Page 122 - The Combined Finite-Discrete Element Method

MUNJIZA-NBS CONTACT DETECTION ALGORITHM IN 2D 105

case of the Munjiza-NBS algorithm, linked lists are used instead. This is what makes
the Munjiza-NBS algorithm very efficient both in terms of RAM and CPU requirements.
Linked lists reduce memory requirements significantly.
To further reduce CPU time, singly connected lists are used. The representation of
mapping is performed in two stages:
STAGE 1: Mapping of all discrete elements onto the rows of cells (y-direction) is per-
formed, and a singly connected list of discrete elements for each row i y (where i y =
1, 2, 3 ...n y ) is formed (Figure 3.41). There exist n y of these lists in total. Some of the
lists are empty, others contain only one discrete element, etc. These lists are referred to
as the y-lists, and each y-list is identified by the row of cells it is formed for, and is thus
referred to as the y iy list. For instance, the y 10 list is empty, the y 7 list contains discrete
elements 7, 4 and 1, etc.
It is worth noting that the discrete elements in each of the lists follow each other in
a descending numerical order. For instance, the first discrete element on the list y 6 is
discrete element 9, while the last discrete element on this list is discrete element 3.
This is because the discrete elements are mapped using a loop over discrete elements
in ascending numerical order, i.e.
Loop over all discrete elements (i=1; i≤N;i++)
{ calculate integerised coordinate

y − y min
i y = Int (3.60)
d
and place the discrete element onto the y iy list
}

y iy

10
9

8 2
7 10 7 4 1
6 9 8 6 3

5 5
4
3

2
1

Figure 3.41 Singly connected lists for rows of cells.