Brode-Ahlrichs decomposition

A close look at the example of figure 2 will show that as the values of I increase then the number of pair forces required to be generated drops for that I. This means that processor 0 will always end up doing more work than processor 1, which in turn does more work than processor 2 etc. Better load balancing can therefore be achieved if this workload is spread more evenly. This can be done by using Brode-Ahlrichs decomposition [11] and is shown schematically in figure 3. Code to implement this scheme is given in reference [5]. 

In practise, Brode-Ahlrichs decomposition is usually combined with a Verlet neighbour list for each atom. One nice feature of this is that it is only necessary for each node to hold the neighbourlist for the atoms it is responsible for. This means that the full neighbourlist, which can taJce up large amounts of memory, can be distributed over each processor in the system, with each one storing only a partial neighbourlist. 

Figw e 3. Brodc-Ahlrichs decomposition for a 9 atom and 10 atom system. The rows represent atom i and the columns represent atom j. Each circle represents an interaction to be calculated. Reading across a row gives the interactions to be computed for atom i. Note that Brode-Ahlrichs decomposition is slightly more efficient for systems containing odd numbers of atoms, as it gives prefect loeid-balancing in this case. 

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See also in sourсe #XX -- [ , ]

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