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Purpose: The purpose of this study is to further advance the multiple space/time subdomain framework with model reduction. Existing linear multistep (LMS) methods that are second-order time accurate, and useful for practical applications, have a significant limitation. They do not account for separable controllable numerical dissipation of the primary variables. Furthermore, they have little or no significant choices of altogether different algorithms that can be integrated in a single analysis to mitigate numerical oscillations that may occur. In lieu of such limitations, under the generalized single-step single-solve (GS4) umbrella, several of the deficiencies are circumvented. Design/methodology/approach: The GS4 framework encompasses a wide variety of LMS schemes that are all second-order time accurate and offers controllable numerical dissipation. Unlike existing state-of-art, the present framework permits implicit–implicit and implicit–explicit coupling of algorithms via differential algebraic equations (DAE). As further advancement, this study embeds proper orthogonal decomposition (POD) to further reduce model sizes. This study also uses an iterative convergence check in acquiring sufficient snapshot data to adequately capture the physics to prescribed accuracy requirements. Simple linear/nonlinear transient numerical examples are presented to provide proof of concept. Findings: The present DAE-GS4-POD framework has the flexibility of using different spatial methods and different time integration algorithms in altogether different subdomains in conjunction with the POD to advance and improve the computational efficiency. Originality/value: The novelty of this paper is the addition of reduced order modeling features, how it applies to the previous DAE-GS4 framework and the improvement of the computational efficiency. The proposed framework/tool kit provides all the needed flexibility, robustness and adaptability for engineering computations. [ABSTRACT FROM AUTHOR]

In this paper, a kinetic equation of Euler–Bernoulli beam is established with variable order fractional viscoelastic model. An effective numerical algorithm is proposed. This method uses a combination of shifted Bernstein polynomial and Legendre polynomial to approximate the numerical solution. The effectiveness of the algorithm is tested and verified by mathematical examples. The dynamic behavior of viscoelastic beams made of two materials under various loading conditions is studied. [ABSTRACT FROM AUTHOR]

An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates. • The fractional order governing equation of a viscoelastic plate is established. • Shifted Legendre polynomials algorithm is used to solve the governing equation. • The feasibility and efficiency of the proposed algorithm are verified. • Transverse displacements of viscoelastic plate are calculated directly in the time domain. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models. Design/methodology/approach: Determine the discrete integral operator of periodic functions and develop an iterative algorithm determining steady-state solutions by a multiplication of matrices only. Findings: An alternative method to creating finite-difference relations directly determining steady-state solutions in the time domain. Research limitations/implications: Reduction of software and hardware requirements for determining steady-states of electromagnetic. Practical implications: A unified approach for directly finding steady-state solutions for ordinary nonlinear differential equations presented in the normal form. Originality/value: Eliminate the necessity of solving high-order finite-difference equations for steady-state analysis of electromagnetic devices described by circuit models. [ABSTRACT FROM AUTHOR]

This paper studies linear stochastic approximation (SA) algorithms and their application to multiagent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multiagent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multidimensional linear SA algorithms and characterize the behavior of the multidimensional Friedkin–Johnsen model over random interaction networks. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed filtering problem for continuous-time stochastic systems over sensor networks subject to Markovian switching topologies. Due to limited communication energy and bandwidth, an event-based communication scheme is proposed with the aim to decrease the transmission frequency. An individual triggering condition is put forward to regulate the communication rates for each component of the system state in order to better reflect the engineering requirements. The aim of this paper is to design a distributed filter over sensor networks with Markovian switching topologies such that the dynamics of the estimation error is exponentially mean-square bounded. It is shown that, with the proposed event-based distributed filtering algorithm, the exponential mean-square boundedness of the estimation errors is guaranteed if the sensor network is distributively detectable and the combined communication topology is strongly connected. A numerical example is presented to illustrate the usefulness of the developed algorithm. [ABSTRACT FROM AUTHOR]

