Fast Algorithm For Evaluation Research Articles

Calibration and fast evaluation algorithms for homogeneous orthotropic polynomial yield functions

Calibration and fast evaluation algorithms for homogeneous orthotropic polynomial yield functions

Algorithm for fast evaluation of in-plane fiber orientation in reinforced plastics using light microscopy images

Methods for evaluating the orientation of carbon fibers in reinforced plastics vary in complexity and are application specific. Here, we report an algorithm that quickly evaluates in-plane fiber orientation based on determining the correlation coefficient of adjacent regions in microscopy images. The result is not the fiber orientation of individual fibers, but the principal fiber orientation of small image areas. This method is applicable to large areas due to its low computation time and captures varying fiber orientations, making it suitable for the study of injection molded samples with complex geometries. A great advantage is that no information about the fibers or the matrix, or their combination, is needed prior to the analysis. This approach is also suitable for samples with surface defects. Demonstrations of this technique are given for Polyamide 6 and Polypropylene with 30 weight % carbon fibers of different fiber lengths.

A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions

AbstractWe study a fully‐discrete stabilizer‐free weak Galerkin (SFWG) finite element method for the initial‐boundary value problem of variable‐order Caputo time‐fractional diffusion equation. Optimal convergence order in norm for fully‐discrete SFWG scheme is obtained. Furthermore, we develop a fast evaluation algorithm to improve the computational efficiency. Numerical experiments are performed to verify theoretical results.

Fast Evaluation Algorithms for Elementary Algebraic and Inverse Functions Using the FEE Method

Fast Evaluation Algorithms for Elementary Algebraic and Inverse Functions Using the FEE Method

Fast transforms over finite fields of characteristic two

We describe new fast algorithms for evaluation and interpolation on the “novel” polynomial basis over finite fields of characteristic two introduced by Lin et al. (2014). Fast algorithms are also described for converting between their basis and the monomial basis, as well as for converting to and from the Newton basis associated with the evaluation points of the evaluation and interpolation algorithms. Combining algorithms yields a new truncated additive fast Fourier transform (FFT) and inverse truncated additive FFT which improve upon some previous algorithms when the field possesses an appropriate tower of subfields.

Research on Fast Evaluation Algorithm Based on Hopfield Neural Network

The fast evaluation algorithm based on Hopfield neural network (HNN) was presented to solve problems of multiple influencing factors, complex evaluation mechanism, inaccurate evaluation results and slow evaluation process in water quality evaluation. In storage of evaluation criteria information, this algorithm performed orthogonal and symmetric processing of information to guarantee accurate storage of information and steady operation of the network. After storage of the evaluation criteria, the connection weights of the network were determined and the actual measured data input into the HNN model, where such data were evaluated in a fast manner. In addition, the stability of this algorithm was verified, proving that this fast learning algorithm could ensure steady operation of HNN, which converged to the minimum. The fast learning algorithm avoided modular calculations currently applied in the existing algorithms, to greatly reduce the computation. As a result, only one iterative calculation would be needed to obtain the correct water quality evaluation results, which significantly enhanced the speed of water quality evaluation. At the same time, this algorithm accurately saved the evaluation criteria to ensure correctness of the final evaluation results. Finally, this algorithm was applied in surface water environmental quality evaluation and eutrophic water quality evaluation and compared with other algorithms, leading to the conclusion that this algorithm could evaluate water quality of different kinds in a fast and accurate manner.

A fast and stable solver for acoustic scattering problems based on the nonuniform grid approach.

A fast and stable boundary element method (BEM) algorithm for solving external problems of acoustic scattering by impenetrable bodies is developed. The method employs the Burton-Miller integral equation, which provides stable convergence of iterative solvers, and a generalized multilevel nonuniform grid (MLNG) algorithm for fast evaluation of field integrals. The MLNG approach is used here for the removal of computational bottlenecks involved with repeated matrix-vector multiplications as well as for the low-order basis function regularization of the hyper-singular integral kernel. The method is used for calculating the fields scattered by large acoustic scatterers, including nonconvex bodies with piece-wise smooth surfaces. As a result, the algorithm is capable of accurately incorporating high-frequency effects such as creeping waves and multiple-edges diffractions. In all cases, stable convergence of the method is observed. High accuracy of the method is demonstrated by comparison with the traditional BEM solution. The computational complexity of the method in terms of both the computation time and storage is estimated in practical computations and shown to be close to the asymptotic O(N log N) dependence.

Multicomponent transport in laminar flames

The transport fluxes and transport coefficients derived from the kinetic theory of polyatomic gas mixtures are discussed. The mathematical structure of transport linear systems and numerical algorithms for fast evaluation of accurate transport coefficients are presented. The impact of thermal diffusion and volume viscosity on flame structures and of thermodynamic nonidealities on cold mixing layers are investigated.

