Civil Engineering Reference
In-Depth Information
3000
RG_100M
2500
MG_100M
2000
KD_100M
1500
1000
500
0
Uniform
Line
Cross
Circle
Spiral
Cluster
Point distributions
Figure 8.47
CPU time for various distributions of 100 million points.
cluster distribution than that for other distributions. Kd-tree insertion was not very stable
either, as rapid increase in the CPU time was observed for the insertion of the cross and the
spiral distributions. For the insertion of 100 million points, similar changes from 1 million
points to 10 million points are observed, except that the effects are more pronounced. For the
case of large point sets of 100 million points, the cluster distribution is the worst distribution
pattern for regular grid insertion, whereas cross and spiral distributions are tough cases for
the kd-tree insertion. The multi-grid insertion scheme is the most stable and efficient out of the
three insertion methods over the range of points inserted and the distribution patterns tested.
One more example of point distribution with mixed patterns to simulate practical MG
problems is shown in Figure 8.48, in which there is a more gradual change in nodal spac-
ing between points. The number of points has been increased progressively from 2 million
points to 10 million points in order to check the performance of various insertion schemes
as the number of points increases in the system. As shown in Table 8.9, for this mildly non-
uniform point distribution pattern, the performance of the insertion schemes is very simi-
lar as in the case of uniform distribution of randomly generated points. Compared to the
Figure 8.48
Point distribution with mixed patterns of 10000.
