Computation times for

Execution times for the higher level subroutines FLASH and ELIPS will be highly dependent on the problems involved. The times required per iteration can be estimated from times for lower level subroutines and the descriptions given for FLASH and ELIPS. Computation times for two specific cases calculated with FLASH and one case claculated with ELIPS are included in Table J-1 to show approximate magnitudes required. 

The results obtained with the two methods confirm the measured data with a good precision, with less computational time for the specialised code than the general code. This validation on three representative test bloeks can lead to many applications of modelling of the thin-skin regime. 

Before the data can be visualised, ie displayed in a two or three-dimensional representation, the ultrasonic responses from the interior of the test-piece must be reconstructed from the raw ultrasonic data. The reconstruction process projects ultrasonic indications into 3D space. As well as reconstructing the entire ultrasonic data set within an acquisition file, it is possible to define an arbitrary sub-volume of the test object over which reconstruction will take place. The image resolution may also be defined by the user. Clearly, larger volumes or greater resolution will increase the computation time for both the reconstruction and visualisation processes. 

Fig. 3. Average computation time for one step using EGO.VIII on a DEC-Alpha 3300L workstation (175 MHz) for simulation systems of varying size. The insets show some of the protein-water systems used for the benchmark simulations.

Organic molecule calculations can be done routinely to good accuracy on workstation-class hardware. It is advisable to examine tabulations of results in order to choose a method with acceptable accuracy and computational time for the property of interest. The trend toward having microcomputer versions of computational chemistry codes is making calculations on small organic molecules even more readily accessible. 

You can choose to calculate all nonbonded interactions or to truncate (cut off) the nonbonded interaction calculations using a switched or shifted function. Computing time for molecular mechanics calculations is largely a function of the number of nonbonded interactions, so truncating nonbonded interactions reduces computing time. You must also truncate nonbonded interactions for periodic boundary conditions to prevent interaction problems between nearest neighbor images. 

Choose the DIIS SCF convergence accelerator to potentially speed up SCF convergence. DIIS often reduces the number of iterations required to reach a convergence limit. However, it takes memory to store the Fock matrices from the previous iterations and this option may increase the computational time for individual iterations because the Fock matrix has to be calculated as a linear combination of the current Fock matrix and Fock matrices from previous iterations. 

Note Configuration Interaction significantly increases computing time. For calculations of ground-state energies, MINDO/3, MNDO, AMI, and PM3 methods may already include in their parameters some effects of Configuration Interaction. 

The response factors are characteristic for the layer buildup of the selected wall and are calculated before (by a preprocessor program) or at the beginning ol the simulation. Numerical reasons limit the time step to approximately 10 to 60 min, depending on the thickness and material properties of the wall layers. The method allows the calculation of surface temperatures and heat fluxes bur not the determination of the temperature distribution within the wall. Due to the precalculation of these response factors, the computer time for the simulation might be significantly reduced. 

The computation time for calculations of energy losses to the ground can be quite significant because of the three-dimensional heat conduction problem. Simplified methods are given in ISO/FDIS 13370 1998. ... 

The performance is (as expected) very good. MMX provides relative (and absolute) stabilities with a MAD of only 1.2 kcal/mol, which is better than the estimates from the combined theoretical methods in Table 11.31. Considering that force field calculations require a factor of 10 less computer time for these systems than the ab initio methods combined in Table 11.31, this clearly shows that knowledge of the strengths and weakness of different theoretical tools is important in selecting a proper model for answering a given question. 

A practical ABS is very complicated and needs a fine grid for describing its geometry. This would lead to an extremely long computation time for finding the optimal design. Today,... 

A typical computation such as the ones described here used about 100 adaptively placed mesh points and required about 5 minutes on a Cray 1-S. Of course, larger reaction mechanisms take more time. Also, simpler transport models can be used to reduce computation time. Since the solution methods are iterative, the computer time for a certain simulation can be reduced by starting it from the solution of a related problem. For example, it may be efficient to determine the solution to a problem with a susceptor temperature of 900 K starting from a converged solution for a reactor with a susceptor temperature of 1000 K. In fact, it is typical to compute families of solutions by this type of continuation procedure. 

Kalogerakis and Luus (1983b) compared the computational effort required by Gauss-Newton, simplified quasilinearization and standard quasilinearization methods. They found that all methods produced the same new estimates at each iteration as expected. Furthermore, the required computational time for the Gauss-Newton and the simplified quasilinearization was the same and about 90% of that required by the standard quasilinearization method. 