Modeling the Hysteretic Behavior of Textured and Random Ferroelectric Ceramics

The algorithm for fast evaluation of the hysteresis loops of uniaxial or textured ferroelectric microcrystal or grains with long-range interactions is developed. Two types of ceramic microstructures are considered: 1. Random ceramics with complete isotropic distribution function of the crystallographic orientations of grains; and 2. Textured ceramics with anisotropic distribution function of the crystallographic orientations of grains. The qualitative analysis of the hysteretic behavior in terms of the grain distribution function is successfully demonstrated. Comparison of the calculated results with experimental data for Pb (Mg1/3Nb2/3)O3 PbTiO3 ceramics is presented.

AN ANN APPROACHES ON ESTIMATING EARTHQUAKE PERFORMANCES OF EXISTING RC BUILDINGS

This study aims at developing an artificial intelligence-based (ANN based) analytical method to analyze earthquake performances of the reinforced concrete (RC) buildings. In the scope of the present study, 66 real RC buildings with four to ten storeys were subject to performance analysis according to 19 parameters considered effective on the performance of RC buildings. In addition, the level of performance of these buildings in case of an earthquake was determined on the basis of the 4-grade performance levels specified in Turkish Earthquake Code-2007 (TEC-2007). Thus, an output performance data group was created for the analyzed buildings, in accordance with the input data. Thanks to the ANN- based fast evaluation algorithm mentioned above and developed within the scope of the proposed project study, it will be possible to make an economic and rapid evaluation of four to ten-storey RC buildings in Turkey with great accuracy (about 80%). Detection of post-earthquake performances of RC buildings in the scope of the present study will facilitate reaching important results in terms of buildings, which will be beneficial for Civil Engineers of Turkey and similar countries.

A Poisson mixture model of discrete choice

In this paper, we introduce a new Poisson mixture model for count panel data where the underlying Poisson process intensity is determined endogenously by consumer latent utility maximization over a set of choice alternatives. This formulation accommodates the choice and count in a single random utility framework with desirable theoretical properties. Individual heterogeneity is introduced through a random coefficient scheme with a flexible semiparametric distribution. We deal with the analytical intractability of the resulting mixture by recasting the model as an embedding of infinite sequences of scaled moments of the mixing distribution, and newly derive their cumulant representations along with bounds on their rate of numerical convergence. We further develop an efficient recursive algorithm for fast evaluation of the model likelihood within a Bayesian Gibbs sampling scheme. We apply our model to a recent household panel of supermarket visit counts. We estimate the nonparametric density of three key variables of interest–price, driving distance, and their interaction–while controlling for a range of consumer demographic characteristics. We use this econometric framework to assess the opportunity cost of time and analyze the interaction between store choice, trip frequency, search intensity, and household and store characteristics. We also conduct a counterfactual welfare experiment and compute the compensating variation for a 10%–30% increase in Walmart prices.

A fast algorithm for evaluation of normalized Hermite functions

An algorithm for computing the normalized Hermite Functions, h n (x) in floating point arithmetic is presented. The algorithm is based on an efficient numerical evaluation of certain closed contour integrals in the complex plane. For large degree n, the algorithm is significantly faster than the O(n) complexity of the well known three term recurrence relation. Comparable accuracy is achieved in no more than $O(\sqrt{n})$ operations, and for arguments bounded away from $\pm \sqrt {2n}$ , only $O(\sqrt{\ln{n}})$ operations.

Adaptive Nonuniform-Grid (NG) Algorithm for Fast Capacitance Extraction

A novel method for computing the capacitance matrices of arbitrary shaped three-dimensional geometries is presented. The proposed approach combines a novel nonuniform-grid (NG) algorithm for fast evaluation of potentials due to given source distributions with an iterative solution of the pertinent integral equations. The NG algorithm is based on the observation that locally the potential produced by a finite size source can be interpolated from its samples at a small number of points of a nonuniform spherical grid. This observation leads to a multilevel algorithm comprising interpolation and aggregation of potentials. The resulting hierarchical algorithm attains an O(N) asymptotic complexity and memory requirements. The computational efficiency is further improved for quasi-planar geometries by the use of adaptive grids

Nonuniform grid time domain (NGTD) algorithm for fast evaluation of transient wave fields

A novel algorithm to efficiently compute transient wave fields produced by known three-dimensional source constellations is proposed. The algorithm uses domain decomposition concepts and comprises two steps to be repeated for each subdomain considered. In the first step, delay- and amplitude- compensated fields, produced by sources residing inside each subdomain are computed at a sparse set of points surrounding the observation domain. In the second step, total fields in the observer domain are evaluated by interpolation, delay and amplitude restoration, and aggregation of subdomain fields. The proposed scheme is well-suited to accelerate the solution of time domain integral equations by marching on in time, to carry out time domain physical optics calculations, and to realize near- to far-field transformations of transients. Moreover, the scheme automatically adapts to, and takes advantage of, special geometrical features of the source-observer constellation studied, a key benefit when analyzing quasi-planar configurations. In addition, it realizes a seamless transition from the dynamic to the quasi-static regime, thus facilitating a unified treatment of electrically large and small problems. Last but not least, the scheme is remarkably simple to implement.