Abstract To efficiently analyze electromagnetic scattering of electrically-large complex objects, a novel version of multilevel directional simply sparse method (MLDSSM) based on well-conditioned electric field integral equation (WEFIE) is proposed in this paper. When the complex target is analyzed, the condition number of impedance matrix of electric field integral equation (EFIE) is very poor. In this paper, the WEFIE is applied to improve the convergence property of EFIE. Meanwhile, an efficient version of MLSSM algorithm based on directional grouping scheme is applied to further accelerate the matrix-vector multiplication. Numerical results of differently shaped objects were presented to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Purpose: To design, control and evaluate photovoltaic (PV) systems, an accurate model is required. Accuracy of PV models depends on model parameters. This study aims to use a new algorithm called improved social spider algorithm (ISSA) to detect model parameters. Design/methodology/approach: To improve performance of social spider algorithm (SSA), an elimination period is added. In addition, at the beginning of each period, a certain number of the worst solutions are replaced by new solutions in the search space. This allows the particles to find new paths to get the best solution. Findings: In this paper, ISSA is used to estimate parameters of single-diode and double-diode models. In addition, effect of irradiation and temperature on I–V curves of PV modules is studied. For this purpose, two different modules called multi-crystalline (KC200GT) module and polycrystalline (SW255) are used. It should be noted that to challenge the performance of the proposed algorithm, it has been used to identify the parameters of a type of widely used module of fuel cell called proton exchange membrane fuel cell. Finally, comparing and analyzing of ISSA results with other similar methods shows the superiority of the presented method. Originality/value: Changes in the spider's movement process in the SSA toward the desired response have improved the algorithm's performance. Higher accuracy and convergence rate, skipping local minimums, global search ability and search in a limited space can be mentioned as some advantages of this modified method compared to classic SSA. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a novel direct method for indefinite algebraic linear systems. It is well adapted for sparse linear systems, such as those of two-dimensional (2-D) finite elements problems, especially for coupled systems. Design/methodology/approach: The proposed method is developed on an example of an indefinite symmetric matrix. The algorithm of the method is given next, and a comparison between the numbers of operations required by the method and the Cholesky method is also given. Finally, an application on a magnetostatic problem for classical methods (Gauss and Cholesky) shows the relative efficiency of the proposed method. Findings: The proposed method can be used advantageously for 2-D finite elements in stepping methods without using a block decomposition of matrices. Research limitations/implications: This method is advantageous for direct linear solving for 2-D problems, but it is not recommended at this time for three-dimensional problems. Originality/value: The proposed method is the first direct solver for algebraic linear systems proposed since more than a half century. It is not limited for symmetric positive systems such as many of direct and iterative methods. [ABSTRACT FROM AUTHOR]

The occurrence of economic management crisis has seriously affected the production and operation of enterprises, the stability of capital markets and even the economic security of the entire country and the world. The use of higher mathematics in economic management is very beneficial to the economic restructuring. For example, in the Lagrangian method for solving the constraint optimization problem, the correlation function can be listed in the Lagrangian fractional calculus equation for the economic management early warning problem with many independent variables. Then take one of the factors as the dependent variable and other factors as fixed constants, and bring them into the Lagrangian fractional calculus equation, you can find the variable solution and get the extreme value of the economic management early warning algorithm. Therefore, this paper combines normative research and empirical research to study the algorithm design, theoretical analysis and numerical experiments of Lagrangian-based methods for solving constrained optimization problems. The Lagrangian fractional calculus method is used to evaluate the early warning algorithm of economic management, improve the prediction accuracy and practicability of the model, and conduct empirical research. It is expected to find a way to effectively determine whether a listed company is caught in an economic management crisis and provide early warning for the listed company's own management. [ABSTRACT FROM AUTHOR]

Purpose Estimating the punching process’s impact on the operating parameters of an electrical motor is a special problem especially in the case of fractional power motors. The purpose of this paper is to discuss a method of numerical modelling that is useful for this case.Design/methodology/approach The proposed multi-physical FEM approach is based on using professional software in the process of modelling and determining the operating parameters of a low power motor. The basic elements of the approach are built FEM models for which the parameters characterising the damaged portions of the magnetic material were determined. The material properties of this zone were determined both by measurement and by a new analytical approach described in this paper.Findings The paper formulates the impact of punching on the operating parameters of a low power motor. Moreover, it formulates the analytical algorithm for the estimation of properties of material in damaged zones.Research limitations/implications Experimental verification will still be needed to check the model’s accuracy and applicability to various magnetic materials.Practical implications The paper provides an easy approach enabling the calculation of motor operating parameters and a simple and useful algorithm to estimate magnetic material properties in the damaged zone.Originality/value The analytical algorithm, as presented here, in conjunction with the measurement results is useful and applicable to estimating the magnetic material properties, which form the basis for accurate FEM calculation. [ABSTRACT FROM AUTHOR]

