Simultaneous convergence

A decision must be made whether the two recycle loops, units 10 and 11, are to be converged simultaneously or separately. Simultaneous convergence, as illustrated by Fig. 4-8o, is approached by checking and reestimating both tear streams once in each iteration. Separate convergence proceeds by converging the... 

Simultaneous convergence (SC) methods in which all the equations are solved at the same time simultaneously by using Newtons... 

Simultaneous Convergence Methods One drawback of some tearing methods is their relatively limited range of application. For example, the BP methods are more successful for distillation, and the SR-type methods are considered better for mixtures that exhibit a wide range of (pure-component) boiling points (see, however, our remarks above on modified BP and SR methods). Other possible drawbacks (at least in some cases) include the number of times physical properties must be evaluated (several times per outer loop iteration) if temperature- and composition-dependent physical properties are used. It is the physical properties calculations that generally dominate the computational cost of chemical process simulation problems. Other problems can arise if any of the iteration loops are hard to converge. 

Convergence of the simultaneous convergence method was obtained in five... 

Murphree efficiencies are easily incorporated within simultaneous convergence algorithms (something that is not always easy, or even possible, with some tearing methods). (As an aside, note that vaporization... 

Solving the NEQ Model Equations In general, a nonequilibrium model of a column has many more equations than does an equivalent equilibrium-stage model. Nevertheless, we use may essentially the same computational approaches to solve the nonequilibrium model equations simultaneous convergence (Krishnamurthy and Taylor, op. cit.) and continuation methods [Powers et al., Comput Chem. Engng., 12, 1229 (1988)]. Convergence of a nonequilibrium model is likely to be slower than that of the equilibrium model because of the greater... 

If Eqs (49) and (50) are satisfied simultaneously, convergence of the MCSCF procedure is reached. 

Derivative-based optimization methods, where the optimization algorithm is used to simultaneously converge the recycles and determine the decision variables that improve the objective function (Biegler et al., 1999 Edgar et al., 2001). 

The necessary ingredients for successful drug discovery are thus close intermeshing of chemistry, pharmacology, and clinical medicine. However, the state of the art in each discipline must be sufficiently advanced to allow the simultaneous convergence of the three disciplines toward the creation of novel therapy. 

As T becomes diagonal, S simultaneously converges to the eigenvector matrix of T ... 

The ideal Monte Carlo experiment should probe the physical and structural properties of the protein during the folding process, while simultaneously converging to the global minimum structure or native state. Although a great deal of effort has already been expended on the development of computational models for this purpose, most have focused on energy functions or structural analysis. Very few have examined the ther-... 

Understand the nature of algorithms that optimize the process while simultaneously converging the recycle loops and design specifications associated with the process simulation. 

Introduction to Naphtali-Sandholm Simultaneous Convergence Method... 

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