Computational time

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. 

The basic requirements for the Mephisto model was satisfactory accuracy, that means prediction of amplitude, position and phase relation between the various signals, and short computation times, typically a few minutes for the simulation of a whole Cscan, compatible with an intensive use. These a priori contradictory characteristics have been contented by means of appropriate approximations based on physical considerations. 

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. 

The value of detennines how much computer time and memory is needed to solve the -dimensional Sj HjjCj= E Cj secular problem in the Cl and MCSCF metiiods. Solution of tliese matrix eigenvalue equations requires computer time that scales as (if few eigenvalues are computed) to A, (if most eigenvalues are... 

The relative shift of the peak position of the rotational distiibution in the presence of a vector potential thus confirms the effect of the geometric phase for the D + H2 system displaying conical intersections. The most important aspect of our calculation is that we can also see this effect by using classical mechanics and, with respect to the quantum mechanical calculation, the computer time is almost negligible in our calculation. This observation is important for heavier systems, where the quantum calculations ai e even more troublesome and where the use of classical mechanics is also more justified. 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

This hierarchical extrapolation procedure can save a significant amount of computer time as it avoids a large fraction of the most time consuming step, namely the exact evaluation of long range interactions. Here, computational... 

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.

Because of the use of the focusing method [18], more than four calculations are actually carried out for each group. However, the focusing method saves computer time by permitting the use of less extensive finite-difference grids. 

The procedure is computationally efficient. For example, for the catalytic subunit of the mammalian cAMP-dependent protein kinase and its inhibitor, with 370 residues and 131 titratable groups, an entire calculation requires 10 hours on an SGI 02 workstation with a 175 MHz MIPS RIOOOO processor. The bulk of the computer time is spent on the FDPB calculations. The speed of the procedure is important, because it makes it possible to collect results on many systems and with many different sets of parameters in a reasonable amount of time. Thus, improvements to the method can be made based on a broad sampling of systems. 

Several groups have previously reported parallel implementations of multipole based algorithms for evaluating the electrostatic n-body problem and the related gravitational n-body problem [1, 2]. These methods permit the evaluation of the mutual interaction between n particles in serial time proportional to n logn or even n under certain conditions, with further reductions in computation time from parallel processing. 

Supported by NSF ASC-9318159, NSF CDA-9422065, NTH Research Resource RR08102, and computer time from the North Carolina Supercomputing Center. An earlier version of this paper was presented at the Eighth SIAM Conference on Parallel Processing for Scientific Computing. 

It is true that the structure, energy, and many properties ofa molecule can be described by the Schrodingcr equation. However, this equation quite often cannot be solved in a straightforward manner, or its solution would require large amounts of computation time that are at present beyond reach, This is even more true for chemical reactions. Only the simplest reactions can be calculated in a rigorous manner, others require a scries of approximations, and most arc still beyond an exact quantum mechanical treatment, particularly as concerns the influence of reaction conditions such as solvent, temperature, or catalyst. 

The profits from using this approach are dear. Any neural network applied as a mapping device between independent variables and responses requires more computational time and resources than PCR or PLS. Therefore, an increase in the dimensionality of the input (characteristic) vector results in a significant increase in computation time. As our observations have shown, the same is not the case with PLS. Therefore, SVD as a data transformation technique enables one to apply as many molecular descriptors as are at one s disposal, but finally to use latent variables as an input vector of much lower dimensionality for training neural networks. Again, SVD concentrates most of the relevant information (very often about 95 %) in a few initial columns of die scores matrix. 

If computing time does not play the major role that it did in the early 1980s, the [12-6] Lennard-Jones potential is substituted by a variety of alternatives meant to represent the real situation much better. MM3 and MM4 use a so-called Buckingham potential (Eq. (28)), where the repulsive part is substituted by an exponential function ... 

The mathematical form of the PEF is in almost every case a compromise between speed and accuracy. As computer power continually increases, ideally following Moore s Law, and the cost/performance ratio is getting better, one might think that there is no longer a need to sacrifice accuracy to save computational time. This is not really true, because in direct proportion to the CPU speed is the rise in the scientists interest in calculating larger and larger molecules (in fact, their interest always rises faster than the CPU speed). 

A second idea to save computational time addresses the fact that hydrogen atoms, when involved in a chemical bond, show the fastest motions in a molecule. If they have to be reproduced by the simulation, the necessary integration time step At has to be at least 1 fs or even less. This is a problem especially for calculations including explicit solvent molecules, because in the case of water they do not only increase the number of non-bonded interactions, they also increase the number of fast-moving hydrogen atoms. This particular situation is taken into account... 

The problem with most quantum mechanical methods is that they scale badly. This means that, for instance, a calculation for twice as large a molecule does not require twice as much computer time and resources (this would be linear scaling), but rather 2" times as much, where n varies between about 3 for DFT calculations to 4 for Hartree-Fock and very large numbers for ab-initio techniques with explicit treatment of electron correlation. Thus, the size of the molecules that we can treat with conventional methods is limited. Linear scaling methods have been developed for ab-initio, DFT and semi-empirical methods, but only the latter are currently able to treat complete enzymes. There are two different approaches available. 

Using semi-einpirical methods, which are also based on approximate solutions of the Schrodingcr equation but use parameterized equations, the computation times can be reduced by twu orders of magnitude. HyperChem from Hypercubc,... 

Ifnited atom force fields (see Ifnited versiisAll Atom Forcehiclds" on page 28 ) arc sometimes used for bioraoleciiles to decrease the number of nonbonded in teraction s and the computation time. Another reason for using a simplified poten tial is to reduce the dimensionality of the potential energy surface. This, in turn, allows for more samples of the surface. 

TTyperChem can perform qiiantnm mechanics MO calculations on molecules con laming 1 00 or more atoms. There Is no restriction on the n umber of atom s. but larger structures may require excessive computing times and computer main mem-... 

Molecular dynamics simulations are el ficient for searching the conformational space of medium-sized molecules and peptides. Different protocols can increase the elTicieiicy of the search and reduce the computer time needed to sample adequately the available conformations. 

In deed, sem i-cmpirical meth ods can sorn etim cs be more accurate than sorn e poorer flt ini/io m ethods, which require much longer computation times. 

The amount of computation for MP2 is determined by the partial tran si ormatioii of the two-electron integrals, what can be done in a time proportionally to m (m is the u umber of basis functions), which IS comparable to computations involved m one step of(iID (doubly-excitcil eon figuration interaction) calculation. fo save some computer time and space, the core orbitals are frequently omitted from MP calculations. For more details on perturbation theory please see A. S/abo and N. Ostlund, Modem Quantum (. hern-isir > Macmillan, Xew York, 198.5. 

While INDO calciilaiioii s have more pariuiieiers an d are som ewh ill more complex that CXDO ciilciilatioim. they require csseii tiiilly no extra computation time and in most siluiilions they are superior to CNDO ciilculatioiis. 

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