Civil Engineering Reference
In-Depth Information
0.113176
0.889994
0.998621
0.999989
1.000000
0.214217
0.968209
0.999812
0.999998
1.000000
0.293152
0.942202
0.994724
0.999455
0.999943
0.08455
0.819511
0.975196
0.988742
0.993422
Figure 6.31
Polyhedral elements and their
γ
-qualities under GETMe transformations.
Table 6.6
Co-ordinates of polyhedral elements before GETMe
transformations
Node
Tetrahedron
Hexahedron
Pentahedron
Pyramid
1
(0, 0, 0)
(0, 1, 0)
(0, 0, 0)
(0, 0, 0)
2
(20, 0, 0)
(3, 0, 0)
(1, 0, 0)
(5, 0, 0)
3
(5, 2, 0)
(2, 2, 0)
(1,
3
, 1 )
(15, 5, 0)
4
(0, 0, 30)
(0, 2, 0)
(0, 0, 4)
(5, 10, 0)
5
(0, 0, 2)
(1, 0, 1)
(0, 0, 1)
6
(8, 0, 2)
(1,
3
, 2 )
7
(2, 2, 4)
8
(0, 2, 8)
4/5
1/2
1/2
1/2
λ
carried out to each mesh, and the results are presented in Table 6.7, in which NE = number
of tetrahedra, γ
min
= minimum γ-quality, γ
mean
= mean γ-quality and Aver = average values of
the ten test runs. It can be seen that the performance of all three node-smoothing schemes is
quite different in which LO gives the best results in terms of both γ
min
and γ
mean
values, fol-
lowed by GETMe and then QL. As for the average CPU time for ten cycles of node smooth-
ing, QL took 6.14 s, LO took 42.69 s and GETMe took 21.94 s on a PC i7 CPU 870 at
2.93 GHz running on XP mode Compaq Visual Fortran with QuickWin graphics supports.
There are three major parameters in the GETMe scheme, namely, λ to control the rate
of convergence of transformation, weight factor w for elements connected to the node and
