Page 113 - The Combined Finite-Discrete Element Method

96 CONTACT DETECTION

For array D to contain a meaningful representation of spatial distribution of discrete
elements, all three arrays are sorted relative to the integerised x and y coordinates, i.e.
relative to the content of arrays X and Y.
The first sorting relative to the contents of array X is performed as shown in Figure 3.23.
In the case where the content of array X is the same, sorting relative to the content of
array Y is performed as shown in Figure 3.25.
After the sorting operation is completed, no information is lost. Array D still contains
the discrete element ‘names’ (i.e. numbers), while arrays X and Y contain the cell onto
which a particular discrete element is mapped. For instance, after the sorting operation, it
is still evident from arrays D, X and Y that discrete element 1 is mapped onto cell (4,7),
while the discrete element 3 is mapped onto cell (4,6) and discrete element 7 is mapped
onto cell (3,7) (Figure 3.24).

Sorted array X 3 4 4 4 5 5 5 6

Array Y 7 6 5 7 8 7 6 6

Array D 7 3 5 1 2 4 6 8

Figure 3.23 Arrays sorted relative to content of array X.

Sorted array X 3 4 4 4 5 5 5 6

Array Y 7 5 6 7 6 7 8 6

Array D 7 5 3 1 6 4 2 8

Figure 3.24 Sorting arrays relative to the content of array Y.

Sorted array X 3 4 4 4 5 5 5 6

Array Y 7 5 6 7 6 7 8 6

Array D 7 5 3 1 6 4 2 8

Figure 3.25 First stage of the binary search for cell (5,7).