Dynamic load balancing for the simulation of granular materials

We discuss the simulation of granular materials and the problems encountered when parallelizing these simulations. The main problem of inadequately balanced loads can be mitigated via the use of a dynamic load balancing procedure. We discuss a mapping of this procedure onto a deterministic cellular automaton and show that the time needed for convergence from an initially unbalanced state grows like tau proportional Palpha, with P being the number of processors and alpha = 0.089 +- 0.009. This convergence time can be considered "fast", enabling this algorithm to track fluctuations in the particle density as the simulation progresses. We then discuss the implementation of this algorithm on a Paragon XP/S 10 and a CRAY T3D