT_O09,
PYRAMID__UNIT_O13,
PYRAMID__UNIT_O18,
PYRAMID__UNIT_O27,
PYRAMID__UNIT_O48,
Monomial exponents: 0 0 0
1 1.33333
5 1.33333
6 1.33333
8 1.33333
8 1.33333
9 1.33333
13 1.33333
18 1.33333
27 1.33333
48 1.33333
Exact 1.33333
Monomial exponents: 0 0 1
1 0.333333
5 0.333333
6 0.333333
8 0.333333
8 0.333333
9 0.333333
13 0.333333
18 0.333333
27 0.333333
48 0.333333
Exact 0.333333
Monomial exponents: 2 0 0
1 0
5 0.266667
6 0.266667
8 0.266667
8 0.266667
9 0.266667
13 0.266667
18 0.266667
27 0.266667
48 0.266667
Exact 0.266667
Monomial exponents: 0 2 0
1 0
5 0.266667
6 0.266667
8 0.266667
8 0.266667
9 0.266667
13 0.266667
18 0.266667
27 0.266667
48 0.266667
Exact 0.266667
Monomial exponents: 0 0 2
1 0.0833333
5 0.133333
6 0.133333
8 0.133333
8 0.133333
9 0.133333
13 0.133333
18 0.133333
27 0.133333
48 0.133333
Exact 0.133333
Monomial exponents: 2 0 1
1 0
5 0.0444444
6 0.0444444
8 0.0444444
8 0.0444444
9 0.0444444
13 0.0444444
18 0.0444444
27 0.0444444
48 0.0444444
Exact 0.0444444
Monomial exponents: 0 2 1
1 0
5 0.0444444
6 0.0444444
8 0.0444444
8 0.0444444
9 0.0444444
13 0.0444444
18 0.0444444
27 0.0444444
48 0.0444444
Exact 0.0444444
Monomial exponents: 0 0 3
1 0.0208333
5 0.0766667
6 0.0773148
8 0.0666667
8 0.0647619
9 0.0669312
13 0.0666504
18 0.0666667
27 0.0666667
48 0.0666667
Exact 0.0666667
Monomial exponents: 4 0 0
1 0
5 0.0632099
6 0.0634921
8 0.0632099
8 0.0632099
9 0.0634921
13 0.0664669
18 0.113778
27 0.114286
48 0.114286
Exact 0.114286
Monomial exponents: 2 2 0
1 0
5 0.0632099
6 0.0634921
8 0.0632099
8 0.0632099
9 0.0634921
13 0.0634921
18 0.0632099
27 0.0634921
48 0.0634921
Exact 0.0634921
Monomial exponents: 0 4 0
1 0
5 0.0632099
6 0.0634921
8 0.0632099
8 0.0632099
9 0.0634921
13 0.0664669
18 0.113778
27 0.114286
48 0.114286
Exact 0.114286
Monomial exponents: 2 0 2
1 0
5 0.00740741
6 0.00740741
8 0.0118519
8 0.0126984
9 0.0126984
13 0.0126984
18 0.0118519
27 0.0126984
48 0.0126984
Exact 0.0126984
Monomial exponents: 0 2 2
1 0
5 0.00740741
6 0.00740741
8 0.0118519
8 0.0126984
9 0.0126984
13 0.0126984
18 0.0118519
27 0.0126984
48 0.0126984
Exact 0.0126984
Monomial exponents: 0 0 4
1 0.00520833
5 0.0508889
6 0.0523148
8 0.0355556
8 0.0330884
9 0.0392038
13 0.0379673
18 0.0355556
27 0.0380952
48 0.0380952
Exact 0.0380952
Monomial exponents: 4 0 1
1 0
5 0.010535
6 0.010582
8 0.00855967
8 0.00818342
9 0.00793651
13 0.00894583
18 0.0154074
27 0.0142857
48 0.0142857
Exact 0.0142857
Monomial exponents: 2 2 1
1 0
5 0.010535
6 0.010582
8 0.00855967
8 0.00818342
9 0.00793651
13 0.00793651
18 0.00855967
27 0.00793651
48 0.00793651
Exact 0.00793651
Monomial exponents: 0 4 1
1 0
5 0.010535
6 0.010582
8 0.00855967
8 0.00818342
9 0.00793651
13 0.00894583
18 0.0154074
27 0.0142857
48 0.0142857
Exact 0.0142857
Monomial exponents: 2 0 3
1 0
5 0.00123457
6 0.00123457
8 0.00493827
8 0.00544218
9 0.00466742
13 0.0047619
18 0.00493827
27 0.0047619
48 0.0047619
Exact 0.0047619
Monomial exponents: 0 2 3
1 0
5 0.00123457
6 0.00123457
8 0.00493827
8 0.00544218
9 0.00466742
13 0.0047619
18 0.00493827
27 0.0047619
48 0.0047619
Exact 0.0047619
Monomial exponents: 0 0 5
1 0.00130208
5 0.0351593
6 0.0371881
8 0.0192593
8 0.0170978
9 0.0261261
13 0.02387
18 0.0192593
27 0.0238095
48 0.0238095
Exact 0.0238095
PYRAMID_FELIPPA_RULE_PRB
Normal end of execution.
28 August 2014 08:12:06 AM