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The simulation of slowly varying electromagnetic fields is possible for very large, realistic problems with finite-difference implicit time-domain (FDiTD) and frequency-domain (FDFD) formulations on the basis of the consistent Finite-Integration Technique (FIT). Magneto-quasistatic time-domain formulations combined with implicit time marching schemes require the repeated solution of real-valued symmetric systems. The solution of driven frequency domain problems usually consists in the solution of one non-Hermitean system. Preconditioned conjugate gradient-type methods are well-suited for this task. They allow the efficient solution even for consistent singular or near-singular systems, which typically arise from formulations for slowly varying electromagnetic fields using the Maxwell-Grid-Equations of the FI-Method. Numerical results for TEAM workshop 11 benchmark problem and for a large practical problem, a shading ring sensor, show that the presented algorithms are capable of solving realistic problems for large numbers of unknowns in acceptable calculation times on contemporary medium sized workstations. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we develop algorithms to independently draw from a family of conjugate posterior distributions over the structural parameterization when sign and zero restrictions are used to identify structural vector autoregressions (SVARs). We call this family of conjugate posteriors normal‐generalized‐normal. Our algorithms draw from a conjugate uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization and transform the draws into the structural parameterization; this transformation induces a normal‐generalized‐normal posterior over the structural parameterization. The uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization has been prominent after the work of Uhlig (2005). We use Beaudry, Nam, and Wang's (2011) work on the relevance of optimism shocks to show the dangers of using alternative approaches to implementing sign and zero restrictions to identify SVARs like the penalty function approach. In particular, we analytically show that the penalty function approach adds restrictions to the ones described in the identification scheme. [ABSTRACT FROM AUTHOR]

SUMMARY This special issue contains a selection of papers from the Sixth International Workshop on the Numerical Solution of Markov Chains, held in Williamsburg, Virginia on September 16-17, 2010. The papers cover a broad range of topics including perturbation theory for absorbing chains, bounding techniques, steady-state and transient solution methods, multilevel algorithms, preconditioning, and applications. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: This paper concerns the analysis of an iterative scheme delivering approximate control laws for the tracking regulation problems for nonlinear systems. The procedure can be applied to finite‐ and infinite‐dimensional systems, and the underlying methodology derives from the geometric methods, which have been developed for both linear and nonlinear systems. In the nonlinear case, the main tool is the center manifold theorem. Indeed, in the geometric methodology, under the assumption that the signals to be tracked are generated by a finite‐dimensional exo‐system, the desired control is obtained by solving a pair of operator equations called the regulator equations. In this paper, we extend the concept of regulator equations to what we refer to as the dynamic regulator equations. Just as it is generally quite difficult to solve the regulator equations, it can be equally difficult to solve the dynamic regulator equations. As the authors have already shown in the linear case, a straightforward attempt to solve the dynamic regulator equations leads to a singular system, which can be regularized to obtain an iterative scheme that provides approximate control laws that provide accurate tracking with very a small tracking error after only a couple of iterations. In this paper, we generalize the iterative scheme to nonlinear systems and provide error estimates for the first 3 iterations. Both finite‐ and infinite‐dimensional examples are given to validate the estimates. We comment that the method has also been applied to a wide range of nonlinear distributed parameter examples described in the references. [ABSTRACT FROM AUTHOR]

Summary: This paper studies a low‐communication algorithm for solving elliptic PDEs on high‐performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accuracy and scalability, especially on more difficult problems. In addition, an updated convergence proof is presented based on heuristic assumptions that are supported by numerical evidence. Furthermore, a new performance model is developed that shows increased performance benefits for NIRD when problems are more expensive to solve using traditional methods. Finally, extensive testing on a variety of elliptic problems provides additional insight into the behavior of NIRD and additional evidence that NIRD achieves excellent convergence on a wide class of elliptic PDEs and, as such, should be a very competitive method for solving PDEs on large parallel computers. [ABSTRACT FROM AUTHOR]

This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain Ω⊂ℝ2$$ \Omega \subset {\mathrm{\mathbb{R}}}^2 $$. Here, the temporal partial derivative is in the sense of Caputo with order α∈(0,1)$$ \alpha \in \left(0,1\right) $$, and the spatial partial derivatives are of Riesz type with orders β,γ∈(0,1)$$ \beta, \gamma \in \left(0,1\right) $$ in x$$ x $$‐ and y$$ y $$‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