This paper presents several numerical techniques to generate solitary-wave profiles of the Benjamin equation. The formulation and implementation of the methods focus on some specific points of the problem: on the one hand, the approximation of the nonlocal term is accomplished by Fourier techniques, which determine the spatial discretization used in the experiments. On the other hand, in the numerical continuation procedure suggested by the derivation of the model and already discussed in the literature, several algorithms for solving the nonlinear systems are described and implemented: the Petviashvili method, the Preconditioned Conjugate Gradient Newton method and two Squared-Operator methods. A comparative study of these algorithms is made in the case of the Benjamin equation; Newton's method combined with Preconditioned Conjugate Gradient techniques, emerges as the most efficient. The resulting numerical profiles are shown to have a high accuracy as travelling-wave solutions when they are used as initial conditions in a time-stepping procedure for the Benjamin equation. The paper also explores the generation of multi-pulse solitary waves. [ABSTRACT FROM AUTHOR]

In this paper, we consider using multiple noisy binary sensors to track a target that moves as a Markov Chain in a finite discrete environment, with symmetric probability of false alarm and missed detection. We study two policies. First, we show that the greedy policy, whereby $m$ sensors are placed at the $m$ most-likely target locations, is one-step optimal in that it maximizes the expected maximum a posteriori (MAP) estimate. Second, we show that a policy in which the $m$ sensors are placed in the second through $(m+1)$ st most likely target locations achieves equal or slightly worse expected MAP performance, but leads to significantly decreased variance on the MAP estimate. The result is proven for $m = 1$ , and Monte Carlo simulations give evidence for $m > 1$. Both policies are closed loop, index-based active sensing strategies that are computationally trivial to implement. Our approach focuses on one-step optimality because of the apparent intractability of computing an optimal policy via dynamic programming in belief space. However, Monte Carlo simulations suggest that both policies perform well over arbitrary horizons. [ABSTRACT FROM AUTHOR]

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch–Kuhn–Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper considers a class of stochastic source-seeking problems to drive a mobile robot to the minimizer of a source signal. Our approach is first analyzed in an obstacle-free scenario, where measurements of the signal at the robot location and information of a contact sensor are required. We extend our results to environments with obstacles under mild assumptions on the step size. Our approach builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithms to a ball whose size depends on the step size that contains the location of the source. The novelty relies in that we consider nondifferentiable convex functions, a fixed step size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov function theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in a two-dimensional scenarios. [ABSTRACT FROM AUTHOR]

This paper is concerned with a general class of distributed constrained optimization problems over a multiagent network, where the global objective function is represented by the sum of all local objective functions. Each agent in the network only knows its own local objective function, and is restricted to a global nonempty closed convex set. We discuss the scenario where the communication of the whole multiagent network is expressed as a sequence of time-varying general unbalanced directed graphs. The directed graphs are required to be uniformly jointly strongly connected and the weight matrices are only row-stochastic. To collaboratively deal with the optimization problems, existing distributed methods mostly require the communication graph to be fixed or balanced, which is impractical and hardly inevitable. In contrast, we propose a new distributed projection subgradient algorithm which is applicable to the time-varying general unbalanced directed graphs and does not need each agent to know its in-neighbors’ out-degree. When the objective functions are convex and Lipschitz continuous, it is proved that the proposed algorithm exactly converges to the optimal solution. Simulation results on a numerical experiment are shown to substantiate feasibility of the proposed algorithm and correctness of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we study the interacting multiple model (IMM) estimator for networked control systems with packet loss but without packet acknowledgment (ACK). The ACK is a signal sent by the actuator to inform the estimator of whether control packets are lost or not. A system with ACK is usually called a transmission control protocol (TCP) like system; otherwise, it is called a user datagram protocol (UDP) like system. We show that the stability of the IMM estimator for UDP-like systems is determined by the observation packet arrival rate (p.a.r.) and is independent of the control p.a.r. and control inputs. The IMM estimator is stable if the observation p.a.r. is greater than a critical value. We show that this critical value is the same as the critical value for the stability of the optimal estimator for its corresponding TCP-like system. If control inputs eventually tend to zero, the error covariance of the IMM estimator converges to that of the optimal estimator for TCP-like systems. We characterize the impact of the control/observation p.a.r. and the control input on estimation performance. Finally, we prove that the average estimation performance of the IMM estimator approximates that of the optimal estimator within a finite bound, and is superior to that of the linear minimum mean square error estimator. [ABSTRACT FROM AUTHOR]

