CPU Requirements Research Articles

Evaluation of greedy, myopic and less-greedy heuristics for the single machine, total tardiness problem

Simple, yet highly effective modifications to the net benefit of relocation (NBR) heuristic of Holsenback and Russell provide significant improvements in solution quality without any increase in computational effort by tempering the greedy nature of the original NBR heuristic. Two lemmas reduce the size of the search while adhering to optimality conditions. Experimentation compares the modified NBR heuristic (M-NBR) with the two leading heuristics of the literature. Testing on 25, 50 and 100-job problems over a wide range of due dates and tardiness factors shows the M-NBR algorithm to be the best single-pass heuristic to date. We show that a composite heuristic, employing the better of the M-NBR and another leading heuristic solution, consistently produces near-optimal solutions with negligible CPU requirements.

Validation of two conformational searching methods applied to sucrose: simulation of NMR and chiro-optical data

The potential energy hypersurface of sucrose has been examined by molecular mechanics calculations (MM3(92)) interfaced with two different algorithms for conformational searching. The first uses the systematic grid-search approach. The second algorithm, which has a lower CPU requirement, is the so-called CICADA procedure (Channels In Conformational space Analyzed by Driver Approach). This method drives selected torsional angles to explore the low-energy regions and permits full geometry relaxation. Using the grid-search approach, the adiabatic relaxed map of sucrose was calculated as a function of the glycosidic torsion angles, and three families of stable conformers were identified. The CICADA procedure found all minima and also the low-energy conversion pathways for the disaccharide in agreement with those located by the grid-search approach. The method appears to be more efficient for determining the global energy minimum. Beside locating structures at energy minima, transition states and low-energy pathways were also identified. In order to assess the validity of the potential energy surfaces, comparisons were made between experimental and theoretical values of some spectral properties. Optical rotation values were taken from the literature, whereas the NOESY volumes were measured at 400 MHz. Theoretical data were calculated taking into account all the accessible conformations derived from either the grid-search or the CICADA method. NMR relaxation data were calculated using averaging methods appropriate for both slow and fast internal motions. The present study demonstrates the ability of the new CICADA method to reproduce the potential energy surface of a flexible molecule and therefore successfully to simulate its spectral properties.

Comparison of three FMM techniques for solving hybrid FE-BI systems

By virtue of its low operation count, the application of the fast multipole method (FMM) results in a substantial speed-up of the boundary-integral (BI) portion of the hybrid finite-element/boundary-integral technique, independent of the shape of the BI contour. Previously, various versions of the fast multipole method have been proposed, each introducing a different approximation to the implementation of the boundary integral. The main goal of this paper is to provide a comparison of the various FMM approaches on the basis of implementation, CPU time, and accuracy. To gain an appreciation of the differences among the various FMM methodologies, a large portion of the paper is devoted to a discussion of the algorithms at a tutorial level. Flow charts and pseudo-code are also given, at sufficient detail to facilitate their implementation. We present quantitative CPU and memory requirements, using the scattering by a groove as the basis for comparison, and conclude that the FMM can accelerate the BI computation without any significant deterioration in accuracy. A simpler FMM-based algorithm results in a much smaller execution time but has a larger error. However, it turns out that a third algorithm, designated the windowed FMM, provides a very good compromise with respect to error and execution time. The paper concludes with the presentation of some three-dimensional applications for which a hybrid FE-BI technique, in conjunction with a fast-integral algorithm, is well suited.

The reduction of numerical entropy generated by unsteady Shockwaves

AbstractThe computation of slowly moving Shockwaves is considered. A numerical error is introduced into the solution during an explicit computation, which results in the generation of spurious entropy. The generation of this spurious entropy and its effect on the pressure wave in Euler flows is examined, in one dimension by considering a moving shock in a constant area duct, and in two dimensions by considering an unsteady aerofoil flow. An efficient temporal discretisation is presented, whose advantages over the explicit scheme are two-fold. First, the numerical entropy generation due to shock motion is eliminated, and second, the CPU requirements for a two-dimensional unsteady computation are reduced by a factor of five from that required for the explicit scheme, for no loss of accuracy.

