Robust process simulation using interval methods

Ideally, for the needs of robust process simulation, one would like a nonlinear equation solving technique that can find any and all roots to a problem, and do so with mathematical certainty. In general, currently used techniques do not provide such rigorous guarantees. One approach to providing suc...

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Bibliographic Details
Published in:Computers & chemical engineering Vol. 20; no. 2; pp. 187 - 199
Main Authors: Schnepper, C.A., Stadtherr, M.A.
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 1996
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Simulation
Software
Theoretical computing
Non linear equation
Parallel algorithm
Equation system solving
Simulation
Computing
Newton method
ISSN:0098-1354, 1873-4375
Online Access:Get full text
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Summary:Ideally, for the needs of robust process simulation, one would like a nonlinear equation solving technique that can find any and all roots to a problem, and do so with mathematical certainty. In general, currently used techniques do not provide such rigorous guarantees. One approach to providing such assurances can be found in the use of interval analysis, in particular the use of interval Newton methods combined with generalized bisection. However, these methods have generally been regarded as extremely inefficient. Motivated by recent progress in interval analysis, as well as continuing advances in computer speed and the availability of parallel computing, we consider here the feasibility of using an interval Newton/generalized bisection algorithm on process simulation problems. An algorithm designed for parallel computing on an MIMD machine is described, and results of tests on several problems are reported. Experiments indicate that the interval Newton/generalized bisection method works quite well on relatively small problems, providing a powerful method for finding all solutions to a problem. For larger problems, the method performs inconsistently with regard to efficiency, at least when reasonable initial bounds are not provided.
ISSN:0098-1354
1873-4375
DOI:10.1016/0098-1354(95)00014-S