Histogram methodΒΆ

The histogram-based method works differently than the first two methods in such a way, that it is a global method that requires three distinct steps for a single adjustment. In each of these steps the following takes place: a partial histogram needs to be created over the workload, e.g. number of particles, along one direction on each domain, then these are supplied to the method, where a global histogram is computed. With this global histogram a distribution function is created. This is used to compute the optimal (possible) width of domains in that direction. For the second and third steps the computation of the global histograms and distribution functions take place in subsystems, being the results of the previous step. The result is the most optimal distribution of domains according to the Staggered-grid method, at the cost of global exchange of work, due to the global adjustment, which makes the method not well suited to highly dynamic systems, due to the need of frequent updates. On the other hand the method is well suited for static problems, e.g. grid-based simulations.

Note: Currently the order of dimensions is: z-y-x.

Required number of vertices

  • two, one describing the lower left front point and one describing the upper right back point of the domain

Additional requirements

  • partial histogram created over the workload on the local domain in the direction of the current correction step

Advantages

  • supplies an optimal distribution of domains (restricted by width of bins used for the histogram)

  • only three steps needed to acquire result

Disadvantages

  • expensive in cost of communication, due to global shifts

  • requires preparation of histogram and shift of work between each of the three correction steps