Computer CPU Time Research Articles

Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities

Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon absorption in optical media is proceeded conventionally through the iterative solution of nonlinear algebraic equations. Here, we study three approaches for the field update including simple noniterative explicit schemes. By comparing them to the analytical results for optical pulse propagation in long nonlinear media (nonlinear phase incursion for the pump wave of about π radians), we demonstrate convincingly that simple noniterative FDTD updating schemes, which are commonly believed to be inaccurate and unstable, produce accurate results and drastically speed up the computation as compared to ADE approaches. Such schemes can significantly reduce the CPU time for nonlinear computations, especially in 3-D models.

Application of Scale Relativity (ScR) Theory to the Problem of a Particle in a Finite One-Dimensional Square Well (FODSW) Potential

In the present work, and along the lines of Hermann, ScR theory is applied to a finite one-dimensional square well potential problem. The aim is to show that scale relativity theory can reproduce quantum mechanical results without employing the Schrödinger equation. Some mathematical difficulties that arise when obtaining the solution to this problem were overcome by utilizing a novel mathematical connection between ScR theory and the well-known Riccati equation. Computer programs were written using the standard MATLAB 7 code to numerically simulate the behavior of the quantum particle in the above potential utilizing the solutions of the fractal equations of motion obtained from ScR theory. Several attempts were made to fix some of the parameters in the numerical simulations to obtain the best possible results in a practical computer CPU time within limited local computer facilities [1,2]. Comparison of the present results with the corresponding results obtained from conventional quantum mechanics by solving the Schrödinger equation, shows very good agreement. This agreement was improved further by optimizing the parameters used in the numerical simulations [1,3]. This represents a new example where scale relativity theory, based on a fractal space-time concept, can accurately reproduce quantum mechanical results without invoking the Schrödinger equation.

Geometrical MTF computation method based on the irradiance model

The Modulation Transfer Function (MTF) is a measure of an optical system’s ability to transfer contrast from the specimen to the image plane at a specific resolution. It can be computed either numerically by geometrical optics or measured experimentally by imaging a knife edge or a bar-target pattern of varying spatial frequency. Previously, MTF accuracy was generally affected by the size of the mesh on the image plane. This paper presents a new MTF computation method based on the irradiance model, without counting the number of rays hitting each grid. To verify the method, the MTF in the sagittal and meridional directions of an axis-symmetrical optical system is computed by both the ray-counting and the proposed methods. It is found that the grid size meshed on the image plane significantly affects the MTF of the ray-counting method, sometimes with significantly negative results. The proposed irradiance method is immune to issues of grid size. The CPU computation time for the two methods is approximately the same.

A second-order and two-scale computation method for heat conduction equation with rapidly oscillatory coefficients

This paper presents a second-order and two-scale computation method of initial-boundary value problem for heat conduction equation with rapidly oscillating coefficients. This method can be applied to heat conduction analysis of composite materials. The main advantages of this method are that it can greatly save computer memory and CPU time, and it possesses good precision at the same time. Finally numerical results show that the presented method is effective and reliable.

An efficient, second order method for the approximation of the Basset history force

The hydrodynamic force exerted by a fluid on small isolated rigid spherical particles are usually well described by the Maxey–Riley (MR) equation. The most time-consuming contribution in the MR equation is the Basset history force which is a well-known problem for many-particle simulations in turbulence. In this paper a novel numerical approach is proposed for the computation of the Basset history force based on the use of exponential functions to approximate the tail of the Basset force kernel. Typically, this approach not only decreases the cpu time and memory requirements for the Basset force computation by more than an order of magnitude, but also increases the accuracy by an order of magnitude. The method has a temporal accuracy of O(Δt2) which is a substantial improvement compared to methods available in the literature. Furthermore, the method is partially implicit in order to increase stability of the computation. Traditional methods for the calculation of the Basset history force can influence statistical properties of the particles in isotropic turbulence, which is due to the error made by approximating the Basset force and the limited number of particles that can be tracked with classical methods. The new method turns out to provide more reliable statistical data.

