Mesh optimisation - Finite Element Mesh Generation - page 379

Hence, the process will converge for meshes of finite size if we impose a minimum increase
in mesh quality for each cycle of local transformations. The optimisation procedure can
actually be speeded up if transformations are only carried out when there is an increase of
at least 1% in the mean quality of the elements involved.

6.4.4 Examples of optimisation by face/edge swap
Delaunay triangulations of 10,000 randomly generated points are constructed, which
are optimised by topological transformations T 23 , T 32 , T 44 and T 56 , as shown in Figure
6.53. As T 32 and T 44 are the more frequently used operations, two cycles of each swap-
ping scheme will be applied to a number of tetrahedral meshes, and the results are shown
in Tables 6.15 and 6.16. As seen from these tables, on the average of 7842 scans for swap

After optimisation

Before optimisation

Figure 6.53 Optimisation of Delaunay triangulation of 1000 points.

Table 6.15 Optimisation of Delaunay triangulation by swap T 32
Mesh Scan T 32 γ ο min γ ο mean γ min γ mean

1 7795 7254 0.000168 0.42538 0.0005664 0.49239

2 7799 7278 0.000147 0.42552 0.0002921 0.49307

3 7977 7365 0.000276 0.42064 0.0006907 0.48786

4 7820 7249 0.000232 0.42694 0.0004755 0.49456

5 7820 7309 0.000148 0.42667 0.0006892 0.49373

Aver 7842 7291 0.000194 0.42503 0.0005428 0.49232

Table 6.16 Optimisation of Delaunay triangulation by swap T 44
Test Scan T 44

γ ο min γ ο mean γ min γ mean

1 40,137 1902 0.0000580 0.42644 0.0000580 0.43027

2 39,242 1813 0.0003305 0.42238 0.0003305 0.42605

3 39,587 1826 0.0001507 0.42742 0.0001507 0.43103

4 39,479 1826 0.0001166 0.42106 0.0001166 0.42491

5 39,766 1837 0.0001956 0.42669 0.0001956 0.43032

Aver 39,642 1841 0.0001703 0.42482 0.0001703 0.42852