Integration algorithm is an important mean to solve the discrete time equations of structural dynamics in earthquake engineering. In this paper, a new model‐based explicit integration algorithm, featured by optimization‐based integration parameter updating, is developed for a more accurate and efficient solution of structural dynamic problems. The new integration algorithm is designed to yield minimum error and controllable numerical dispersion under the premise of stability by defining objective functions and constraints. Numerical properties of the new integration algorithm are investigated in details using the amplification matrix method for a linear elastic single degree‐of‐freedom system. Meanwhile, representative numerical examples and complex structure examples are analyzed and compared with other representative algorithms. As a result, the proposed algorithm yields comparable numerical characteristics with other methods, but exhibits pronounced superiority in controllable algorithmic dissipation, higher precision, and better efficiency. Therefore, the new integration algorithm possesses extensive application prospect in solving complicated linear and nonlinear structural dynamic problems. [ABSTRACT FROM AUTHOR]

Recently, for signal processing such as echo cancellation and equalization it is required to develop IIR-adaptive digital filters. This paper proposes a new-type IIR- adaptive algorithm based on the orthogonalization method, considers the convergence of the algorithm, and verifies its effectiveness by simulation. White's algorithm is one of IIR-adaptive algorithms reported thus far and Feintuch's algorithm is known as its approximation algorithm. This paper also derives an IIR-adaptive algorithm using both Feintuch's algorithm and the orthogonalization method, First, it can be shown that a generalized algorithm (IIR-LI) of IIR-learning identification method based on previous heuristic methods can be derived using the idea of Feintuch's algorithm and the conjugate gradient method. Next, a new IIR-adaptive algorithm (IIR-AACG) based on the orthogonalization principle of the conjugate gradient method is presented. Further, by applying the orthogonalization method to a past input vector sequence we derive an IIR-Affine projection algorithm (1IR-AP). Finally, these algorithms are compared by computer simulation to verify the effectiveness of the orthogonalization method. [ABSTRACT FROM AUTHOR]

gggggAssume that an n × n dot matrix is stored in consecutive n words of a computer with one word being n bit. This paper discusses eight operations to rotate or transpose the dot matrix in horizontal/vertical! slant direction. As is well known, such operations form a group. This paper presents a unified description of the algorithms, and it is shown that all eight algorithms can be derived by suit- ably setting the constants in the unified algorithm. Then it is shown that the algorithms can be transformed to each other by simple transformation rules for the constants, and those transformation rules are shown to form a group. The foregoing algorithms for the dot matrix are not unique, and there can be different descriptions for the algorithm producing the same result. Consequently, there can be various versions of the eight algorithms as well as versions of transformation rules. This paper shows that one of the two groups formed by the transformation rules is isomorphic to the group of algorithms, but the other is not isomorphic. [ABSTRACT FROM AUTHOR]

This paper presents the dispersion characteristics of the FD-TD algorithm by showing the numerical phase and group velocities of the TEM, TE or TM modal solutions. For the TEM wave propagation, there exist three fundamental directions to which phase and group velocities can be expressed by only a single variable (wave number k or frequency ω). Those special directions were chosen to show the dispersive nature of the FD-TD algorithm of which the group and phase velocities depend explicitly on frequencies. In view of similarities between the TLM and FD-TD algorithms, a comparison of phase velocity characteristics of both methods was made. Under the special condition where the stability factor s is larger than ½, the FD-TD algorithm is found less dispersive than that of the original TLM. However, newly developed symmetrical TLM method appears less dispersive than the FD-TD algorithm. In the numerical simulation of waveguide modal solutions, it was found that there exists an optimum frequency which provide least numerical error in the FD-TD application. A procedure, which determines the stability factor s and the maximum allowed frequency Fmax for the best numerical results, is proposed in this paper. [ABSTRACT FROM AUTHOR]

The information storage algorithm of a Hopfield-type network is a kind of self-correlation learning. This algorithm needs the condition in which vectors of learning patterns cross at right angles to each other. This paper proposes n method to make this condition easier. To this purpose, threshold is used. An investigation of how to decide quantity is included. This paper discusses a network with units whose state is 1 or 0. Fixing method of threshold has not been proposed before to this type of network. It is, therefore, proposed in this research; the goal is to facilitate learning patterns. [ABSTRACT FROM AUTHOR]

In this paper, we consider the effect of adding a coarse mesh correction to the two‐grid algorithm for the mixed Navier–Stokes/Darcy model. The method yields both L2 and H1 optimal velocity and piezometric head approximations and an L2 optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier–Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method. [ABSTRACT FROM AUTHOR]