Hybrid pattern search and simulated annealing for fuzzy production planning problems

In this paper, the hybridization of PS (Pattern Search) method and SA (Simulated Annealing) are incorporated in the optimization process. This is in order to look for the global optimal solution for the fitness function and decision variables as well as minimum computational CPU time. The real strength of SA approach has been tested in a case study problem of industrial production planning. This is due to the great advantage of SA for being easily escaping from trapped in local minima by accepting up-hill move through a probabilistic procedure in the final stages of optimization process. In the Ph.D. Thesis by Vasant (2008) [4] , 16 different techniques were provided of heuristic and meta-heuristic approaches in solving industrial production problems with nonlinear cubic objective functions, eight decision variables and 29 constraints. In this paper, fuzzy technological problems have been solved using hybrid techniques of pattern search and simulated annealing (HSAPS). The simulated and computational results are compared to other various evolutionary techniques.

Designing of devices for wideband matching of power traveling-wave tubes with a coupled resonator chain

A simulation technique is proposed for devices providing for wideband matching of slow-wave systems that are coupled resonator chains. The technique requires the minimum CPU time for computations. A traveling-wave tube section including matching elements and a waveguide energy output are designed. The results of numerical and experimental tests of the proposed technique are presented.

Multirate Analysis Method for a Power Electronic System by Circuit Partitioning

Various fast and efficient computation techniques for a power converter simulation have been researched. According to the conventional methods, a single step size for a whole circuit is selected for the numerical integration. A real-power electronic system, however, is multirate in that its currents and voltages nonuniformly vary spatially and temporally, and its subcircuits have different transient rates. A simulation that selected an appropriate step size for each subcircuit independently would, therefore, be more efficient. Several multirate analysis techniques have already been proposed; this paper proposes a new method that divides the whole circuit into subcircuits by applying an explicit integration formula to series inductors and/or parallel capacitors, and then integrates subcircuits by applying an implicit formula with independent integration step sizes. As analysis examples, this method is applied to an ac-dc converter, a benchmark test circuit, and a dc-link inverter control system. The proposed method's effectiveness at reducing computational steps and CPU times is investigated, and its performance and efficiency are validated.

An efficient algebraic method for computing eigensolution sensitivity of asymmetric damped systems

In this paper, an efficient algebraic method for the computation of eigensolution derivatives of asymmetric damped systems with distinct eigenvalues is presented. By introducing an additional and new normalization condition, we construct two extended systems of linear equations with nonsingular coefficient matrices which are transpose to each other. We can compute the derivatives of the eigenvalues and their associated right and left eigenvectors by solving the two systems, respectively. In this way, the CPU computation time and the storage space are considerably reduced. Finally, a numerical example is included to demonstrate the validity of the proposed method.

Efficient Calculation of Statistical Moments for Structural Health Monitoring

Wireless networks of smart sensors with computations distributed over multiple sensor packages have shown considerable promise in providing low-cost structural health monitoring. In these networks, microprocessors are typically embedded in individual smart sensor packages. The efficiency of embedded computational algorithms is of critical importance because the size, cost, and power requirements of the sensor arrays are central concerns. Here, very efficient methodologies are presented to compute statistical moments of a measured response time-history. These moments: the mean, standard deviation, skewness, and kurtosis are often used to characterize a measured irregular response. Two alternative approaches are presented, each of which can save substantial computer memory requirements and CPU time in certain applications. The first approach reconsiders the computational benefits of computing statistical moments by separating the data into bins and then computing the moments from the geometry of the resulting histogram, which effectively becomes a one-pass algorithm for higher moments. One benefit is that the statistical moment calculations can be carried out to arbitrary accuracy such that the computations can be tuned to the precision of the sensor hardware. The second approach is a new analytical methodology to combine statistical moments from individual segments of a time-history such that the resulting overall moments are those of the complete time-history. This methodology could be used to allow for parallel computation of statistical moments with subsequent combination of those moments, or for combination of statistical moments computed at sequential times. A worked example is presented comparing two implementations of the new methodologies with conventional calculations in monitoring the global performance of an offshore tension leg platform. Accuracy, efficiency, and storage requirements of the calculation methods are compared with those of conventional methods. The results show that substantial CPU and memory savings can be attained with no loss in accuracy and that more dramatic savings can be attained if a slight reduction in accuracy is acceptable.

Convergence analysis of truncated incomplete Hessian Newton minimization method and application in biomolecular potential energy minimization

This paper gives a general convergence analysis to the truncated incomplete Hessian Newton method (T-IHN). It shows that T-IHN is globally convergent even with an indefinite incomplete Hessian matrix or an indefinite preconditioner, which may happen in practice. It also proves that when the T-IHN iterates are close enough to a minimum point, T-IHN has a Q-linear rate of convergence, and an admissible line search steplength of one. Moreover, a particular T-IHN algorithm is constructed for minimizing a biomolecular potential energy function, and numerically tested for a protein model problem based on a widely used molecular simulation package, CHARMM. Numerical results confirm the theoretical results, and demonstrate that T-IHN can have a better performance (in terms of computer CPU time) than most CHARMM minimizers.

