Civil Engineering Reference
In-Depth Information
Table 7.6
Estimating the number of additional layers for convergence
Division
1
2 × 2 × 2
3 × 3 × 3
4 × 4 × 4
5 × 5 × 5
6 × 6 × 6
Zonal insertion of 10 million points, N
x
= 215
NE
67,464,342
67,464,342
67,464,342
67,464,342
67,464,342
67,464,342
NB
147,072
284,383
631,810
1,230,369
2,175,883
3,547,541
NT
67,611,414
71,983,723
76,850,496
82,399,338
88,780,183
96,182,524
NR
4,234,998
8,754,344
13,704,627
19,139,958
25,170,641
0.0628
0.1298
0.2031
0.2837
0.3731
μ
= NR/NE
1.12
1.16
1.21
1.27
1.34
λ
CPU Time
115.5
126.25
137.41
151.37
167.62
188.99
μ
*
0.0931
0.1897
0.3106
0.4513
0.6363
1.67
1.70
1.85
2.02
2.28
λ
*
Zonal insertion of 20 million points, N
x
= 271
NE
135,018,138
135,018,138
135,018,138
135,018,138
135,018,138
135,018,138
NB
236,282
568,667
1,263,026
2,460,783
4,351,733
7,095,280
NT
135,254,420
142,008,870
149,502,380
157,952,381
167,603,326
178,777,499
NR
6,422,065
13,221,216
20,473,460
28,233,455
36,664,081
μ
= NR/NE
0.0476
0.0979
0.1516
0.2091
0.2715
1.07
1.11
1.14
1.18
1.23
λ
CPU Time
232.5
255.05
277.27
299.9
328.66
360.69
μ
*
0.0970
0.1926
0.2899
0.4136
0.5514
2.19
2.17
2.18
2.34
2.49
λ
*
Zonal insertion of 30 million points, N
x
= 311
NE
202,594,412
202,594,412
202,594,412
202,594,412
202,594,412
202,594,412
NB
303,892
853,194
1,895,403
3,691,170
6,527,964
10,642,326
NT
202,898,304
211,652,978
221,298,077
232,105,002
244,383,071
258,518,694
NR
8,205,372
16,808,262
25,819,420
35,260,695
45,281,956
μ
= NR/NE
0.0405
0.0830
0.1274
0.1740
0.2235
1.05
1.08
1.10
1.13
1.16
λ
CPU Time
350.5
379.38
409.74
441.82
481.3
524.08
0.0824
0.1690
0.2605
0.3732
0.4952
μ
*
2.14
2.19
2.25
2.42
2.57
λ
*
Zonal insertion of 40 million points, N
x
= 342
NE 270,141,497 270,141,497 270,141,497 270,141,497 270,141,497 270,141,497
NB 337,677 1,137,523 2,527,204 4,921,467 8,703,523 14,190,462
NT 270,479,174 281,053,809 292,652,576 305,504,726 320,174,364 336,983,137
NR 9,774,789 19,983,875 30,441,762 41,329,344 52,651,178
μ
= NR/NE 0.0362 0.0740 0.1127 0.1530 0.1949
λ
1.03 1.05 1.07 1.09 1.11
CPU Time 475 510.21 549.51 591.23 638.19 706.74
μ
*
0.0741 0.1569 0.2447 0.3436 0.4879
λ
*
2.11 2.24 2.32 2.45 2.78
Note: NT = total number of tetrahedra generated; NE = number of tetrahedra in the convex hull; NB = number of bound-
ary tetrahedra connected to auxiliary corner points; NR = NT-NB-NE = number of redundant tetrahedra between zones.
