Speculative parallel processing applied to modelling of initial problems
A. Jordan, J. Forenc, Marek Tudruj · COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering · 2005
Purpose To present a new parallel method for solving differential equations that describe transient states in physical systems. Design/methodology/approach The proposed speculative method first solves a differential equation with a large integration step to determine initial data for parallel computations in sub-intervals of time, then speculatively computes in parallel solutions in all the sub-intervals with a smaller integration step and finally composes the final solution from the speculatively computed ones. The basic numerical method applied is the well-known Runge-Kutta algorithm. Findings The speculative method allows important reduction of the computation time of sequential algorithms. The speed-up of the speculative method that we propose, as compared to the sequential execution, depends on the number of sub-intervals that are defined inside the total analysed time interval. The speed-up increases almost linearly with the number of sub-intervals. The good accuracy of computations in the presented example was obtained. Research limitations/implications The proposed method can be applied to non-linear systems without discontinuity points and to stable systems (i.e. systems insensitive to the selection of initial conditions). Practical implications The method can be especially applied for long-lasting computations with a slow convergence of state variables values along with the decrease of integration steps. Originality/value The paper presents an original parallel method for solving differential equations, which significantly speeds up transient states analysis in physical systems.