Multiple scales analysis of chirped Bragg gratings

In this paper, a second-order multiple scales expansion is used to derive coupled-mode equations for a linearly chirped Bragg grating. This eliminates the error in the spectral response introduced by large values of the grating strength when conventional first-order coupled-mode theory is used. The autonomous and nonautonomous formulations of these equations are considered and compared in terms of accuracy and speed of the numerical solution of the resulting two-point boundary-value problem for the reflectance of the grating. These solutions are compared with the characteristic matrix solution taken as a reference. By using the fundamental matrix method, the autonomous formulation is found to be as accurate as the characteristic matrix method but faster in terms of computer CPU time.

NEW VERSION OF TWA USING TWO-DIMENSIONAL NON-UNIFORM FAST FOURIER MODE TRANSFORM (2D-NUFFMT) FOR FULL-WAVE INVESTIGATION OF MICROWAVE INTEGRATED CIRCUITS

In this paper, a novel version of the transverse wave approach (TWA) based on two-dimensional non-uniform fast Fourier mode transform (2D-NUFFMT) is presented and developed for full- wave analysis of RF integrated circuits (RFICs). An adaptive mesh reflnement is applied in this advanced TWA process and CPU computation time is evaluated throughout 30GHz patch antenna, application belonging to wireless systems. The TWA in its novel version is favorably compared with the conventional one in presence of AMT technique in the context of EM simulations. Another version of TWA is outlined to illustrate a computationally e-cient way to handle an arbitrary mesh for RFICs analysis with high complexity problems.

Bound analysis in univariately truncated Generalized High Dimensional Model Representation for random-data partitioning: Interval GHDMR

Generalized High Dimensional Model Representation (GHDMR) method is based on a divide-and-conquer philosophy and it approximately reduces the N-dimensional interpolation to N number of one-dimensional interpolations. It is an exact representation which uses Dirac delta functions as the weight functions. GHDMR's components with multivariances higher than univariance are quite complicated and we prefer to use only its constant and univariate terms. In this work, we try to construct a new high dimensional model representation based method, Interval GHDMR, to be used when a random discrete multivariate data set which has construction errors coming from incapabilities or limited capabilities of the measurement devices or tools is given and an analytical structure for a multivariate function that passes through the nodes of this data set is to be determined. The errors coming from the construction of the data set that describes the sought multivariate function result in a band structure for the sought function instead of an analytical structure. The main purpose, here, is to estimate the total error formed through the given method in the given multivariate interpolation problem and, to this end, to partition the given multivariate data into at most univariate data and to determine an approximate band structure (or interval) for the sought function. By this way, the computational complexity and CPU time needed for computer based applications of the problem decrease.

Evaluation of modal incremental dynamic analysis, using input energy intensity and modified bilinear curve

AbstractIn this paper, a technique for the study of nonlinear performance of structures in different levels of earthquakes is developed. In this method, the Incremental Dynamic Analysis (IDA) curves are not achieved from nonlinear dynamic analysis of multi‐degree‐of‐freedom (MDF) structure. However, the procedure of constructing these curves is based on modelling of the entire structure with several single‐degrees‐of‐freedom (SDF) structures and evaluating them through the modal pushover analysis method. An innovative idea for approximating pushover curves that is based on error distribution is introduced in this investigation. Furthermore, the total input energy applied towards the SDF oscillator, which gets converted into MDF structure, is used as intensity measure to impose the different levels of scaled earthquakes.This technique possesses all the advantages of the IDA method in studying the performance of structures in different levels of earthquake. In addition, it benefits from easy usage, high solving speed and less computational CPU time and in attendance with the modified bilinear curves. In this paper, six earthquake records have been applied over four different 4, 8, 12 and 16‐storey structures. The structural responses derived by this method, in the format of multi‐modal incremental curves, containing maximum displacement, drift, hinge rotation and hysteretic energy at the end of the earthquake, have been compared with the IDA method. Comparison of the results is found to have acceptable precision and reveals good agreement between two methods. Copyright © 2008 John Wiley & Sons, Ltd.

