Speculative parallel processing applied to modelling of initial problems

Abstract

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.

Citation

Jordan, A., Forenc, J. and Tudruj, M. (2005), "Speculative parallel processing applied to modelling of initial problems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 1, pp. 127-144. https://doi.org/10.1108/03321640510571093