Civil Engineering Reference
In-Depth Information
Table 6.9
Convergence characteristics of QL, LO and GETMe
QL
LO
GETMe
Cycle
NM
NM
NM
γ
min
γ
mean
γ
min
γ
mean
γ
min
γ
mean
0
0.000015
0.39299
0.000015
0.39299
0.000015
0.39299
1
0.000268
0.4391
30,018
0.000551
0.47608
96,392
0.000268
0.45755
65,062
2
0.000268
0.44857
16,849
0.001008
0.51875
96,174
0.000268
0.47924
53,434
3
0.000268
0.4505
7491
0.000418
0.53743
95,854
0.000268
0.4873
45,048
4
0.000268
0.45087
2417
0.001154
0.5456
95,648
0.000268
0.49082
38,971
5
0.000268
0.45094
617
0.001154
0.54961
95,778
0.000268
0.49258
34,284
6
0.000268
0.45096
135
0.001154
0.55188
95,950
0.000268
0.49356
30,482
7
0.000268
0.45096
26
0.001154
0.5533
96,092
0.000268
0.49415
27,592
8
0.000268
0.45096
6
0.001154
0.55424
96,141
0.000268
0.49451
25,018
9
0.000268
0.45096
1
0.001154
0.55488
96,188
0.000268
0.49473
23,177
10
0.000268
0.45096
1
0.001154
0.55532
96,194
0.000268
0.49487
21,456
Table 6.10
Combined scheme
NM
γ
min
γ
mean
0.000015
0.39299
0.000268
0.4391
30,018
0.000268
0.44857
16,849
0.000268
0.4505
7491
0.000268
0.45087
2417
0.000268
0.48072
55,836
0.000268
0.48962
45,156
0.000268
0.49292
38,396
0.000856
0.53103
96,227
0.00052
0.54503
95,994
0.001154
0.55055
95,844
methods, a combined scheme might be the most effective. As a numerical experiment, a
combined scheme (4 + 3 + 3) consisting of four cycles of QL, followed by three rounds of
GETMe and then further optimised with three cycles of LO is tested, as shown in Figure
6.34. The average results on a number of meshes are given by γ
min
= 0.001154 and γ
mean
=
0.55055. Relative to the three smoothing methods, the combined scheme gives the best
performance on both γ
min
and γ
mean
, and in terms of the CPU time, it is similar to that of
GETMe.
6.3.3.5 Examples: Node smoothing for hexahedral meshes
Examples of various size and characteristics using the three generic smoothing schemes,
namely, QL, LO and GETMe, will be presented in this section. The quality of a hexahedral
mesh depends on its elements, which are measured in turn based on the associated tetrahe-
dra at the vertices. The η value presented in Section 6.2.4 can be used in general; however,
in order to extend the quality measure also to inverted elements, the γ-quality of tetrahedral
elements will be used.
