Civil Engineering Reference
In-Depth Information
Before optimisation, µ = 0.6006
After optimisation, µ = 0.8308
Figure 6.21
Optimisation of quadrilateral and triangular elements.
Table 6.4
Smoothing a mixed mesh by QL, GETMe and a combined scheme
QL
GETMe
Combined scheme
Cycle
μ
min
μ
mean
NM
μ
min
μ
mean
NM
μ
min
μ
mean
NM
0
0.10014
0.6006
0.10014
0.6006
0.10014
0.6006
1
0.39294
0.7985
32
0.19559
0.7133
32
32
2
0.43302
0.8232
25
0.27505
0.7610
37
0.43302
0.81118
31
3
0.43302
0.8239
15
0.39369
0.7851
35
26
4
0.43302
0.8236
8
0.40485
0.7985
34
0.43302
0.82921
27
5
0.43302
0.8236
3
0.41122
0.8067
35
17
6
0.43302
0.8236
0
0.41122
0.8109
29
0.43302
0.83077
15
7
0.43302
0.8236
0
0.41817
0.8135
29
12
8
0.43302
0.8236
0
0.41817
0.8154
28
0.43302
0.83077
13
9
0.43302
0.8236
0
0.41817
0.8165
25
9
10
0.43302
0.8236
0
0.41817
0.8177
26
0.43302
0.83077
12
achieves the converged μ
min
and μ
mean
values virtually in the first four iterations. Hence, if QL
is used for mesh optimisation, five cycles will, in general, be sufficient.
There are 3450 triangles and 1233 quadrilaterals in the second mixed mesh of randomly
generated points, as shown in Figure 6.22, to test the performance of QL smoothing, the
GETMe and a combined scheme for mixed meshes of more elements. The results of μ
min
and μ
mean
values for triangles and quadrilaterals of applying five cycles of QL, five cycles
of GETMe and the combined scheme consisting of five cycles of QL followed by five cycles
of GETMe are presented in Table 6.5, in which Ti
i
and Q
i
are, respectively, the quality of
triangles and quadrilaterals after the i
th
smoothing cycle. QL achieves higher values in μ
mean
both for triangles and quadrilaterals; on the other hand, GETMe achieves better results
in μ
min
values. Extremely high-quality mesh is produced by the combined scheme with the
best results in μ
min
and μ
mean
values for both triangles and quadrilaterals. Hence, for effi-
ciency consideration, we can just apply a few cycles of QL to a mixed mesh, and in case