A Lagrangian dynamic subgrid-scale model of turbulence

The dynamic model for large-eddy simulation of turbulence samples information from the resolved velocity field in order to optimize subgrid-scale model coefficients. When the method is used in conjunction with the Smagorinsky eddy-viscosity model, and the sampling process is formulated in a spatially local fashion, the resulting coefficient field is highly variable and contains a significant fraction of negative values. Negative eddy viscosity leads to computational instability and as a result the model is always augmented with a stabilization mechanism. In most applications the model is stabilized by averaging the relevant equations over directions of statistical homogeneity. While this approach is effective, and is consistent with the statistical basis underlying the eddy-viscosity model, it is not applicable to complex-geometry inhomogeneous flows. Existing local formulations, intended for inhomogeneous flows, are most commonly stabilized by artificially constraining the coefficient to be positive. In this paper we introduce a new dynamic model formulation, that combines advantages of the statistical and local approaches. We propose to accumulate the required averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to in-homogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model be purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are slightly superior to those of the spatially (planar) averaged dynamic model. The relationship between the model and vortical structures in isotropic turbulence, as well as ejection events in channel flow, is investigated. Computational overhead is kept small (about 10% above the CPU requirements of the spatially averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

Monte Carlo analysis of a Schottky diode with an automatic space-variable charge algorithm

An efficient one-dimensional ensemble Monte Carlo simulator that improves the study of carrier transport by including a space-variable charge algorithm has been developed. The algorithm is automatically implemented in regions with remarkable concentration gradients. In this way is possible to study devices in which the carrier concentration varies by several orders of magnitude along the device and/or when we are interested in the population of states rarely occupied by the carriers (tails of distribution functions, hot electrons, etc) without excessive CPU requirements. In the present work this technique is used to study a Schottky barrier diode over a wide range of forward bias (80 - 800 mV). In particular, the exponential behaviour of the current - voltage characteristic, the agreement of this with the experimental results, the distribution function and the recombination velocity of carriers close to the metal - semiconductor interface confirm the validity of the implemented algorithm.

An efficient implementation of Berenger's perfectly matched layer (PML) for finite-difference time-domain mesh truncation

An efficient three-dimensional (3-D) implementation of the perfectly matched layer (PML) type of absorbing medium is presented. The technique combines a new eight-unknown time domain formulation in regions in which there is only one nonzero conductivity with the original 12-unknown formulation in the edge and corner regions where nonzero conductivities overlap. Numerical examples of radiation and guided wave problems are included to demonstrate that the modified formulation provides accuracy comparable to the original split field formulation while substantially reducing the memory and CPU requirements of the PML regions.

AWE implementation for electromagnetic FEM analysis

Although full wave electromagnetic systems are large and cumbersome to solve, typically only a few parameters, such as input impedance, S parameters, and far field pattern, are needed by the designer or analyst. A reduced order modelling of these parameters is therefore an important consideration in minimising the CPU requirements. The asymptotic waveform evaluation (AWE) method is one approach to construct a reduced order model of the input impedance or other useful electromagnetic parameters. The authors demonstrate its application and validity when used in conjunction with the finite element method to simulate full wave electromagnetic problems.

Non-LTE treatment of FE II in astrophysical plasmas

We describe our implementation of an extremely detailed model atom of singly ionized iron for NLTE computations in static and moving astrophysical plasmas. Our model atom includes 617 levels, 13,675 primary permitted transitions and up to 1.2 million secondary transitions. Our approach guarantees that the total iron opacity is included at the correct wavelength with reasonable memory and CPU requirements. We find that the lines saturate the wavelength space, such that special wavelength points inserted along the detailed profile functions may be replaced with a statistical sampling method. We describe the results of various test calculations for novae and supernovae.