This paper presents feedback sensitivity functions analysis of implicit Lyapunov function-based control system in case of finite-time stabilization problem. The Gang of Four is chosen as a feedback sensitivity tool. The results can be used for parametric tuning of control algorithms in order to guarantee desired closed-loop sensitivity specifications. The obtained results are supported by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates a periodic review fuzzy inventory model with lead time, reorder point, and cycle length as decision variables. The main goal of this study is to minimize the expected total annual cost by simultaneously optimizing cycle length, reorder point, and lead time for the whole system based on fuzzy demand. Two models are considered in this paper: one with normal demand distribution and another with a distribution-free approach. The model assumes a logarithmic investment function for lost-sale rate reduction. Furthermore, two separate efficient computational algorithms are explained to obtain the optimal solution. Some numerical examples are given to illustrate the model. [ABSTRACT FROM AUTHOR]

Multi-criteria decision analysis presumes trade-off between different criteria. As a result, the optimal solution is not unique and can be represented by the Pareto frontier in the objective space. Each Pareto solution is a compromise between different objectives. Despite a limited number of Pareto optimal solutions, the decision-maker eventually has to choose only one option. Such a choice has to be made with the use of additional preferences not included in the original formulation of the optimization problem. The paper represents a new approach to an automatic ranking that can help the decision-maker. In contrast to the other methodologies, the proposed method is based on the minimization of trade-off between different Pareto solutions. To be realized, the approach presumes the existence of a well-distributed Pareto set representing the entire Pareto frontier. In the paper, such a set is generated with the use of the directed search domain algorithm. The method is applied to a number of test cases and compared against two existing alternative approaches. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a propagator matrix method applied to logging-while-drilling tools is introduced and extended to deal with the anisotropic and radially inhomogeneous earth formations. This method expands the Maxwell's equations in the transverse direction, constructs the relationship between propagator matrix and reflection matrix, and obtains the solution by using the reflection matrix. We systematically derived the formulas of propagator matrix method in isotropic media, uniaxially anisotropic media, fully anisotropic media, and radially inhomogeneous media respectively. In order to obtain the propagator matrix in complex media, we used the fourth-order Runge-Kutta scheme. Numerical experiments show that, compared with traditional methods, the propagator matrix method has wide range of applications while maintaining low computational costs and high accuracy. All algorithms presented in the paper have been parallelized and implemented on a high-performance computing platform. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT The present paper delineates a three-step algorithm for the analytic network process (ANP) structure design. When defining the decision goal and the alternative set, one can use the three-step algorithm proposed in this paper, first, to specify the decision criteria, and second, to outline the structure of the ANP problem. To ease the process of ANP structure design, we present two novel data structures: the multiple-effect tree and the multiple-criteria tree. The multiple-effect tree helps explore the apparent consequences of a given event or state-known in this paper as the decision alternatives-whereas the multiple-criteria tree is considered the missing link between the multiple-effect tree and the ANP structure. Employing the approach presented in this paper will help detect any mistakes in the ANP structure design. A numerical example is provided in the final section of the paper to better articulate the ideas. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Ludwig's algorithm is an algorithm that is widely used in physical optics method. However, the problem of singularity always exist both in the original Ludwig's algorithm and the Ludwig's algorithm based on triangular mesh. Because of this, the problem of singularity is studied further in this paper and a more logical solution to the problem is presented. The validity of the solution given can be seen from the numerical results. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 400–403, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22168 [ABSTRACT FROM AUTHOR]

This paper presents a simple approach to determine the time-step size required in the alternate-direction-implicit finite-difference time-domain (ADI-FDTD) method in order to obtain a desired numerical dispersion accuracy. The Courant number, the desired dispersion accuracy, and the maximum mesh size Δmax = max(Δx, Δy, Δz) are governed by the numerical dispersion relation, which can be solved by a simple root-finding algorithm to evaluate the Courant number and hence the time-step size for a given mesh size and accuracy. The time-step size is independent of the aspect ratio. To determine if ADI-FDTD is more efficient than the Yee's FDTD, this paper provides a simple relation to evaluate the relative Courant–Friedrich–Levy number (CFLN) from the Courant number and the aspect ratio. The ADI-FDTD method is more efficient than Yee's FDTD when the aspect ratio is high or the mesh density is very large. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 487–490, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20012 [ABSTRACT FROM AUTHOR]

