Setting Convergence Criteria

In setting up an optimization calculation, you can use two convergence criteria the root-mean-square gradient and the number of optimization cycles. 

You should terminate a geometry optimization based upon the root-mean-square gradient, because the number of cycles needed to minimize a molecule varies according to th e initial forces on the 

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Process of calculation of a current is carried out before achievement of the set convergence criterion. By default in Ansys CFX, results of calculation of a current remain in the form of a file containing all irrformation on a current, sufficient to renew calculation from last condition. It is possible to specify to the program to keep and intermediate conditions that will allow to visualize to a time history of a pattern of a current. Thus, in a file of results co-ordinates of all knots of a desing grid and value of critical parameters of a current are stored in these knots. 

Care needs to be taken if some components are present in trace quantities. If an estimated concentration is 0.5 ppm and the calculated value is 1 ppm, the scaled error is 100%. This is much too large an error for most variables and yet the absolute error might be acceptable for a trace component. In other situations, it might be necessary to define trace components with a high precision. A trace component threshold can be set, below which the convergence criterion is ignored. 

SC (simultaneous correction) method. The MESH equations are reduced to a set of N(2C +1) nonlinear equations in the mass flow rates of liquid components ltJ and vapor components and the temperatures 2J. The enthalpies and equilibrium constants Kg are determined by the primary variables lijt vtj, and Tf. The nonlinear equations are solved by the Newton-Raphson method. A convergence criterion is made up of deviations from material, equilibrium, and enthalpy balances simultaneously, and corrections for the next iterations are made automatically. The method is applicable to distillation, absorption and stripping in single and multiple columns. The calculation flowsketch is in Figure 13.19. A brief description of the method also will be given. The availability of computer programs in the open literature was cited earlier in this section. 

Iterative resolution methods obtain the resolved concentration and response matrices through the one-at-a-time refinement or simultaneous refinement of the profiles in C, in ST, or in both matrices at each cycle of the optimization process. The profiles in C or ST are tailored according to the chemical properties and the mathematical features of each particular data set. The iterative process stops when a convergence criterion (e.g., a preset number of iterative cycles is exceeded or the lack of fit goes below a certain value) is fulfilled [21, 42, 47-50],... 

The use of basis sets containing diffuse functions with density functional methods requires added care in the computations. Thus in the B3LYP calculations the evaluation grid was expanded both in terms of additional radial shells and added grid points per shell. Also the SCF convergence criterion was tightened. 

To illustrate the characteristics of the combination of these three calculational procedures, Example 2-7 was selected. The statement of this example is presented in Table 2-2. The temperature profiles obtained by use of the Kb method on the basis of the corrected compositions found by use of the 6 method [Eqs. (2-27) and (2-28)] are presented in Table 2-3. The constants a and b in the expression for Kb [Eq. (2-31)] were found by use of the K values for /-C4H10 at 510 and 960°R. The values of 0 and the calculated values of D at the end of each trial are also listed in this table. The vapor rates computed by use of the constant-composition method, the temperatures found by the Kp method, and the corrected compositions are presented in Table 2-4. The solution sets d, and bi are presented in Table 2-5. To satisfy the convergence criterion, twelve trials were required and 2.60 seconds of computer time on an AMDAHL 470 V/6 computer using a WATFIV compiler. 

When both the F/s and Gfs are normalized, the sum of their squares is meaningful as a measure of how far a given set of trial values of the variables are from the solution set. In the examples presented in this chapter, the convergence criterion used was that , the square root of the average of the euclidean norm, must be less than some small preassigned number e, say = 10 4. 

To start kinetic analysis of an ADH reaction curve, the highest absorbance under analysis is taken as Amk to predict the best Caw for the current rim of kinetic analysis of reaction curve. The estimated Amk is then used to predict the second Caid for the second run of kinetic analysis of reaction curve (Fig. 10). Such an iterative kinetic analysis of reaction curve can predict Amk consistent with Ame for 0.31 mmol/L ethanol when reaction duration is just 6.0 min and the convergence criterion is set for absorbance change below 0.0015 in Amk- Usually convergence is achieved with 7 runs of the iterative kinetic analysis of reaction. Moreover, it is resistant to the change of ADH activities by 50% and coefficients of variation (CV) are below 5% for final ethanol levels from 20 pmol/L to 310 pmol/L in reaction solutions. 

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