Another preprocessing algorithm for generalized one-dimensional fast multipole method

The fast multipole method (FMM), which is originally an algorithm for fast evaluation of particle interactions, is also effective for accelerating several numerical computations. Yarvin and Rokhlin proposed “generalized” FMM using the singular value decomposition (SVD), which gives the optimum low-rank approximation. Their algorithm reduces the computational costs of the FMM evaluation and frees the FMM from analytical approximation formulae. However, the computational complexity of the preprocessing for an N× N matrix is O( N 3) because of the SVD, and it requires orthogonal matrices of the low-rank approximations. In this paper we propose another preprocessing algorithm for the generalized FMM. Our algorithm runs in time O( N 2) even with the SVD and releases the low-rank approximations from orthogonal matrices. The triangularization by the QR decomposition with sparsification, which reduces the costs of the FMM more than the diagonalization, is enabled. Although the algorithm by Yarvin and Rokhlin can be accelerated to O( N 2) using the QR decomposition, our preprocessing algorithm outperforms it in fast spherical filter, fast polynomial interpolation and fast Legendre transform.

Signal evaluation for high-speed confocal measurements.

The confocal-detection principle is open especially for use in medical applications. For inspection systems applications for technical objects in reflection confocal setups are of growing importance. For such applications the confocal measurements need to have a very short measuring time. A fast detection system is needed and to satisfy this requirement only a small number of height levels are measured and a fast-evaluation algorithm is used. Drawbacks of the reduction of height levels are a greater influence of noise and additional systematic errors on the measured heights. Study the effects of the reduction are calculated, different evaluation algorithms are analyzed, and the optimization of the parameters is discussed.

Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2

We address the problem of synthesizing a generalized Gaussian noise with exponent 1/2 by means of a nonlinear memoryless transformation applied to a uniform noise. We show that this transformation is expressable in terms of a special function known under the name of the Lambert W function. We review the main methods for numerical evaluation of the relevant branch of the (multivalued) Lambert W function with controlled accuracy and complement them with an original rational function approximation. Based on these methods, synthesis of the generalized Gaussian noise can be performed with arbitrary accuracy. We construct a simple and fast evaluation algorithm with prescribed accuracy, which is especially suited for Monte Carlo simulation requiring large numbers of realizations of the generalized Gaussian noise.

A real-time scheme of cubic parametric curve interpolations for CNC systems

In this paper, the popular finite forward differencing algorithm for fast evaluation of points on a cubic parametric curve is modified for its application to CNC systems so that the inherent accumulative error in the calculation of one piece of curve will not propagate to the whole composite curve. Using specified tolerances, a computationally non-intensive method of analysis for the computation of step size has been developed. Tolerance, velocity, acceleration and jerk analyses are conducted based on computer simulation results. The interpolation scheme method developed in this paper has been analyzed and proven to be accurate, adaptive to the curvature of a curve, reduces jerk, and can be easily implemented in CNC systems. Finally, the paper explains why the algorithm developed here is natural for cubic parametric curve interpolations.

Fast evaluation of potential and force field in particle systems using a fair-split tree spatial structure

We consider the following force field computation problem: given a duster of n particles in 3-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard Jones. Since there are n(n−1)/2pairs, direct method requires θ(n2) time. In this paper, we report our computational experiences with a new O(nlogn) time algorithm for fast evaluation of potential and force field in large Lennard – Jones clusters. This algorithm is based on a fair-split tree which guarantees O(nlogn)worst-case time complexity without any restriction on particle distributions. For randomly generated particle systems, our implementation outperforms the direct method when the number of panicles is 500 or larger This is the lowest cross over point ever reported in the literature.

Fast algorithms for data reduction in modern optical three-dimensional profile measurement systems with MMX technology

Confocal microscopy and white-light interferometry are two promising methods for the three-dimensional microstructure analysis of technical and biologic specimens. For both methods the specimen is scanned through the focus position by means of an actuator. A large series of intensity frames is acquired. These data are used for the final calculation of the topography. We demonstrate that the multimedia extended (MMX) instruction set, which is implemented in modern Intel microprocessors, can be used for effective real-time preprocessing and for fast evaluation algorithms. So this new technique enables the implementation of more-complex algorithms with acceptable run times even on standard computer technology. The possibilities of the MMX instruction set are discussed for confocal microscopy and for white-light interferometry.