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

Summary form only given. 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 3D Ising model and design parallel algorithms for sweep spin selection for them on both homogeneous and hierarchical clusters.