Optimal Placement of PMUs by Integer Linear Programming

This letter presents a simple optimal placement algorithm of phasor measurement units (PMU) by using integer linear programming. Cases with and without conventional power flow and injection measurements are considered. The measurement placement problems under those cases are formulated as an integer linear programming which saves the CPU computation time greatly. Simulation results show that the proposed algorithm can be used in practice.

A combined neural network and DEA for measuring efficiency of large scale datasets

Data Envelopment Analysis (DEA) is one of the most widely used methods in the measurement of the efficiency and productivity of Decision Making Units (DMUs). DEA for a large dataset with many inputs/outputs would require huge computer resources in terms of memory and CPU time. This paper proposes a neural network back-propagation Data Envelopment Analysis to address this problem for the very large scale datasets now emerging in practice. Neural network requirements for computer memory and CPU time are far less than that needed by conventional DEA methods and can therefore be a useful tool in measuring the efficiency of large datasets. Finally, the back-propagation DEA algorithm is applied to five large datasets and compared with the results obtained by conventional DEA.

Application of the Genetic Algorithm to Calculate the Interaction Parameters for Multiphase and Multicomponent Systems

A method based on the Genetic Algorithm (GA) was developed to study the phase behavior of multicomponent and multiphase systems. Upon application of the GA to the thermodynamic models which are commonly used to study the VLE, VLLE and LLE phase equilibria, the physically meaningful values for the Binary Interaction Parameters (BIP) of the models were obtained. Using the method proposed in this work the activity coefficients for components at infinite dilution, obtained from the local composition based models, can be accurately predicted comparing to the experimental data available in the literature. In this work, a Global Optimization Procedure (GOP) based on the GA was developed to obtain the binary interaction parameters of the Wilson, NRTL and the UNIQUAC models for a number of systems at various temperatures. The VLE, VLLE and LLE values of the binary interaction parameters for the activity coefficients models were compared with those reported in the literature for the systems studied in this work. The results showed that the values reported for the binary interaction parameters can predict the activity coefficients at infinite dilutions for the components in the VLE, VLLE and LLE systems studied in this work. In order to confirm the accuracy of the results, the values for the activity coefficients at infinite dilution in binary solutions were compared with those reported in the literature. The comparison showed that the models studied using the proposed method can predict the physically meaningful binary interaction parameters among the species present in solutions. In addition to the accuracy, simplicity, generality and short CPU computation time of the proposed method should be mentioned as some of its clearest advantages.

Rough Sets-Assisted Subfield Optimization for Alternating Current Plasma Display Panel

Plasma display panel technology employs a pulse-number modulation method to generate the gradation of the display. However, this method can create a false contour distortion when moving pictures are reproduced. In this paper, we propose an effective subfield optimization technique which is based on measuring motion picture distortion. To this end, we propose two applications of the measurements. One is optimum selection of the codewords to improve performance, and the other is the application of rough sets theory to subfield optimization, which reduces computational CPU time. Simulation results show that dynamic false contouring can be effectively reduced by this optimization technique, and the complexity can be minimized, using rough sets theory.

Limit analysis of structures containing flaws based on a modified elastic compensation method

The elastic compensation method (ECM) based on the conventional linear elastic finite element method is a simple and effective method for structural limit analysis. However, for structures containing flaws, computational errors of the ECM are relatively greater and numerical singularity is often caused before a better solution can be achieved. Firstly, the present paper employs the Banach's contraction mapping theorem in mathematical analysis to discuss the convergence problem of the iterative method of the ECM. The discussions demonstrate that only when iterative elastic modulus sequences are contraction mappings can a good limit load solution be obtained. Secondly, a modified elastic compensation method (KtECM) is proposed, in which iterative elastic modulus sequences of structural main load-carrying elements can satisfy the condition of contraction mapping. Moreover, an adjustable factor related with structural stress concentration factor (Kt) is introduced to define a rational nominal stress and to dynamically balance the computational precision and CPU time consumed. Finally, we perform limit load analyses for several representative structures containing flaws. These solutions obtained by the KtECM are compared with results from the analytical method, the elastic-plastic analysis method (EPAM) and the ECM. It reaches the conclusion that the KtECM can provide good estimations of plastic limit loads for structures containing flaws. The KtECM has the advantages of simplicity, high efficiency and convenience for engineering applications.