This paper describes EM Wave Simulation, a windows-based animated electromagnetic wave simulation package, developed as a supplementary tool for teaching electromagnetic field theory at the undergraduate level. For the purpose of rapid display of electromagnetic wave images, the implemented algorithm assumes a structure sandwiched between two perfect electric conductor planes and employs a 2½-dimensional finite-difference time-domain (FDTD) method on a staggered grid, which is suitable for simulating simplified electromagnetic wave propagation in indoor environments. Frequency-domain spectral information can be extracted with the built-in one- and two-dimensional discrete Fourier transforms facilities. A user-friendly mouse-and-menu-driven interface allows user to set up simulations containing complex geometries in a straightforward fashion. Simulated results, in both time and frequency domains, can be displayed in real-time on the computer screen, which makes the application ideal for use in interactive undergraduate teaching. Some sample simulations are discussed in the paper to illustrate its principal functionality. © 2002 Wiley Periodicals, Inc. Comput Appl Eng Educ 9: 208–219, 2001; Published online in Wiley InterScience (www.interscience.wiley.com.); DOI 10.1002/cae.10001 [ABSTRACT FROM AUTHOR]

In this paper, we present a far-field pattern calculation technique in the body-of-revolution finite-difference time-domain (BOR–FDTD) method. Because the BOR–FDTD solves two- and half-dimensional problems, it has different features from the three-dimensional FDTD method in the far-field pattern calculation. A monopole antenna fed by a coax is used to validate the technique described in this paper. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 47–50, 2001. [ABSTRACT FROM AUTHOR]

This paper presents an MLP-type neural network with some fixed connections and a backpropagation-type training algorithm that identifies the full set of solutions of a complete system of nonlinear algebraic equations with n equations and n unknowns. The proposed structure is based on a backpropagation-type algorithm with bias units in output neurons layer. Its novelty and innovation with respect to similar structures is the use of the hyperbolic tangent output function associated with an interesting feature, the use of adaptive learning rate for the neurons of the second hidden layer, a feature that adds a high degree of flexibility and parameter tuning during the network training stage. The paper presents the theoretical aspects for this approach as well as a set of experimental results that justify the necessity of such an architecture and evaluate its performance. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper shows that the learning identification (the normalized LMS) algorithm can be expressed by a first-order IIR lowpass filter having rapidly varying coefficients as a function of output signal to be sent to an unknown system to be estimated. Based on the expression, this paper studies the estimation error of adaptive filters obtained by the learning identification algorithm. It is pointed out that the mean of estimation error given by the conventional analysis corresponds to the output fluctuation which can be computed by replacing varying coefficients of the lowpass filter with its arithmetic mean. However, the output fluctuation is affected by the time constant specified by the coefficients of the lowpass filter and it has a characteristic that it increases rapidly when time constant is short and decreases slowly when it is long. This means that the actual estimation error becomes larger than the result given by the conventional analysis. According to the analysis shown in this paper, it can be seen that the estimation error consists of elements for which the portion increased by the effect of time constant become fewer anti-proportionally to the number of the tap, and those elements which increase at a constant rate independently of the number of the tap. It was shown also by simulation using white noise that the difference between the estimation error obtained in actual estimation operation which occurs when the number of the tap is small and the result given by the conventional analysis can be explained well by the analysis by simulation using white noise. [ABSTRACT FROM AUTHOR]

In this paper, a numerical analysis algorithm has been derived for the analysis of the problem of plane wave diffraction by a multilayered grating. This algorithm is based on the Yasuura method with the smoothing procedure and can be applied to the problems of arbitrary multilayered dielectric (or metallic) grating with smoothly shaped grooves. The convergence of the approximate solution obtained by the present algorithm has been investigated numerically. It was demonstrated that a highly accurate approximate solution can be computed by the introduction of the smoothing procedure. The present algorithm is applicable to problems of a multilayered grating over the range from infrared to visible. As a numerical example, the diffraction efficiency of the multilayered diffraction grating made of alternate lamination of the high-index and low-index dielectric layers deposited on a metal grating is calculated by the algorithm in this paper. The following items are confirmed: (1) by coating dielectric films, the power absorption of the incident light by the metal grating is reduced in a specific wavelength region; and (2) in a multilayered grating, anomalous resonant absorption occurs by the coupling of the guided mode excited by the dielectric thin film and the diffracted wave. [ABSTRACT FROM AUTHOR]

