ar X iv : h ep - l at / 9 20 80 03 v 2 5 A ug 1 99 2 . A PARALLEL CLUSTER LABELING METHOD FOR MONTE CARLO DYNAMICS

We present an algorithm for cluster dynamics to efficiently simulate large systems on MIMD parallel computers with large numbers of processing nodes. The method divides physical space into rectangular cells which are assigned to processing nodes and combines a serial procedure, by which clusters are labeled locally inside each cell, with a nearest neighbor relaxation process in which processing nodes exchange labels until a fixed point is reached. By controlling overhead and reducing inter-processor communication this method attains good performance and speed-up. The complexity and scaling properties of the algorithm are analyzed. The algorithm has been used to simulate large twodimensional Ising systems (up to 27808 × 27808 sites) with Swendsen-Wang dynamics. Typical updating times on the order of 82 nanosecs/site and efficiencies larger than 90% have been obtained using 256 processing nodes on the CM-5 supercomputer.