Computational load

Alternative superstructures to those in Figs. 16.26 and 16.27 can be developed. On the one hand, it is desirable to include many structural options to ensure that all features which are candidates for an optimal solution have been included. On the other hand, including more and more structural features increases the computational load dramatically. Thus care should be taken not to include unnecessary features in the superstructure. 

Various techniques exist that make possible a normal mode analysis of all but the largest molecules. These techniques include methods that are based on perturbation methods, reduced basis representations, and the application of group theory for symmetrical oligomeric molecular assemblies. Approximate methods that can reduce the computational load by an order of magnitude also hold the promise of producing reasonable approximations to the methods using conventional force fields. 

The QM/MM methods have their own disadvantages, the obvious one being the computational load added to the already complex calculation of the electronic structure. 

Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

In distributed systems, each participating site must be equipped with a desktop or a laptop computer loaded with the distributed data collection system software to collect and enter data locally. In addition, each site is provided with necessary storage devices such as tapes, zip diskettes, and CDs and peripheral devices such as printers. Collected data are transferred periodically to the central location as files saved on storage devices, via phone modems, by FTP, or through wireless communications, where they are managed by a centralized data management system. 

In summary, in the equilibrium-chemistry limit, the computational problem associated with turbulent reacting flows is greatly simplified by employing the presumed mixture-fraction PDF method. Indeed, because the chemical source term usually leads to a stiff system of ODEs (see (5.151)) that are solved off-line, the equilibrium-chemistry limit significantly reduces the computational load needed to solve a turbulent-reacting-flow problem. In a CFD code, a second-order transport model for inert scalars such as those discussed in Chapter 3 is utilized to find ( ) and and the equifibrium com-... 

The use of 3D models for tubular cells is particularly interesting, especially for studying the new geometries. In the literature the applications are very few and the reason is the large computational load. Here some of the results of current research conducted by the research group at Politecnico di Torino are shown. A first application is the 3D model of the tubular cell by Siemens. The calculated temperature field is shown in Figure 7.14. 

This increased computation load is as expected for such a problem due to the use of a detailed model with rigorous thermodynamics. 

Efficiency in terms of properly distributing and balancing the computational loads. 

For a given value of R, eqs. (29), (30), and (31) can be solved readily for Pj and p° using the Newton-Raphson method. It is easy to arrange the linearized equations so that the coefficient matrix is upper triangular with only one non-null column above the diagonal. The solution therefore does not add appreciably to the computational load of the inside loop. 

Given the very heavy computational load of GP, it would not be the method of choice for problems which yield to simpler approaches. However the above data show that it can be very beneficial on problems that have defeated other methods. 

It was found that the method was biased towards flexible molecules, so that an entropy term was included, based on the number of rotatable bonds in a molecule. This approach could also be used to set up an SAR hypothesis based on the best consensus alignment, but once the alignment has been generated, it is likely that the SAR could be better handled using CoMFA. The appealing feature of this work is the introduction of shape, polarity and conformation space its drawback is the heavy computational load. 

Therefore, the numerical integration in the LMBW equation can be performed on a much smaller z-domain compared to the BGY equation. This significantly reduces computational load for the equations having two z-dimensions. Moreover, the LMBW equation does not involve the assumption of a pairwise interaction potential inherent in the BGY equation [14], which constitutes a benefit for further extensions to systems with nonadditive potentials. 

A second proposition relies on the idea that the on-line optimization problem is unconstrained after a certain time step in the finite moving horizon. Where in the finite horizon that happens is determined by examining whether the state has entered a certain invariant set (Mayne, 1997). Once that happens, then closed-form expressions can be used for the objective function from that time point the end of the optimization horizon, p. The idea is particularly useful for MFC with nonlinear models, for which the computational load of the on-line optimization is substantial. A related idea was presented by Rawlings and Muske (1993), where the on-line optimization problem has a finite control horizon length, m, and infinite prediction horizon length, p, but the objective function is truncated, because the result of the optimization is known after a certain time point. 

It is impossible to derive a general model that applies to all application domains and all computer systems." In theory, one can predict performance from first principles, but this would require a detailed understanding of every part of the computation and how its memory access (data communication) patterns interact with the computer s hardware and operating system. Except for small computational kernels, it is not feasible to acquire such understanding. In practice, a more satisfactory approach is to construct a fairly high level model using approximate functional forms for the amount of computation, load balance, and overheads. 

A more precise description for this class is full wavefunction methods, where the basic variable is the full many-body wavefunction. The main problem with full wavefunction approaches is that the computational load increases drastically with the number of electrons N. At the Hartree-Fock level, the load increases as and the scaling with N increases steadily, the more... 

Because DFT-based techniques have the electronic density p r) as the basic variable, the computational load scales moderately with the number of electrons N, 0 N ). Thus they are able to handle significantly more atoms than traditional quantum chemical approaches that retain the full electronic many-body wavefunction as the basic variational quantity. This favorable scaling currently makes DFT-based techniques most promising for ab initio studies of M/C interfaces, and therefore we will emphasize this group of methods in our review. 

Tape users have an additional problem to overcome. What if you type in a program in several sittings The next day, you come to your computer, load and run the Proofreader, then try to load the partially completed program so that you can add to it. But since the Proofreader is trying to hide in the cassette buffer, it is wiped out ... 

The overall design procedure is summarized in Fig. 3. It should be noted that the design techniques are deployed in order of increasing computational load and design data requirements. This allows most design options to be rejected... 

The simplest method to correct for the inadequacy of the pairwise-additivity assumption is to use a classical polarization model" to allow for the induction of one or more dipoles in each molecule due to the electric field of the surrounding molecules. The details of such calculations are given elsewhere. Because of the multibody nature of such a calculation, and the need for iteration over all the molecules in the system, this adds a factor of 3-10 to the computational load of an MC simulation. 

---