Globality is still present since the influence of particle is felt throughout the domain, but more care and computational effort is given to its near field. The fast parallel algorithm has to reflect that dual nature, otherwise an efficient implementation will never be obtained. Moreover, the domain decomposition can no longer ignore the spatial distribution of the vortices. Nearby vortices are strongly coupled computationally, so it makes sense to assign them to the same processor.
Binary bisection is used in the host to spatially decompose the domain.
Then, only the vortices are sent to the processors where a binary tree is locally built on top of them. For example, Figure 12.17 shows the portion of the data structure assigned to processor 1 in a 4-processor environment. A processor whose vortices are located at the center of the domain is involved in more costly interactions than a peripheral processor. To achieve the best possible load balancing, that central processor could send a copy of its data to more than half of the other processors and hence itself be responsible for a smaller fraction of the work associated with its vortices. Before a decision is made on which one is going to visit and which to receive, we minimize the number of pairs of processors that need to exchange their data structure.