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Waveform relaxation for concurrent dynamic simulation of distillation columns

Published: 03 January 1989 Publication History

Abstract

The need for cost-effective, high-speed computing is essential in many aspects of chemical engineering practice, notably for the simulation of large-scale dynamic systems. The arrival of powerful, highly concurrent message-passing multicomputers potentially offers such economical large-scale computing capability [13,14]. Development of appropriate, efficient algorithms which realize this potential must therefore become an important area of ongoing research and development in chemical engineering. Desired orders-of-magnitude speedup strongly motivates the use of novel algorithmic approaches for large-scale simulation.
Initially, we are developing a simplified binary distillation simulation using the waveform relaxation paradigm [1-7]. Waveform relaxation has proven successful for the concurrent simulation of large-scale VLSI circuits [1-3,6,7] and is therefore a promising approach. Rather than an end in itself, however, we expect that results of this research effort will prove relevant to more general concurrent dynamic simulation including rigorous multicomponent distillation and chemical process flowsheeting.
We describe the implementation effort (which generalizes the pre-existing CONCISEVLSI circuit simulator, [6]), the simplified distillation model, design issues and current status including a sketch of the underlying waveform relaxation algorithm and its realization. Elsewhere we report further observations as well as speedup results [15].

References

[1]
Lelarasmee, E., et oi., "The W~veform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits,~ IEEE Trans. on CAD o! Int. Circ. and Sys., CAD-l(3), July 1982, pp. '131- 145.
[2]
White, J. and A.L. Sangiovanni-Vincentelli, "Partitioning Algorithms and Parallel Implementations of Waveform Relaxation Algorithms for Circuit Simulation," IEEE Proc. of i$CAS '85, Kyoto, July 1985, pp. 221-224.
[3]
Saleh, R. A., et al., "Parallel Waveform-Newton Algorithms for Circuit Simulation," IEEE Proe. o/ ISCAS '87, July 1987, pp. 660-663.
[4]
Miekkala, U. and O. Nevanlinna, "Convergence of Dynamic Iteration Methods for Initial Value Problems,' Siam J. Sci. Star. Comput., 8(4), July 1987, pp. 459-482.
[5]
Skelboe, S., "Stability Properties of Implicit Multirate Formulas," Proc. European Conf. on Circuit Theory and Design (ECCTD '$7), Volume 2, Paris, Sept. 1987, pp. 795--806.
[6]
Mattisson, S., CONCISE: A Concurrent Simulation Program, Ph.D. Thesis, Lurid Institute of Technology, Dept. of Applied Electronics, 1986.
[7]
DumlugSl, D., "The Segmented Waveform Relaxation Method for Mixed-Mode Simulation of Digital MOS VLSI Circuits," Ph.D. Thesis, Katholieke Universiteit Leuven, Dept. of Elektrotechniek, 1986.
[8]
Vandewalle, S. and D. Roose, ~The Paral}el Waveform Relaxation Multigrid Methodf Proc. Third SIAM Conf. on Parallel Process. /or Sei. Comp., Los Angeles, Dec. 1987.
[9]
Brayton, R. K., et al., "A New Efficient Algorithm for Solving Differential-Algebraic Systems using Inplicit Backward Differentiation Formula~,' Proc. of IEEE, 60(1), Jan. 1972, pp. 98-108.
[10]
Ortega, J. M. and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
[11]
Holland, C. D. and A. I. Liapis, Computer Methods /or Solvin9 Dynamic Separation Problems, McGraw Hill, New Yor~, 1983.
[12]
Skogestad, S., Studies of Robust Control o/Distillation Columns, Ph.D.Thesis, California Institute of Technology, Chem. Engineering, 1987.
[13]
Seitz, C. L, "The Cosmic Cube," CA CM, 28, January 1985, pp. 22-33.
[14]
Fox, G., et al., Solving Problems on Concurrent Processors, 1988 (in press).
[15]
Skjellum, A., M. Morari and S. Mattisson, "Concurrent Dynamic Simulation of Distillation Columns via Waveform Relaxation," (contributed paper) intl. Conf. on Vector and Parallel Comp., Troms0, Norway, June 1988.
[16]
Seitz, C. L., et al., The C Programmer's Abbreviated Guide to Multicomput~r Programming, Caltech Computer Science, CS-TR-88-1, January 1988.

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cover image ACM Conferences
C3P: Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
January 1989
1787 pages
ISBN:0897912780
DOI:10.1145/63047
  • Editor:
  • Geoffrey Fox
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 03 January 1989

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  • (2001)Newton-type decomposition methods in large-scale dynamic process simulationComputers & Chemical Engineering10.1016/S0098-1354(00)00656-625:7-8(951-961)Online publication date: Aug-2001
  • (1999)A multirate parallel-modular algorithm for dynamic process simulation using distributed memory multicomputersComputers & Chemical Engineering10.1016/S0098-1354(99)00002-223:6(733-761)Online publication date: Jun-1999
  • (1994)BibliographyParallel Computing Works!10.1016/B978-0-08-051351-5.50027-0(877-970)Online publication date: 1994
  • (1993)Rapid convergence of waveform relaxationApplied Numerical Mathematics10.1016/0168-9274(93)90049-W11:1-3(211-224)Online publication date: 1-Jan-1993
  • (1990)Distributed Model Evaluation for the Waveform Relaxation MethodProceedings of the Fifth Distributed Memory Computing Conference, 1990.10.1109/DMCC.1990.555442(622-628)Online publication date: 1990
  • (1990)Concurrent DASSL Applied to Dynamic Distillation Column SimulationProceedings of the Fifth Distributed Memory Computing Conference, 1990.10.1109/DMCC.1990.555439(595-604)Online publication date: 1990
  • (1989)What have we learnt from using real parallel machines to solve real problems?Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 210.1145/63047.63048(897-955)Online publication date: 3-Jan-1989

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