Civil Engineering Reference
In-Depth Information
Figure 8.71
Sphere.
Figure 8.72
Spiral.
respectively, along the diagonals, over the surface of a sphere and on a spiral curve, as
shown in Figures 8.70 through 8.72. These point distributions have been designed to simu-
late a practical case of adaptive refinement meshing of a large number of points, with local
concentration in solid and fluid-mechanic problems. The CPU times in seconds of single-
processor insertion and multi-processor insertion are shown in Table 8.19.
For highly non-uniform point distributions with point concentration within a region of
0.01% of the larger dimension, the multi-grid insertion could be applied. As the multi-grid
is just a regular grid on top of another regular grid, the parallel insertion designed for regu-
lar grid can also be readily extended to multi-grid insertion with very little modifications.
However, it is more difficult for the parallelisation of kd-tree insertion, as the cells of a kd-
tree partition is not in alignment going from one cell to the adjacent cells.
Table 8.19
CPU time(s) for non-uniform distribut
i
ons of 10 million points
Uniform
Diagonal
Sphere
Spiral
Single processor
81.7
100.1
79.1
102.5
Multi-processor
18.9
29.5
22.7
29.4
Speed up
4.3
3.4
3.5
3.5
