HPC optimal parallel communication algorithm for the simulation of fractional-order systems

TL;DR

This paper introduces a parallel algorithm for simulating fractional-order systems using Caputo derivatives, optimizing performance with MPI and OpenMP on a BlueGene/P cluster, and demonstrates its effectiveness through a chaotic circuit example.

Contribution

It presents a novel parallel algorithm for fractional-order system simulation that improves efficiency using MPI and OpenMP, with practical validation on a chaotic circuit model.

Findings

Parallel algorithms significantly reduce simulation time.

Hybrid MPI and OpenMP approaches enhance performance.

Numerical results reveal complex bifurcation and chaos in fractional systems.

Abstract

A parallel numerical simulation algorithm is presented for fractional-order systems involving Caputo-type derivatives, based on the Adams-Bashforth-Moulton (ABM) predictor-corrector scheme. The parallel algorithm is implemented using several different approaches: a pure MPI version, a combination of MPI with OpenMP optimization and a memory saving speedup approach. All tests run on a BlueGene/P cluster, and comparative improvement results for the running time are provided. As an applied experiment, the solutions of a fractional-order version of a system describing a forced series LCR circuit are numerically computed, depicting cascades of period-doubling bifurcations which lead to the onset of chaotic behavior.