Civil Engineering Reference
In-Depth Information
P
k
= P
k
+ P
k-1
End loop k
n = P
Np
Set {Q
k
= 0, k = 1,n}
Loop: i = 1,Ne
Loop: j = 1,3
j1=V
i
mod(j,3)
+
;
j2=V
i
mod(j+1,3)+1
; k1 = min(j1,
j2); k2 = max(j1,
j2); m = P
k1
1
m = m - 1
If (Q
m
= 0) then
j
Q
m
= 3(i - 1) + j;
T=0
i
else
k = Q
m
; i* = (k + 2)/3; j* = k - 3(i* - 1)
j1*=V
i
mod(j*,3)+1
;
j2*=V
i
mod(j*+1,3)+1
k2* = max(j1*, j2*)
If (k2* ≠ k2) go to 1
j
j*
T=i*;T=i
i
i*
L = m - 1
While (Q
L
≠ 0) L = L - 1
Q
m
= Q
L+1
; Q
L+1
=
0
End if
End loop j
End loop i
2.5.2 Find the neighbouring elements of a tetrahedral mesh
Let
=
i
1
be the set of tetrahedral elements, with vertices
V
i
j
(j = 1,2,3,4) for the
j
th
vertex of element i. We are going to find
T
i
j
, the j
th
neighbour (opposite to the j
th
vertex) of
element i, and
T
i
j
= 0
if there is no neighbour on a boundary triangular face. The concept of
the algorithm is based on the fact that two elements are neighbours if they share a common
face, and a triangular face is uniquely defined by the three nodes on the face. The neigh-
bour searching algorithm for tetrahedral mesh is very similar to that for triangular meshes,
except that, in the matching process, 3 − 1 = 2 more nodes have to be checked for the match-
ing faces connected to the same minimum node (
k
1) of the face, as shown in Figure 2.26. For
the sake of clarity, two working arrays P and Q have been used in the
pseudo-code
of the
neighbour searching algorithms. However, in the actual implementation, the two working
arrays P and Q are merged into one such that the connection information of array Q is also
stored in P, i.e. {P
NP+k
= Q
k
, k = 1,n}. In this case, the size of array P has to be greater than
N
P
+ n, where N
P
is number of nodes, and n is the number of connections in the mesh. As
the number of connections in an FE mesh is directly proportional to the number of nodes
or elements, the complexity of the neighbour searching algorithm is basically linear with
respect to the number of nodes/elements.
{.
Ti
=
,
N
}
k
2*
=
k
2?
i
*
i
k
3*
=
k
3?
k
1
Figure 2.26
Adjacent elements
i
and
i
* share a common face
k
1-
k
2-
k
3.