This paper presents a method of numerical analysis by the multiple input describing function for the self-excited oscillation in a nonlinear system with hysteresis. In the traditional analysis by the describing function, the decribing function for the hysteresis is determined in an analytic form, and a very complex calculation is required to perform a highly accurate analysis including the harmonic components of the self-excited oscillation. Consequently, in practice, it has been impossible to determine analytically the describing function for the multiple input. Furthermore, the calculation is impossible for the describing function, where the hysteresis characteristics contain a minor loop. From such a viewpoint, this paper proposes a method and algorithm for the analysis of self-excited oscillation. In the proposed method, the describing function is determined numerically by the digital simulation of the hysteresis, and the discrete Fourier transform and its inverse are applied to the result. But this method, the describing function can be determined numerically even for the cases of multiple input and the case with a minor loop. Thus, the self-excited oscillation can be analyzed considering the harmonic components and the multiple mode. As an example, the self-excited oscillation of the nonlinear system is analyzed for the case where the linear part is represented by a second-order transfer function or by a sum of such functions. [ABSTRACT FROM AUTHOR]

As a method of solving the electromagnetic scattering by perfectly conducting cylinders, the discrete singularity method is discussed. For this method, a finite number of singular points is distributed within the scatterer and the wave function composed of a linear combination of solutions (each of which is derived from a helmholtz equation with each single singularity among the many) is matched with the incident wave function on the boundary. The remaining important problem in this method is how to distributed these singularities in order to obtain the accurate solution with faster convergence and with fewer number of singular points for an arbitrary configuration of the scatterer. The purpose of this paper is to present a reasonable solution to this problem. The essential of the method is that by making as unknown quantities, not only the unknown amplitude coefficients involved in the linear combination of the solutions, but also the coordinates of the singularities, the scattered wave is matched on the boundary in the sense of the least squares. This problem is linear in the amplitude coefficient but nonlinear in the singularity coordinate. Thus we solve this problem by using the algorithm by marquardt et al, of a nonlinear optimization process. This paper considers the general description and indicates its effectiveness by showing a few examples of the scattering problem of rectangular cylinders. [ABSTRACT FROM AUTHOR]

This paper proposes a design method for the FIR two-channel perfect quadrature mirror filter (QMF) with the linear phase. The two-channel perfect QMF can be designed by Vetterli's method, where a system of equations representing the condition for the perfect reconstruction of the signal is solved. The filter designed by this method, however, does not, in general, have good frequency characteristics. This paper presents the design for the two-channel QMF with a perfect reconstruction and a good amplitude characteristic. The method is based on Vetterli's method, and a constraint to approximate the amplitude charac- teristic in the frequency domain is added to the condition of perfect reconstruction in time domain. Then Remez' algorithm is applied to the derived system of equations. The construction of the two-channel perfect QMF, when the coefficient is quantized, also is discussed. Furthermore, a method is shown in which the two-dimensional (2-D) perfect QMF is designed by applying the McClellan transformation to the obtained 1-D QMF. The condition for the McClellan transformation for the perfect reconstruction is derived. [ABSTRACT FROM AUTHOR]

The delay time concept is widely adopted in literature to model the two‐stage failure process of most industrial systems which can be divided into normal stage (from new to an initial point of a defect) and defective stage (from defect arrival point to failure). Most existing delay time models assume that the normal and defective stages are independent. A generalized delay time model is proposed in this paper by considering the dependence between the normal and defective stages which is reflected in the fact that they share the same external shock process. According to the definition of shot‐noise process, external shocks will incur random hazard rate increments in the two stages. The failure state is self‐announcing, whereas the defective state can only be detected by block‐based inspection or opportunistic inspection offered by unexpected shutdown due to unavoidable external factors. The system is correctively replaced upon the occurrence of a system failure or preventively replaced at the detection of a defective state. Based on the stochastic failure model and maintenance policy, this paper evaluates system reliability performance and average long‐run cost rate via a Markov‐chain based approach. Finally, a case study on a steel convertor plant is given to demonstrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