A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable with respect to the source distribution if and only if it is decomposable with respect to each smaller sized distribution (in the reduction). The notion of reduction of distributions has previously been proposed to improve the complexity of decomposability verification. In this paper, we address the problem of generating (optimal) reductions of distributions automatically. A (partial) solution to this problem is provided, which consists of an incremental algorithm for the production of candidate reductions and a reduction validation procedure. In the incremental production stage, backtracking is applied whenever a candidate reduction that cannot be validated is produced. A strengthened substitution-based proof technique is used for reduction validation, while a fixed template of candidate counter examples is used for reduction refutation; put together, they constitute our (partial) solution to the reduction verification problem. In addition, we show that a recursive approach for the generation of (small) reductions is easily supported. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the problems of state space model identification of multirate processes with unknown time delay. The aim is to identify a multirate state space model to approximate the parameter-varying time-delay system. The identification problems are formulated under the framework of the expectation maximization algorithm. Through introducing two hidden variables, a new expectation maximization algorithm is derived to estimate the unknown model parameters and the time-delays simultaneously. The effectiveness of the proposed algorithm is validated by a simulation example. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel augmented complex-valued normalized subband adaptive filter (ACNSAF) algorithm is proposed for processing the noncircular complex-valued signals. Based on the augmented statistics, the proposed algorithm is derived by computing a constraint cost function. Due to contain all second-order statistical properties, the ACNSAF algorithm can process the circular and noncircular complex-valued signals simultaneously. Moreover, the stability and mean square steady-state analysis of the proposed algorithm is derived by using the energy conservation principle. Computer simulation experiments on complex-valued system identification, prediction and noise cancelling show that the proposed algorithm achieves the improved mean square deviation and prediction gain compared to the ACNLMS algorithm. And the simulation results are consistent with the analysis results. [ABSTRACT FROM AUTHOR]

Purpose Ordinary differential equations (ODEs) are widely used in the engineering curriculum. They model a spectrum of interesting physical problems that arise in engineering disciplines. Studies of different types of ODEs are determined by engineering applications. Various techniques are used to solve practical differential equations problems. This paper aims to present a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages. In this work, the successive differentiation method (SDM) for solving linear and nonlinear and homogeneous or non-homogeneous ODEs is presented. The algorithm uses the successive differentiation of any given ODE to determine the values of the function’s derivatives at a single point, mostly x = 0. The obtained values are used to construct the Taylor series of the solution of the examined ODE. The algorithm does not require any new assumption, hence handles the problem in a direct manner. The power of the method is emphasized by testing a variety of models with distinct orders, with constant and variable coefficients. Most of the symbolic and numerical computations can be carried out using computer algebra systems.Design/methodology/approach This study presents a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages.Findings This method is applied to a variety of well-known equations, such as the Bernoulli equation, the Riccati equation, the Abel equation and the second-order Euler equation, some with constant and variable coefficients. SDM handles linear and nonlinear and homogeneous or nonhomogeneous ODEs in a direct manner without any need to restrictive conditions. The method works effectively to the Volterra integral equations, as will be discussed in a coming work.Originality/value The method can be extended to a wide range of engineering problems that are modeled by differential equations. The method is simple and novel and highly accurate. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an improvement of Huang's moving knots method (Huang et al.) for solving the PDE on the contours of Equidistribution Principle (EP-contours). Firstly, a new moving knots strategy is generated by discovering a significant factor ignored (dropped) by Huang (Huang et al.). The proposed strategy ensures that arbitrary initial knots could asymptotically converge to the EP-contours. Then the moving knots strategy and PDE are simulated by using multi-quadric (MQ) quasi-interpolation step by Step (3.3, 3.4). Error estimates of the algorithm are given. At last, numerical experiments are provided to illustrate the validity of the algorithm. Both theoretical analysis and numerical results show that the proposed algorithm benefits the methods in Huang et al. and Wu. [ABSTRACT FROM AUTHOR]

