Foam::lduAddressing
The class contains the addressing required by the lduMatrix: upper, lower and losort.
The addressing can be created in two ways: either with references to upper and lower in which case it stores references or from labelLists, in which case it stores the addressing itself. Additionally, the losort addressing belongs to the class is as on lazy evaluation.
The ordering of owner addresses is such that the labels are in increasing order, with groups of identical labels for edges "owned" by the same point. The neighbour labels are also ordered in ascending order but only for groups of edges belonging to each point. An example is given below:
owner neighbour
0 1
0 20
1 2
1 21
2 3
2 22
3 4
3 23
4 5
4 24
5 6
5 25
6 7
6 26
7 8
7 27
8 9
8 28
9 10
9 29
There exists an alternative way of addressing the owner list: instead of repeating the same label in the owner list, it is possible to address the start of each point neighbours in the neighbour list. This reduces the size of owner addressing from a list over all edges to a list over all points + 1:
Owner start list: 0 2 4 6 8 10 12 14 16 18
We shall use the second form of the addressing for fast lookup of edge label from the known owner and neighbour, using the following algorithm: -# take the owner label and position the start of lookup using the owner start list -# loop through all neighbours of this owner (ending at the start of lookup of owner + 1) until the match with current neighbour is found. The index used on the neighbour list for the match is the edge index.
While owner start addressing allows us to find the edge owned by the points, it is also necessary to find the edges for which the point is a neighbour. Losort addressing lists the edges neighboured by the point and we shall use the same trick as above to address into this list. Thus, for every point the losort start gives the address of the first face to neighbour this point.
lduAddressing.C