The efficient computation of Green's functions for uniaxial anisotropic layered media is investigated. Both field and mixed‐potential layered medium Green's functions (LMGFs) are discussed for different applications. An asymptotic subtraction (singularity extraction) and the weighted average method are combined for the acceleration of LMGF computation. A full collection of Sommerfeld and related identities used in the acceleration is summarized and generalized to uniaxial anisotropic medium for both field and mixed‐potential LMGFs. When lossy media are considered, the effective distance from the source to the observation point becomes a complex number depending on the anisotropic ratio of the horizontal to vertical media parameters. In addition, the evaluation of half‐line source potentials, which are introduced to accelerate the scalar potential correction term for vertical currents, is generalized to the complex domain by analytic continuation. Several numerical examples are used to demonstrate the efficiency and accuracy of the resulting algorithms. Key Points: This paper computes Green's functions efficiently in lossy uniaxial anisotropic layered mediaA full collection of Sommerfeld and related identities is summarized and generalized to lossy uniaxial anisotropic medium [ABSTRACT FROM AUTHOR]

Since Compton cameras were introduced in the use of single photon emission computed tomography, various types of conical Radon transforms, which integrate the emission distribution over circular cones, have been studied. Most of previous works did not address the attenuation factor, which may lead to significant degradation of image quality. In this paper, we consider the problem of recovering an unknown function from conical projections affected by a known constant attenuation coefficient called an attenuated conical Radon transform. In the case of a fixed opening angle and vertical central axis, new explicit inversion formula is derived. Two‐dimensional numerical simulations were performed to demonstrate the efficiency of the suggested algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a surrogate‐based iterative importance sampling (IS) method is proposed to efficiently evaluate failure probability (FP) of engineering structures. The surrogate is constructed by the training points centered at the most probable failure point (MPP), which is estimated by an approximate algorithm without any additional evaluations of the real limit state function (LSF), and the IS method using the estimated MPP is further obtained; and an iterative procedure combined with the surrogate and the IS method is finally proposed to improve the accuracy of the estimated result for the FP. Three numerical examples are employed to demonstrate the accuracy of the proposed method, and further, an inside flap of an aircraft is employed to demonstrate the practical application of the proposed method in engineering problems. The results show that the reasonable estimated result of the FP within the range of 10−3‐10−5 can be evaluated by the proposed method with only hundreds of the evaluations of the real LSF. [ABSTRACT FROM AUTHOR]

Summary: Domain of attraction plays an important role in stability analysis and safety verification of nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like functions, we propose iteration algorithms for computing inner estimates of domains of attraction for a class of switched hybrid systems, where the state space is composed of several regions and each region is described by polyhedral sets. Starting with an initial inner estimate of domain of attraction, we firstly present a theoretical framework for obtaining a larger inner estimate by iteratively computing multiple Lyapunov‐like functions. Successively, the theoretical framework is underapproximatively realized by using S‐procedure and sums of squares programming, associated with the coordinatewise iteration method. Afterwards, for obtaining a required initial inner estimate of domain of attraction, we propose an alternative higher‐order truncation and linear semidefinite programming based method for computing a common Lyapunov function. Especially, a bisection method based improvement is proposed for obtaining better estimates in each iteration step. Finally, we implement proposed algorithms and test them on numerical examples with comparisons. These computation and comparison results show that the advantages of our multiple Lyapunov‐like functions based algorithm. Especially, we provide alternative underapproximations for avoiding the possible numerical problem. [ABSTRACT FROM AUTHOR]

This paper introduces a computational framework to analyze global identification of linearized DSGE models. A formal identification condition is established that relies on the restrictions linking the observationally equivalent state space representations and on the inherent constraints imposed by the model solution on the deep parameters. This condition is next used to develop an algorithm that checks global identification by searching for observationally equivalent model parametrizations. The algorithm is efficient as the identification conditions it employs shrink considerably the space of candidate deep parameter points and the model does not need to be solved at each of these points. The working of the algorithm is demonstrated with two examples. [ABSTRACT FROM AUTHOR]

SUMMARY The paper offers an algorithm for local and global parametric diagnosis in nonlinear analog circuits, including both identification of the faulty parameters and determination their values. The algorithm exploits a nonlinear algebraic type test equations which may possess multiple solutions, corresponding to different sets of the parameters values which meet the test. To find the solutions, the homotopy concept is applied. Since the test equation is not given in explicit analytical form, the simplicial method is used to trace the homotopy path. The proposed approach can be applied to a broad class of analog circuits, including the complementary metal-oxide-semiconductor circuits fabricated in nanometer technology. The developed diagnostic procedure has been implemented in DELPHI, whereas the required by the algorithm repeated circuit analyses are carried out using IsSPICE 4 and both environments have been joined together. For illustration, two numerical examples are given. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Interactive rigid body simulation is an important part of many modern computer tools, which no authoring tool nor game engine can do without. Such high-performance computer tools open up new possibilities for changing how designers, engineers, modelers and animators work with their design problems. This paper is a self contained state-of-the-art report on the physics, the models, the numerical methods and the algorithms used in interactive rigid body simulation all of which have evolved and matured over the past 20 years. Furthermore, the paper communicates the mathematical and theoretical details in a pedagogical manner. This paper is not only a stake in the sand on what has been done, it also seeks to give the reader deeper insights to help guide their future research. [ABSTRACT FROM AUTHOR]