Abstract Numerical stability has been a fundamental challenge in direct time-domain boundary element methods (TD-BEM) for elastodynamics. In this paper, an analytical framework for the evaluation of the critical aspect is presented. By casting a convolution integral-based TD-BEM algorithm in the form of a linear multi-step method with a hybrid amplification matrix and the incorporation of some fundamental characteristics of commonly-used transient Green's functions, a rigorous assessment of the problem is shown to be reducible to a standard spectral analysis in matrix theory by which the stability threshold can be clearly defined. Apt to be relevant to the evaluation of other TD-BEMs, the approach is applied to a regularized time-domain direct boundary element method with optional collocation weights and orders of solution variable projections as illustration. By virtue of the proposed formalism and a systematic parametric study, a proper resolution of the critical aspect for some past schemes as well as the versatility of the generalized TD-BEM algorithm as they pertain to the benchmark finite-domain square-bar and the infinite-domain cavity elastodynamic problems are given as examples. [ABSTRACT FROM AUTHOR]

The classic Luria–Delbrück model can be interpreted as a Poisson compound (number of mutations) of exponential mixtures (developing time of mutant clones) of geometric distributions (size of a clone in a given time). This “three-ingredients” approach is generalized in this paper to the case where the split instant distributions of cells are not i.i.d. : the lifetime of each cell is assumed to depend on its birth date. This model takes also into account cell deaths and non-exponentially distributed lifetimes. Previous results on the convergence of the distribution of mutant counts are recovered. The particular case where the instantaneous division rates of normal and mutant cells are proportional is studied. The classic Luria–Delbrück and Haldane models are recovered. Probability computations and simulation algorithms are provided. Robust estimation methods developed for the classic mutation models are adapted to the new model: their properties of consistency and asymptotic normality remain true; their asymptotic variances are computed. Finally, the estimation biases induced by considering classic mutation models instead of an inhomogeneous model are studied with simulation experiments. [ABSTRACT FROM AUTHOR]

The paper describes an efficient method for reduction of the binary matrices which arise in some school time-tabling problems. It is a development of that described by John Lions. It has been generalized and adapted to fit into the complete timetabling process; to use a more compact data representation and more efficient processing techniques; to take fuller advantage of possible available previous knowledge about the matrix. And it is designed as a structured program, which can readily be coded by the reader in the high level or low level programming language of his choice. Practical tests of the method have shown it to be a good basis for a realistic timetabling algorithm. [ABSTRACT FROM AUTHOR]

Purpose – Critical links in traffic networks are those who should be better protected because their removal has a significant impact on the whole network. So, the purpose of this paper is to identify the critical links of traffic networks. Design/methodology/approach – This paper proposes the definition of the critical link for an urban traffic network and establishes mathematical model for determining critical link considering the travellers’ heterogeneous risk-taking behavior. Moreover, in order to improve the computational efficiency, the impact area of a link is quantified, a partial network scan algorithm for identifying the critical link based on the impact area is put forward and the efficient paths-based assignment algorithm is adopted. Findings – The proposed algorithm can significantly reduce the search space for determining the most critical links in traffic network. Numerical results also demonstrate that the structure of efficient paths has significant impact on identifying the critical links. Originality/value – This paper identifies the critical links by using a bi-level programming approach and proposes a partial network scan algorithm for identifying critical links accounting for travellers’ heterogeneous risk-taking behavior. [ABSTRACT FROM AUTHOR]

Consider a connected network of agents endowed with local cost functions representing private objectives. Agents seek to find an agreement on some minimizer of the aggregate cost, by means of repeated communications between neighbors. Consensus on the average over the network, usually addressed by gossip algorithms, is a special instance of this problem, corresponding to quadratic private objectives. Consensus on the median, or more generally, consensus on a given quantile, is also a special instance of this problem. In this paper we show that optimizing the aggregate cost function regularized by a total variation (TV) term has appealing properties. First, it can be done very naturally in a distributed way, yielding algorithms that are efficient on numerical simulations. Secondly, the optimum for the regularized cost is shown to be also the optimum for the initial aggregate cost function under assumptions that are simple to state. Finally, these algorithms are robust to unreliable agents that keep injecting some false value in the network. This is remarkable enough, and is not the case, for instance, of gossip algorithms that are entirely ruled by unreliable agents as detailed in the paper. [ABSTRACT FROM PUBLISHER]

