Decomposition — Coordination Techniques for Parallel Simulation

  • K. Malinowski
  • A. Y. Allidina
  • M. G. Singh
Part of the Applied Information Technology book series (AITE)


The paper investigates decomposition-coordination techniques which enable tasks to be performed in parallel using parallel-computing facilities when solving large sets of equations resulting from discretization of differential equations. Such an approach for system simulation can be useful in industries where it is vital to improve the speed of simulation.


Local Problem Discretization Scheme Large Scale System Coordinator Problem Dual Method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allidina, A,Y., Malinowski, K. and Singh, M.G., 1982, A note on parallel processing techniques for algebraic equations, ordinary differential equations and partial differential equations, Control Systems Centre Report No. 568, UMIST.Google Scholar
  2. Allidina, A.Y, ed., 1984, Development of hierarchical techniques for the simulation of large scale systems with particular application to the nuclear industry, EEC Project Phase 1 Report, May, 1984.Google Scholar
  3. Allidina, A.Y., Cook, R., Malinowski, K., Plowman, S., Singh, M.G., 1984, Real time simulation study for fast breeder dynamics and control, Interim Report No. 2, December 1984.Google Scholar
  4. Arnold, C.P., Michael, I.P. and Michael, B.D., 1983, An efficient parallel algorithm for the solution of large sparse linear matrix equations, IEEE Transactions on Computers, vol. C-32, No. 3.Google Scholar
  5. Barlow, R.H. and Evans, D.J., 1982, Parallel algorithms for the iterative solution to linear systems, The Computer Journal, vol. 25, No. 1, 1982.CrossRefGoogle Scholar
  6. Blech, R.A. and Arpasi, D.J., 1985, Hardware for a real-time multiprocessor simulator, Distributed Simulation 85, San Diego, California, January 1985.Google Scholar
  7. Brash, F.M. Jr., Van Ness, J.E. and Kang, S.C., Design of Multiprocessor Structures for Simulation of Power-System Dynamics, Report, Electric Power Research Institute, Palo Alto, California 94304.Google Scholar
  8. Burks, A.W., 1981, Programming and structure changes in parallel computers, Proceedings CONPAR 81, Springer-Verlag, Lecture Notes in Computer Science, vol. III, edited by W. Handler.Google Scholar
  9. Crorkin, W., Allidina, A.Y., Malinowski, K. and Singh, M.G., 1985, “Decomposition-coordination Techniques for Parallel Simulation, Part 2”, Large Scale Systems, North Holland.Google Scholar
  10. Evans, D.J. and Haghighi, R.S., 1982, Parallel iterative methods for solving linear equations, Intern. J. Computer Math., vol. II, pp. 247–284.MathSciNetCrossRefGoogle Scholar
  11. Findeisen, M., Bailey, F.N., Brdys, M., Malinowski, K., Tatjewski, P. and Wozniak, A., 1980, “Control and Coordination in Hierarchical Systems”, International Series on Applied Systems Analysis vol. 9, John Wiley and Sons.MATHGoogle Scholar
  12. Franklin, M.A., 1978, Parallel solution of ordinary differential equations, IEE Trans, on Computers, vol. C-27, No. 5.Google Scholar
  13. Halada, L., 1981, A parallel algorithm for solving band systems and matrix inversion, Proceedings CONPAR 81, Springer-Verlag, Lecture Notes in Computer Science, vol. III, edited by W. HandlerGoogle Scholar
  14. Himmelblau, D.M., ed., 1973, “Decomposition of Large Scale Systems (collection of articles on decomposition and coordination techniques”, American Elsevier, New York.Google Scholar
  15. Katz, I.N., Franklin, M.A. and Sen, A., 1977, Optimally stable parallel predictors for Adams-Moulton correctors, Comp. & Maths, with Appls., vol. 3, pp. 217–233.MathSciNetMATHCrossRefGoogle Scholar
  16. Lasdon, L.S., 1970, “Optimisation Theory for Large Systems”, MacMillan, London.Google Scholar
  17. Malinowski, K., Allidina, A.Y., Singh, M.G. and Crorkin, W., 1985, “Decomposition-coordination Techniques for Parallel Simulation — Part 1”, Large Scale Syst ems. North Holland.Google Scholar
  18. Miranker, W.L. and Liniger, W., 1967, Parallel methods for the numerical integration of ordinary differential equations, Math. Comput., vol. 21, pp. 303–320.MathSciNetMATHCrossRefGoogle Scholar
  19. Miranker, W.L., 1981, Numerical methods for stiff equations, Mathematics and Its Applications, 15, D. Reidel Publishing Co.MATHGoogle Scholar
  20. Schendel, U., 1981, On basic concepts in parallel numerical mathematics, Proc. CONPAR 81, Springer-Verlag, Lecture Notes in Computer Science, vol. III, edited by W. Handles.Google Scholar
  21. Singh, M.G., Allidina, A.Y. and Malinowski, K., 1983, Hierarchical simulation techniques, MECO 83, Athens, July.Google Scholar
  22. Singh, M.G. and Titli, A., 1978, “Systems: Decomposition, Optimisation and Control”, Pergamon Press, Oxford.Google Scholar
  23. Suri, R., 1981, “Resource Management Concepts for Large Systems”, Pergamon Press, Oxford.MATHGoogle Scholar
  24. Tao, H.M. and Saeks, R., 1984, Parallel System Simulation, IEEE Trans. on SMC, vol. SMC-14, No. 2.Google Scholar
  25. Travassos, R. and Kaufman, H., 1980, Parallel algorithms for solving nonlinear two-point boundary-value problems which arise in optimal control, J. of Optimisation Theory & Applications, vol. 30, No. 1, January.Google Scholar
  26. Wismer, D.A., 1971, Distributed multilevel systems, rn “Optimisation Methods for Large Scale Systems”, edited by D.A. Wismer, McGraw-Hill, New York.Google Scholar
  27. Worland, P.B., 1976, Parallel methods for the numerical solution of ordinary differential equations, IEEE Trans, on Computers, Oct.Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • K. Malinowski
    • 1
  • A. Y. Allidina
    • 2
  • M. G. Singh
    • 2
  1. 1.Dept. of Automatic ControlTechnical University of WarsawWarsawPoland
  2. 2.Control Systems Centre, UMISTManchesterUK

Personalised recommendations