Efficient simulation based on sweep selection for 2-D and 3-D ising spin models on hierarchical clusters

In this paper, we design parallel Monte Carlo algorithms for the Ising spin model on a hierarchical cluster. A hierarchical cluster can be considered as a cluster of homogeneous nodes which are partitioned into multiple supernodes such that communication across homogenous clusters are represented by a supernode topological network. We consider different data layouts and provide equations for choosing the best data layout under such a network paradigm. We show that the data layouts designed for a homogeneous cluster will not yield as good results as layouts designed for a hierarchical cluster. We derive theoretical results of the performance of the algorithms on a modified version of the LogP model that represents such tiered networking, and present simulation results to analyze the utility of the theoretical design and analysis. Furthermore, we consider the 3-D Ising model and design parallel algorithms for sweep spin selection for them on both homogeneous and hierarchical clusters.