The primary purpose of this paper is to develop and analyze two fast and conservative algorithms for the fractional sine-Gordon equation. The numerical schemes are derived by using the second-and fourth-order difference method in space and the implicit midpoint rule in time to approximate an equivalent system obtained via the energy quadratic method. In addition, the conservation, existence and uniqueness, and convergence of the two schemes are investigated. Based on the properties of the Toeplitz matrix, a fast algorithm is given in the calculation for the proposed schemes. Numerical experiments verify the theoretical analysis of the schemes, showing their efficiency and excellent behavior. • We propose the Hamiltonian formulation of the 2D fractional sine-Gordon equation. • Two linearly implicit energy-preserving schemes are developed for the 2D fractional sine-Gordon equation. • An optimal l ∞ -error estimate for the proposed scheme is established without any restriction on the grid ratio. • A fast algorithm based on the fast Fourier transformation technique is given. [ABSTRACT FROM AUTHOR]

In this paper, the linear quadratic Nash games for infinite horizon nonstandard multiparameter singularly perturbed systems (MSPS) without the nonsingularity assumption that is needed for the existing result are discussed. The new strategies are obtained by solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE). Firstly, the asymptotic expansions for the GCMARE are newly established. The main result in this paper is that the proposed algorithm which is based on the Newton's method for solving the GCMARE guarantees the quadratic convergence. In fact, the simulation results show that the proposed algorithm succeed in improving the convergence rate dramatically compared with the previous results. It is also shown that the resulting controller achieves O(∥ μ ∥2n) approximation of the optimal cost. [ABSTRACT FROM AUTHOR]

Recently, it has been proved that a stationary Brillinger-mixing point process is mixing (of any order) if its moment measures determine the distribution uniquely. In this paper we construct a family of non-ergodic stationary point processes as mixture of two distinct Brillinger-mixing Neyman–Scott processes having the same moment measures. [ABSTRACT FROM AUTHOR]

Adaptive fuzzy interpolative reasoning (AFIR) can overcome the limitation of the conventional fuzzy interpolation techniques because it can find and solve the contradictions of the fuzzy interpolative reasoning (FIR) results in order to ensure that the derived FIR results are consistent. In this paper, we propose a new AFIR method to solve the inconsistencies occurring after the FIR process. The proposed AFIR method is based on the general representative values of polygonal fuzzy sets and the proposed shift and modification techniques. The proposed AFIR method includes a new contradictions solving method to get a higher similarity degree between the AFIR results. In order to demonstrate the higher consistency of the AFIR results obtained by the proposed AFIR method, we apply the proposed AFIR method to deal with the diarrheal disease prediction problem. The experimental results show that the proposed AFIR method outperforms Yang and Shen's AFIR method (2011) and Cheng et al.’s AFIR method (2016) in terms of the degree of similarity between the AFIR results. [ABSTRACT FROM AUTHOR]

In this paper, a meshless numerical algorithm is developed for the solution of two-dimensional diffusion equations with different boundary conditions. The proposed numerical method, which is truly meshless and quadrature-free, is based on the time-marching finite difference scheme, the method of the particular solutions and the singular boundary method. The diffusion equation is transformed into a Poisson-type or a modified Helmholtz equation after the time domain is discretized by the Euler or Houbolt finite difference scheme. [ABSTRACT FROM AUTHOR]

Abstract: Some real-world optimization problems are plagued by a limited hardware availability. This situation can occur, for example, when the optimization must be performed on a device whose hardware is limited due to cost and space limitations. This paper addresses this class of optimization problems and proposes a novel algorithm, namely compact Particle Swarm Optimization (cPSO). The proposed algorithm employs the search logic typical of Particle Swarm Optimization (PSO) algorithms, but unlike classical PSO algorithms, does not use a swarm of particles and does not store neither the positions nor the velocities. On the contrary, cPSO employs a probabilistic representation of the swarm’s behaviour. This representation allows a modest memory usage for the entire algorithmic functioning, the amount of memory used is the same as what is needed for storing five solutions. A novel interpretation of compact optimization is also given in this paper. Numerical results show that cPSO appears to outperform other modern algorithms of the same category (i.e. which attempt to solve the optimization despite a modest memory usage). In addition, cPSO displays a very good performance with respect to its population-based version and a respectable performance also with respect to some more complex population-based algorithms. A real world application in the field of power engineering and energy generation is given. The presented case study shows how, on a model of an actual power plant, an advanced control system can be online and real-time optimized. In this application example the calculations are embedded directly on the real-time control system. [Copyright &y& Elsevier]

