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 t o a problem, and do so with mathematical certainty. In general, curren tly used techniques do not provide such rigorous guarantees. One appro ach to providing such assurances can be found in the use of interval a nalysis, in particular the use of interval Newton methods combined wit h generalized bisection. However, these methods have generally been re garded as extremely inefficient. Motivated by recent progress in inter val 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/generaliz ed bisection method works quite well on relatively small problems, pro viding a powerful method for finding all solutions to a problem. For l arger problems, the method performs inconsistently with regard to effi ciency, at least when reasonable initial bounds are not provided.