The article focuses on the need for fast and accurate numerical simulation techniques due to advances in wireless and microwave communication systems. A number of practical geometries have been left untreated because of their complexity and the inability of existing techniques to deal with requirements for large size and higher resolution. An accurate characterization of the passive and active structures is the first step need for the development of efficient numerical algorithms.

SUMMARY For a Markov reward process, where upper and lower bounds for the transition rates and rewards are known, a new approach to bound the expected reward is presented. Based on a previous paper where sharp bounds have been defined for the problem, but only an inefficient and unstable algorithm is proposed, this paper presents algorithms to compute the bounds by interpreting the problem as a Markov Decision Process. In this way, the well known value and policy iteration algorithms can be adopted to compute reward bounds in a stable and fairly efficient way. Different numerical techniques are presented for computing the reward bounds. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The present paper presents the support vector machine (SVM)-based semi-active control algorithm used for designing general dampers for multistorey structures under earthquakes. First, the linear quadratic regulator (LQR) controller for the numerical model of a multistorey structure formulated using the dynamic dense method is obtained by using the classic LQR control theory. Then, a SVM model is designed and trained to emulate the performance of the LQR controller. Likewise, this SVM model comprises the observers and controllers of the control system. Finally, in accordance with the features of general semi-active dampers, a SVM-based semi-active control strategy is put forward. More specifically, an online auto-feedback semi-active control strategy is developed and then realized by resorting to SVM. In order to numerically verify the control effectiveness of the present control strategy, the time history analysis has been implemented to a structure with general dampers designed by the SVM-based semi-active control algorithm. In numerical simulations, four seismic waves including the El Centro, Hachinohe and Kobe waves, as well as the Shanghai artificial wave, whose peak ground accelerations are all scaled to 0.1 g, are taken into consideration. Comparative results demonstrate that general semi-active dampers designed using the SVM-based semi-active control algorithm is capable of providing higher level of response reduction. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is motivated by some recent work of Fukuda, Ishiwata, Iwasaki, and Nakamura ( Inverse Problems 2009; :015007). We first design an algorithm for computing the eigenvalues of a specially structured matrix from the discrete Bogoyavlensky Lattice 2 (dBL2) system. A Lax representation for the dBL2 system is given in a matrix form. By considering the asymptotic behavior of dBL2 variables, some characteristic polynomials are then factorized. A new algorithm for computing the complex eigenvalues of a specially structured matrix is then introduced. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An automatic aerodynamic optimization, which coupled with parallel adaptive range differential evolution (PARDE), blade profile parameterization and Reynolds-averaged Navier-Stokes (RANS) solver, is developed for three-dimensional axial turbomachinery blades in this paper. RANS is utilized to evaluate the aerodynamic performance of blade design candidates. The non-uniform B-Spline method is used to parameterize the three-dimensional turbomachinery blade profile. PARDE is used as the optimizer and parallel algorithms using PC cluster technology are applied to accelerate the design period. Aerodynamic redesigns of the NASA rotor 37 and a turbine stage are utilized as optimization cases to demonstrate the reliability of the present optimization methodology. The rotor 37 is optimized for the maximization of the isentropic efficiency at the given flow condition, using constraints on the mass flow rate and the total pressure ratio. The isentropic efficiency of the optimum design rotor 37 has 1.66% higher than that of the reference design. A low aspect ratio transonic turbine stage is redesigned for the maximization of the isentropic efficiency with 41 design variables in total. The isentropic efficiency of the optimum turbine stage is 1.6% higher than that of the reference design. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Given the species A1 and A2, the competition among the three different elementary processes 123 is frequently found in thermal and photochemical reaction systems. In the present paper, an analytical resolution of the system (1)–(3), performed under plausible contour conditions, namely, finite initial molar concentrations for both reactants, [A2]0 and [A1]0, and nonzero reaction rate coefficients k1, k2, and k3, leads to the equation [A1] = ((δ[A2]γ - [A2])/β) - α, where α = k1/2k3, γ = β + 1 = 2k3/k2, and δ = ([A2]0 + β[A1]0 + β α))/[A2]0γ. The comparison with a numerical integration employing the fourth-order Runge–Kutta algorithm for the well-known case of the oxidation of organic compounds by ferrate ion is performed. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 562–566, 2010 [ABSTRACT FROM AUTHOR]