Abstract: The Cauchy problems of Laplace''s equation are ill-posed with severe instability. In this paper, numerical solutions are solicited by the method of fundamental solutions (MFS) and the method of particular solutions (MPS). We focus on the analysis of the MFS, and derive the bounds of errors and condition numbers. The analysis for the MPS can also be obtained similarly. Numerical experiments and comparisons are reported for the Cauchy and Dirichlet problems by the MPS and the MFS. The Cauchy noise data and the regularization are also adopted in numerical experiments. Both the MFS and the MPS are effective to Cauchy problems. The MPS is superior in accuracy and stability; but the MFS owns simplicity of algorithms, and earns flexibility for a wide range of applications, such as Cauchy problems. These conclusions also coincide with [37]. The basic analysis of error and stability is explored in this paper, and applied to the Cauchy data. There are many reports on numerical Cauchy problems, see the survey paper in [12]; most of them are of computational aspects. The strict analysis of this paper may, to a certain degree, fill up the existing gap between theory and computation of Cauchy problems by the MFS and the MPS. Moreover, comprehensive analysis and compatible computation are two major characteristics of this paper, which may enhance the study of numerical Cauchy problems forward to a higher and advanced level. [Copyright &y& Elsevier]

Focal underdetermined system solver (FOCUSS) is a powerful method for basis selection and sparse representation, where it employs the \ell \vphantom {Rjlp} -norm with $p\in (0,2)$ to measure the sparsity of solutions. In this paper, we give a systematical analysis on the rate of convergence of the FOCUSS algorithm with respect to $p\in (0,2)$ . We prove that the FOCUSS algorithm converges superlinearly for $0

The problem considered in this paper is to solve periodic Sylvester matrix equations. A new algorithm is presented to derive the least squares solution of the equations. The proposed iteration can converge to the unique solution of the considered matrix equations at finite steps with arbitrary initial condition. A numerical test result is provided to illustrate the convergence and efficiency of the iterative algorithm. [ABSTRACT FROM AUTHOR]

Numerical simulations of high strain rate plastic flow have historically been built in a hypoelastic framework and use radial return (Wilkins’ method) as the solution algorithm. We show how each of these choices can lead to inaccurate and possibly nonconvergent results. We describe an alternative solution procedure based on a simple multiple time scale perturbation theory that is stable, accurate, computationally efficient and simple to implement. Further extension of these results then leads to a strain space formulation that has additional computational advantages. We illustrate our development with numerical experiments. This paper is dedicated to my friend and colleague Christo Christov on the occasion of his 60th birthday, in recognition of his many important and creative contributions to the formulation of continuum mechanics. [ABSTRACT FROM AUTHOR]

This paper presents a fast algorithm for the computation of sliding conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT). The algorithm calculates the values of window i+ N/4 from those of window i, one length-N/4 Walsh Hadamard transform (WHT) and one length-N/4 Modified WHT (MWHT). The proposed algorithm requires O(N) arithmetic operations, which is more efficient than the block-based algorithms of various transforms and the sliding FFT algorithm, but less efficient than the sliding WHT algorithms. Compared to the recently proposed sliding inverse SCHT (ISCHT) algorithm, the proposed algorithm is more efficient for real input but less efficient for complex input. The applications of the sliding CS-SCHT in transform domain adaptive filtering (TDAF) to complex signal channel equalization and real speech signal acoustic echo cancellation are also provided. [ABSTRACT FROM PUBLISHER]

Abstract: This paper presents energy–momentum consistent time-stepping schemes for classical nonlinear thermo-elastodynamics, which include well-known energy–momentum conserving time integrators for elastodynamics. By using the time finite element approach, this time-stepping schemes are not restricted to second-order accuracy. In order to retain the first and second law of thermodynamics in a discrete setting, the equations of motion are temporally discretised by a Petrov–Galerkin method, and the entropy evolution equation by a new Bubnov–Galerkin method. The new aspect in this Bubnov–Galerkin method is the used jump term, which is necessary to avoid numerical dissipation beside the local physical dissipation according to Fourier''s law. The stress tensor in the obtained enhanced hybrid Galerkin (ehG) method is approximated by a higher-order accurate discrete gradient. As additional new features of a monolithic solution strategy, this paper presents a convergence criterion and an initializer routine, which avoids scaling problems in the primary unknowns and leads to a more rapid convergence for large time steps, respectively. Representative numerical examples verify the excellent performance of the ehG time-stepping schemes in comparison to the trapezoidal rule, especially concerning rotor dynamics. [Copyright &y& Elsevier]