The nature of the relationships and constraints in most design problems is such that the use of analytical methods is not feasible. In these circumstances search methods, that require only that the objective function can be computed from arbitrary values of the independent variables, are used. For single variable problems, where the objective function is unimodal, the simplest approach is to calculate the value of the objective function at uniformly spaced values of the variable until a maximum (or minimum) value is obtained. Though this method is not the most efficient, it will not require excessive computing time for simple problems. Several more efficient search techniques have been developed, such as the method of the golden section see Boas (1963b) and Edgar and Himmelblau (2001). 

Model selection, application and validation are issues of major concern in mathematical soil and groundwater quality modeling. For the model selection, issues of importance are the features (physics, chemistry) of the model its temporal (steady state, dynamic) and spatial (e.g., compartmental approach resolution) the model input data requirements the mathematical techniques employed (finite difference, analytic) monitoring data availability and cost (professional time, computer time). For the model application, issues of importance are the availability of realistic input data (e.g., field hydraulic conductivity, adsorption coefficient) and the existence of monitoring data to verify model predictions. Some of these issues are briefly discussed below. 

The path taken when the search is started at k. = 0.5/min and k.sO.5 4/mol/min is shown in Figure 3. This search begins on a steeper slope and the function, in this case, spirals in on the minimum value. Again the correct values of k. s 1.0/min and k = 1.0 ,/mol/min are found. Total computer time for this analysis averaged 3-5 minutes with a Digital Equipment Corporation PDP-11/44 minicomputer. 

The lion s share of the computer-time for the least-squares process has to be provided for forming the Z-matrix. The elements of this matrix are evaluated partly numerically and partly analytically in the calculations of Lifson and Warshel (17). In certain cases, strong parameter correlations may occur. Therefore caution is demanded when inverting the matrix C. Also from investigations other than consistent force-field calculations it is known that such correlations frequently occur among the parameters for the nonbonded interactions (34,35). Another example of force field parameter correlations was encountered by Ermer and Lifson (19) in the course of the calculation of olefin properties. When... 

In optimization using a modular process simulator, certain restrictions apply on the choice of decision variables. For example, if the location of column feeds, draws, and heat exchangers are selected as decision variables, the rate or heat duty cannot also be selected. For an isothermal flash both the temperatures and pressure may be optimized, but for an adiabatic flash, on the other hand, the temperature is calculated in a module and only the pressure can be optimized. You also have to take care that the decision (optimization) variables in one unit are not varied by another unit. In some instances, you can make alternative specifications of the decision variables that result in the same optimal solution, but require substantially different computation time. For example, the simplest specification for a splitter would be a molar rate or ratio. A specification of the weight rate of a component in an exit flow stream from the splitter increases the computation time but yields the same solution. 

Also, like all cubic equations of state,Eqn. (1) requires relatively little computing time for calculating thermophysical properties. 

Dividing surfaces are usually assumed to be perpendicular to the MEP (i.e., that is motion on the dividing surface involves no motion along the MEP) because this assumption saves much computational time. For the dividing surface of TST this result is automatically obtained because the normal mode coordinate of the frequency... 

Model Ref. Average Temporal Correlation Coefficient Computer Time for 24-h Prediction, min Computer Cost for 24-h Prediction, ... 

One of the reasons why a comprehensive CFSD code does not exist, is that the mathematical description of the thermochemical conversion of a packed fuel bed is extremely complex. In other words, the mathematical models we have today are far from able to describe the highly differentiated phenomenology of the conversion system. Today there exist comprehensive models describing the thermochemical conversion of single fuel particles, but from that step to the description of the thermochemical conversion of a packed bed is a great leap. Another reason for the slow progress of computer codes in this area is the limited computational capacity, that is, excessive computational time for these complicated models is required. 

The response to the second question is in terms of relative computation times for energy calculations, geometry optimizations and frequency evaluations on different size molecules. This is addressed in the final chapter of this section. Overview and Cost. 

Concluding this section. Overview of Performance and Cost (Chapter 11), is material which estimates computation times for a number of practical models applied to real molecules , and provides broad recommendations for model selection. 

Higher level calculations, based on higher orders of Moller-Plesset perturbation theory, can also be performed, albeit with the consumption of much more computer time. For example, an MP4SDTQ calculation uses fourth-order Moller-Plesset perturbation theory, includes excitations through quadruples, and gives better energies than MP2 does. 

The computer time per reaction of this algorithms scales with system size as 0(log S) where S is the number of sites in the system. (Note that for all kMC algorithms the total number of reactions in a system is of the order 0(S). So for the first-reaction method the computer time for a whole simulation scales as 0(S log 5).) This logarithmic dependence originates from the data-structures, which are normally trees, that are used to store the reactions and their times. 

---