An algorithm for analysis of polymer filling of molds

AbstractA numerical implementation of the Volume of Fluid (VOF) free surface technique, applied to a filling process governed by a potential flow, is introduced. The implementation is based on a finite element control volume space discretization and uses an implicit time integration. This allows for the accurate tracking of the filling front using large simulation time steps in molds with complex geometries. The approach is validated on comparision with the analytical solution for filling a one‐dimensional tube and with two‐dimensional results obtained with previously‐presented filling algorithms. Examples of the application of the approach in the analysis of structural resin transfer molding (SRTM) are presented. The capability of the method is demonstrated on predicting “race tracking” and “dry spotting” phenomena. The CPU requirement for a typical analysis is on the order of 1 to 20 s on pesonal computers.

An FD-BPM with adaptive mesh for longitudinally varying optical structures

A finite difference beam propagation method (FD-BPM) algorithm using an adaptive mesh is proposed for optimal use of computer memory and minimization of CPU times in three-dimensional longitudinally varying guiding structures. Preliminary results confirming its feasibility and the advantages of the new algorithm both in CPU and computer memory requirements are described in a 2D case using a Y-junction.

Neural networks for statistical recognition of continuous speech

In recent years there has been a significant body of work, both theoretical and experimental, that has established the viability of artificial neural networks (ANN's) as a useful technology for speech recognition. It has been shown that neural networks can be used to augment speech recognizers whose underlying structure is essentially that of hidden Markov models (HMM's). In particular, we have demonstrated that fairly simple layered structures, which we lately have termed big dumb neural networks (BDNN's), can be discriminatively trained to estimate emission probabilities for an HMM. Recently simple speech recognition systems (using context-independent phone models) based on this approach have been proved on controlled tests, to be both effective in terms of accuracy (i.e., comparable or better than equivalent state-of-the-art systems) and efficient in terms of CPU and memory run-time requirements. Research is continuing on extending these results to somewhat more complex systems. In this paper, we first give a brief overview of automatic speech recognition (ASR) and statistical pattern recognition in general. We also include a very brief review of HMM's, and then describe the use of ANN's as statistical estimators. We then review the basic principles of our hybrid HMM/ANN approach and describe some experiments. We discuss some current research topics, including new theoretical developments in training ANN's to maximize the posterior probabilities of the correct models for speech utterances. We also discuss some issues of system resources required for training and recognition. Finally, we conclude with some perspectives about fundamental limitations in the current technology and some speculations about where we can go from here.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An efficient bem solution for three‐dimensional transient heat conduction

This paper presents a computationally efficient numerical solution scheme to solve transient heat conduction problems using the boundary element method (BEM) without volume discretization. Traditionally, a transient solution using BEM is very computer intensive due to the excessive numerical integration requirements at each time increment. In the present work a numerical solution scheme based on the separation of time and space integrals in the boundary integral equation through the use of an appropriate series expansion of the integrand (incomplete gamma function) is presented. The space integrals are evaluated only once in the beginning and within each time increment the additional integrals are obtained from the previously evaluated space integrals by a simple calculation. Three‐dimensional applications are provided to compare the proposed strategy with that used traditionally. The CPU requirements are reduced substantially. The solution scheme presented allows for dynamically changing the time step size as the solution evolves. This feature is not practical in the traditional schemes based on boundary discretization only.

Estimating Effective Properties of Composites from Cross-Sectional Photographs

An algorithm is presented for the rapid evaluation of certain functionals of three-point correlation functions, measured in a plane. This simplifies the estimation of effective physical properties of composite materials from cross-sectional photographs via bounds. More precisely, Fourier coefficients of a reduced three-point correlation function are expressed as inner products of polyharmonic fields. The polyharmonic fields are evaluated with a polyharmonic version of the fast multipole method with a CPU requirement proportional to the number p of fields included and to the number N of points in a discretization of the component interfaces. The Fourier coefficients are related to structural parameters which are used in third-order bounds on conductivity and elastic properties. Inclusion of p polyharmonic fields gives structural parameters with an error decaying at least as 1/ p 3. In a simple application for disks with p = 10, superalgebraic convergence in 1/ N, and a high-order Gaussian quadrature rule for the inner products, the algorithm gives an error of typically 0.05%. A previous algorithm, involving Monte Carlo integration, gives structural parameters with an error of typically 2%.