Purpose: The aim of this article is to propose an exact SPECT region of interest (ROI) reconstruction method using truncated transmission and truncated emission data. Methods: Recently, the authors published two articles in Physics in Medicine and Biology with two results in SPECT ROI emission image reconstruction. The first result states that if the transmission data are truncated but the emission data are not truncated, the emission image can be exactly reconstructed, provided the entire emission image is inside the region where the transmission data are not truncated. The second result states that if the transmission data are not truncated, the emission ROI can be exactly reconstructed with truncated emission data. This article combines these two results and obtains a new result that the emission ROI can be exactly reconstructed if both transmission and emission data are truncated. Results: Computer simulations are performed to verify the proposed ROI image reconstruction algorithm. Conclusions: Exact SPECT ROI image reconstruction is possible using truncated transmission and emission projections with some prior information about the attenuator and the emission distribution. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss the geometric-based algebraic multigrid (AMG) method for two-dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two-level method is proposed by analyzing the relationship between the linear finite element space and higher-order finite element space. And then a geometric-based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high-order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Algebraic multigrid (AMG) is a powerful linear solver with attractive parallel properties. A parallel AMG method depends on efficient, parallel implementations of the coarse-grid selection algorithms and the restriction and prolongation operator construction algorithms. In the effort to effectively and quickly select the coarse grid, a number of parallel coarsening algorithms have been developed. This paper examines the behaviour of these algorithms in depth by studying the results of several numerical experiments. In addition, new parallel coarse-grid selection algorithms are introduced and tested. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm for solving the algebraic Riccati equation (ARE) that has an indefinite sign quadratic term related to weakly coupled large-scale systems is investigated. A novel contribution is that a new iterative algorithm is derived by combining Newton's method and the fixed point algorithm. As a result, for sufficiently small ℇ, we can obtain an ARE solution with a quadratic convergence rate. Moreover, it is possible to calculate the ARE solution for the same dimension of each subsystem. As another important feature, an algorithm for solving the filter ARE is also discussed. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example is given. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(1): 39–48, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20370 [ABSTRACT FROM AUTHOR]

FDTD method plays an important role for simulation of different structures in various fields of engineering, such as RF/microwaves, photonics and VLSI. However, due to the CFL stability constraint, the FDTD time step is still small and the related CPU time is still large for modelling fine geometry where small cell sizes are required to resolve fields. As a result, the unconditionally stable CFL-condition-free ADI-FDTD method is becoming a popular alternative to the FDTD method. The ADI-FDTD method allows the use of larger time steps; however, it comes at the cost of larger errors. To mitigate the problem of these larger errors, in this paper we propose to modify the conventional ADI-FDTD algorithm. The modifications are based on the fact that because the ADI-FDTD is a truncated form of the Crank–Nicolson (CN) method, the truncated terms can be re-introduced approximately into the ADI algorithms to improve accuracy. Two accuracy-improved ADI-FDTD algorithms are derived and then validated for two-dimensional cases. Unfortunately, in the three-dimensional case the proposed methods are not found to be unconditionally stable. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In connection with the method of selecting among sensors connected by a network those sensors that can efficiently acquire information on the object, this paper presents a discussion in a form that explicitly treats the existence of communications delay when the information is received via a network. First, we propose a calculation algorithm that is scalable with respect to the increase in the number of the sensors when the information from several sensors is combined by a Kalman filter and the communications delay is taken into account. When several sensors have different communications delays and these delays change so that the sensor information arrival is unrelated to the actual time, the information is correctly combined. Next, we propose a method for selecting an appropriate sensor when state estimation by this algorithm is performed. This method makes use of the cross-information previously used as a reference for sensor selection. However, the reduction of the information content due to communications delay, affecting the estimated value for the present time, can be expressed quantitatively. These algorithms are verified by numerical experiments and their effectiveness is demonstrated. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(5): 21–31, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20211 [ABSTRACT FROM AUTHOR]