Parallelization Approaches for the Time-Efficient Simulation of Hybrid Dynamical Systems: Application to Combustion Modeling

Abir Ben Khaled
IFP Energies nouvelles, Rueil-Malmaison, France

Mongi Ben Gaid
IFP Energies nouvelles, Rueil-Malmaison, France

Daniel Simon
INRIA and LIRMM-CNRS-Universitå Montpellier Sud de France, DEMAR team, Montpellier, France

Ladda ner artikel

Ingår i: Proceedings of the 5th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools; April 19; University of Nottingham; Nottingham; UK

Linköping Electronic Conference Proceedings 84:4, s. 27-36

Visa mer +

Publicerad: 2013-03-27

ISBN: 978-91-7519-621-3 (print)

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


The need for time-effiicient simulation is increasing in all engineering fields. Potential improvements in computing speeds are provided by multi-core chips and parallelism. However; the efficientt numerical integration of systems described by equation oriented languages requires the ability to exploit parallelism. This paper investigates the problem of the efficient parallelization of hybrid dynamical systems both through the model and through the solver. It is first argued that the parallelism is limited by dependency constraints between sub-systems; and that slackened synchronization between parallel blocks may provide speed-ups at the cost of induced numerical errors; which are theoretically examined. Then two methods for automatic block diagonalization are presented; using bipartite graphs and hypergraphs. The application of the latter method to hybrid dynamical systems; both from the continuous state variables and discontinuities point or view; is investigated. Finally; the model of a mono-cylinder engine is analyzed from equations point of view and a possible split using the hypergraph method is presented and discussed.


Parallel computing; model decomposition; delay error; dependencies constraints; multicore simulation


[1] U. M. Ascher and L. R. Petzold. Computer Methods for Ordinary Di erential Equations and Di erential-Algebraic Equations. SIAM; Philadelphia; PA; USA; 1st edition; 1998.

[2] A. Ben Khaled; M. Ben Gaïd; D. Simon; and G. Font. Multicore simulation of powertrains using weakly synchronized
model partitioning. In E-COSM’12 IFAC Workshop on Engine and Powertrain Control Simulation and Modeling; Rueil-Malmaison; France; October 2012.

[3] Z. Benjelloun-Touimi; M. Ben Gaid; J. Bohbot; A. Dutoya; H. Hadj-Amor; P. Moulin; H. Saafi; and N. Pernet. From physical modeling to real-time simulation : Feedback on the use of modelica in the engine control development toolchain. In 8th Int. Modelica Conference; Germany; March 2011. Linköping University Electronic Press; Linköpings universitet.

[4] F. Bergero; X. Floros; J. Fernández; E. Kofman; and F. E. Cellier. Simulating Modelica models with a stand-alone quantized state systems solver. In 9th Int. Modelica Conference; Munich Germany; September 2012.

[5] G. Bernat; A. Burns; and A. Llamosi. Weakly hard realtime systems. IEEE Trans. on Computers; 50:308–321; April 2001.

[6] T. Blochwitz; T. Neidhold; M. Otter; M. Arnold; C. Bausch; M. Monteiro; C. Clauß; S. Wolf; H. Elmqvist; H. Olsson; A. Junghanns; J. Mauss; D. Neumerkel; and J.-V. Peetz. The functional mockup interface for tool independent exchange of simulation models. In Proceedings of the 8th International Modelica Conference. Linköping University Electronic Press; March 2011.

[7] G. D. Byrne and A. C. Hindmarsh. PVODE; an ODE solver for parallel computers. International Journal of High Performance Computing Applications; 13(4):354– 365; Winter 1999.

[8] F. E. Cellier and E. Kofman. Continuous System Simulation. Springer; 1st edition; March 2006.

[9] C. Faure; M. Ben Gaïd; N. Pernet; M. Fremovici; G. Font; and G. Corde. Methods for real-time simulation of cyberphysical systems: application to automotive domain. In IWCMC’11; pages 1105–1110; 2011. [10] M. C. Ferris and Je rey D. Horn. Partitioning mathematical programs for parallel solution. Mathematical Programming; 80:35–61; 1998.

[11] P. Fritzson. Principles of Object-Oriented Modeling and Simulation with Modelica. Wiley-IEEE Press; 2003.

[12] D. Guibert. Analyse de méthodes de résolution parallèlesmd’EDO/EDA raides. PhD thesis; Université Claude Bernardm- Lyon I; Sep 2009.

[13] G. Karypis and V. Kumar. MeTiS : A software package for partitioning unstructured graphs; partitioning meshes; and computing fill-reducing orderings of sparse matrices. Technical report; Univ. of Minnesota; Dept. of Computer Science; 1998.

[14] E. Kofman and S. Junco. Quantized-State Systems: a DEVSmapproach for continuous system simulation. Trans. of The Society for Modeling and Simulation International; 18(3):123–132; September 2001.

[15] E. A. Lee. Computing foundations and practice for Cyber- Physical Systems: A preliminary report. Technical Report UCB/EECS-2007-72; Univ. of California; Berkeley; May 2007.

[16] M. Sjölund; R. Braun; P. Fritzson; and P. Krus. Towards e- cient distributed simulation in Modelica using transmission line modeling. In EOOLT; pages 71–80; 2010.

[17] P. J. van der Houwen and B. P. Sommeijer. Parallel iteration of high-order Runge-Kutta methods with stepsize control. J. Comput. Appl. Math.; 29:111–127; January 1990.

[18] F. Zhang; M. Yeddanapudi; and P. Mosterman. Zerocrossing location and detection algorithms for hybrid system simulation. In Proc. 17th IFAC World Congress; pages 7967–7972; Seoul; South Korea; July 2008.

[19] Ü. V. Çatalyürek. Hypergraph Models for Sparse Matrix Partitioning and Reordering. PhD thesis; Computer Engineering and Information Science Bilkent University; November 1999.

Citeringar i Crossref