A New Parallelization Approach for Sequential Simulation

Abstract

The procedure for spatial sequential simulation - bi-point or multi-point stochastic simulation - of any type of variable starts with the definition of a random path which the simulation should follow in order to generate a structured image of a given attribute. One problem of these algorithms is related to the effort a single processor is required to undertake, especially when applying them to very large grids of nodes. With the advent of parallel computing and multi-core processors (or multiple execution cores), which are expected to drive a new era of performance and flexibility, providing platforms that can better handle escalating workloads and rapidly evolving usage models, it becomes clear that a scalable parallelization scheme should be developed to allow the usage of such processors to allow for considerable reduction in time spent performing simulations, with clear advantages when used with clusters of multi-processor (or multiple execution core) nodes. The general idea is to partition the universe in a given number of sections, equal in number to double the number of processors or execution cores, in such a way that the locations to be concurrently simulated are sufficiently apart to be outside search range or multi-point template range. This is only applicable in cases where at least one of the dimensions of the area to be simulated is greater then the chosen range in that direction, which is admitted to be true for cases where parallelization is valuable, particularly for very large fine scale models. The number of sections, or regions, at which the volume will be segmented is given by an optimization procedure that maximizes the size of each region and minimizes the number of nodes to be sequentially simulated, based on the number of available processors or execution cores. The results of the proposed parallel simulation method were checked in order to evaluate if they succeeded to reproduce the spatial continuity and spatial patterns of the phenomenon and its distribution function.