Page 109 - The Combined Finite-Discrete Element Method

92 CONTACT DETECTION

implementations using computer languages such as C or C++, which allow pointers, it
is better to use dynamic, purpose-built arrays. More on this can be found in the section
dealing with computational aspects of the combined finite-discrete element method in
Chapter 9.
To achieve the maximum CPU efficiency of the algorithm, it is necessary to min-
imise the number of operations when mapping discrete elements onto the cells. Thus the
mapping is done as follows:

Step 0: Initialisation: this is done by setting all numbers of arrays C and E to −1(empty
lists and/or ends of lists). This step is done only once, i.e. when the computer program
is started:

Loop over all rows of cells(i=1; i≤n cel ; i++)
{ Loop over all cells in a row(j=1;j≤n cel ; j++)
{ set

C[i][j] =−1 (3.32)

}
}
Loop over all discrete elements(k=1; k≤N; k++)
{ set

E[k] =−1 (3.33)

}

Step 1: Mapping of discrete elements onto cells: this operation is done each time discrete
elements move, for instance at each time step. It involves building of a singly connected
list for each cell. This is achieved by looping over all discrete elements, integerising its
coordinates and placing the discrete element onto the corresponding singly connected list:

Loop over all discrete elements (k=1; k≤N;k++)
{ Integerise current coordinates using equation (26) and set

int x k − x min
i = x k = 1 + Int (3.34)
d

int y k − y min
j = y k = 1 + Int
d
Place the discrete element onto the
corresponding singly connected list by

setting E[k] = C[i][j]
(3.35)
and afterwards C[i][j] = k
}