Dynamic simulation and nonlinear‐model‐based product quality control of a crude tower

AbstractThe dynamic stagewise adiabatic flash algorithm is applied to the dynamic simulation of a crude column. This algorithm is based on the implicit integration of the model equations of each stage and the explicit combination of the stage models to form the column model. Stable, efficient integration for the crude column model is observed with simulation CPU requirements that are 20 times faster than real time using a 50 MHz 486 P.C. Specific dynamic of a crude column are identified such as one‐way interaction and inverse action. The dynamic crude column model is used to study product quality control of a crude column using nonlinear‐process‐model‐based control (PMBC) which was tested using two different steady‐state controller models for setpoint tracking and disturbance rejection. Both nonlinear PMBC controllers show good control performance, but are limited by the inherent inverse action of the crude column. Control results for a set of single‐loop PI controllers is also presented as a point of reference.

Differential covariant formalism for solving Maxwell's equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces

A rigorous differential method describing the diffraction properties of lossy periodic surfaces is presented. A nonorthogonal coordinate system and a covariant formalism of Maxwell's equation are used simplifying boundary conditions expression. Only one eigenvalue system, unique for the TE and TM polarizations even for an oblique incidence, needs to be solved. Thus the numerical treatment is very efficient and CPU requirements significantly reduced. Numerical results are successfully compared with those obtained by an integral method using the boundary element method (BEM) as a numerical procedure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Hybrid Tridiagonalization Algorithm for Symmetric Sparse Matrices

This paper considers sequential direct methods for the reduction of a sparse symmetric matrix to tridiagonal form using sequences of orthogonal similarity transformations. Currently, the best published approach combines a bandwidth-reducing preordering algorithm, perhaps Gibbs–Poole–Stockmeyer (GPS), with a band-preserving tridiagonalization such as the EISPACK BANDR routine. This paper introduces a new hybrid tridiagonalization algorithm, BANDHYB, based upon band-preserving reduction techniques that rearrange the elimination sequence of nonzero entries to take better advantage of the sparsity within the band of the permuted matrix. For many practical sparse problems a GPS-BANDHYB approach substantially reduces the CPU requirements of tridiagonalization, compared to a GPS-BANDR scheme, without increasing storage requirements. Over a wide range of sparse problems the new algorithm reduced CPU time by an average of 31%, with reductions of more than 60% observed for some problems.

BLOCK-CORRECTION-BASED MULTIGRID METHOD FOR FLUID FLOW PROBLEMS

Abstract A coupled-point solution procedure employing a multilevel correction strategy is developed and test results are presented in this article. The method is based on the principle of deriving the coarse-grid discretization equations from the fine-grid discretization equations. The adaptive scheme is applied to the sample problems of laminar flow in lid-driven square and cubic cavities and flow over a backward-facing step. The study demonstrates that the multigrid method is robust and rapidly convergent, resulting in improvement in CPU requirements by a factor of approximately S to 15 compared to the sequential signal-grid SIMPLER procedure. The performance of procedure improves, in comparison to the SIMPLER, as the number of grid points increases.

Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics

A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well‐known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.

EFIE time-marching scattering from bodies of revolution and its applications

The authors treat the "entire-tangent" representation of a time-domain electric-field integral equation (TDEFIE) for solving transient scattering problems involving perfectly conducting (PEC) bodies of revolution (BOR). This entire-tangent TDEFIE reduces three-dimensional scattering problems with axial symmetry to two-dimensional problems, thus facilitating the numerical treatment and significantly reducing CPU requirements. Additional refinements and algorithm efficiencies are described. Some numerical results and applications are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>