Civil Engineering Reference
In-Depth Information
E
S
K
C
D
R
F
J
I
B
A
P
Figure 5.16
Tetrahedra ABCD and CBAE are not convex.
E
D
K
C
S
J
I
B
A
P
Figure 5.17
Subdividing tetrahedra ABCD and ADCE.
E
K
D
L
C
S
J
B
A
P
Figure 5.18
Points J and K are in different tetrahedra.
In case a new intersection point is created, there is no actual reduction in the number of
intersection points (tetrahedra) in the
pipe
, which will be referred to as irreducible. George and
Borouchaki (1998) further argued that S can be so located such that the swap of tetrahedra
CBAP and ABCS is still valid yet allows more space to eliminate L by repeating exactly the same
procedure. However, in considering all the tetrahedra centred at a point (D), not only more
Steiner points will be created but also many subdivisions of tetrahedra may be required before
the process converges to some valid numerical solutions, which inevitably would have generated
many elongated tetrahedra. An alternative, which may be simpler, is to just keep those irreduc-
ible intersection points and insert them as Steiner points to the mesh.
5.3.3.2.4 Step 4: Recovering missing faces by element swaps
Following the edge recovery by element swaps, if the three edges of a boundary face are
present, the face, in general, will also exist. However, there are situations where the face is
