HPC optimal parallel communication algorithm for the simulation of fractional-order systems
- 53 Downloads
A parallel numerical simulation algorithm is presented for fractional-order systems involving Caputo-type derivatives, based on the Adams–Bashforth–Moulton 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.
KeywordsFractional-order system Parallel numerical algorithm HPC processing
This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, Project No. PN-II-RU-TE-2014-4-0270.
- 1.Baban A, Bonchiş C, Fikl A, Roşu F (2016) Parallel simulations for fractional-order systems. In: SYNASC 2016, pp 141–144Google Scholar
- 3.Bonchiş C, Kaslik E, Roşu F (2017) Improved parallel simulations for fractional-order systems using hpc. In: CMMSE 2017Google Scholar
- 5.Cottone G, Paola MD, Santoro R (2010) A novel exact representation of stationary colored gaussian processes (fractional differential approach). J Phys A Math Theor 43(8):085002. http://stacks.iop.org/1751-8121/43/i=8/a=085002
- 9.Deng W, Li C (2012) Numerical schemes for fractional ordinary differential equations. In: Numerical Modelling. InTechGoogle Scholar
- 12.Duan JS, Rach R, Baleanu D, Wazwaz AM (2012) A review of the adomian decomposition method and its applications to fractional differential equations. Commun Fract Cal 3(2):73–99Google Scholar
- 19.Redbooks I (2009) IBM System Blue Gene Solution: Blue Gene/P Application Development. VervanteGoogle Scholar
- 21.Zhang W, Cai X (2012) Efficient implementations of the adams-bashforth-moulton method for solving fractional differential equations. In: Proceedings of FDA12Google Scholar