Abstract: It has long been established that when a small-displacement problem involving contact between two or more bodies is solved, conforming algorithm approaches based on BEM are reliable and robust. Nevertheless, the authors have shown in a previous paper that a relative sliding between the bodies in contact, even if small, can originate a fictitious corner in the numerical model, which may alter the stress and the displacement predictions. This problem disappears if a non-conforming algorithm is employed. In this paper a new problem with different features but also presenting artificial alteration of the results is addressed. The compression of a rounded punch on a foundation is analysed for many fillet radii. Conforming and non-conforming algorithms are used. Comparison of results shows that effects of an artificial ‘numerical corner’ may alter even the traction distribution relatively far from it. Consequently, the assumed connection between small displacements and initially conforming discretizations with the use of a conforming approach disappears. An adequate knowledge of the contact problem under consideration is then essential to determine whether the singularity is inherent to the problem or is artificial, a non-conforming algorithm then being recommended in this second case. [Copyright &y& Elsevier]

Abstract: This paper deals with a new systematic approach of the instability problem in acoustic boundary elements models. When a long enough marching-on-time (MOT) computation is carried out, an exponential growth of the pressure magnitude often appears. This unrealistic behaviour is a serious drawback for the method of retarded potential integral equations. In this paper, we show that the instability problem of this type of algorithm can be translated in terms of a polynomial eigenvector problem (PEVP). In the case of the hypersingular derivative Green method, examples are shown of suppressing all numerical instabilities related to open or closed diffracting objects using the PEVP. Among them, the vibroacoustic model of a test structure used by the CNES (Centre National d''Etudes Spatiales) is successfully processed. [Copyright &y& Elsevier]

Implementation of an iterative decomposition (QRD) (IQRD) architecture based on the modified Gram-Schmidt (MGS) algorithm is proposed in this paper. A QRD is extensively adopted by the detection of multiple-input-multiple-output systems. In order to achieve computational efficiency with robust numerical stability, a triangular systolic array (TSA) for QRD of large-size matrices is presented. In addition, the TSA architecture can be modified into an iterative architecture that is called IQRD for reducing hardware cost. The IQRD hardware is constructed by the diagonal and the triangular process with fewer gate counts and lower power consumption than TSAQRD. For a 4 x 4 matrix, the hardware area of the proposed IQRD can reduce about 41% of the gate counts in TSAQRD. For a generic square matrix of order m IQRD, the latency required is 2m time units, which is based on the MGS algorithm. Thus, the total clock latency is only 10m - 5 cycles. [ABSTRACT FROM AUTHOR]

Abstract: A semi-implicit characteristic based split meshfree algorithm is proposed for the numerical solution of incompressible viscoelastic flow in the paper, in which the governing equations are discretized by element free Galerkin method in spatial space and the characteristic based split method is adopted in temporal space. In order to obtain stable and convergent solution at high Weissenberg number, streamline upwind method is chosen to tackle the convective terms in constitutive equations of viscoelastic flow. Meanwhile, mass lumped technique is adopted to accelerate computational efficiency. The method allows the equal order basis to approximate pressure, velocity and extra stress, especially the linear basis that is easy to implement. The planar Poiseuile flow and 4:1 planar contraction flow for an Oldroyd B fluid are investigated. Through these numerical experiments, we find that the method has good stability and the numerical results are in agreement well with those reported by other papers. [Copyright &y& Elsevier]

This paper presents Markov chain Monte Carlo data association (MCMCDA) for solving data association problems arising in multi-target tracking in a cluttered environment. When the number of targets is fixed, the single-scan version of MCMCDA approximates joint probabilistic data association (JPDA). Although the exact computation of association probabilities in JPDA is NP-hard, we prove that the single-scan MCMCDA algorithm provides a fully polynomial randomized approximation scheme for JPDA. For general multi-target tracking problems, in which unknown numbers of targets appear and disappear at random times, we present a multi-scan MCMCDA algorithm that approximates the optimal Bayesian filter. We also present extensive simulation studies supporting theoretical results in this paper. Our simulation results also show that MCMCDA outperforms multiple hypothesis tracking (MHT) by a significant margin in terms of accuracy and efficiency under extreme conditions, such as a large number of targets in a dense environment, low detection probabilities, and high false alarm rates. [ABSTRACT FROM AUTHOR]

Abstract: The main objective of this paper is to study reduction rate of 2D DEM (digital elevation model) data profile after data reduction by the Douglas–Peucker (DP) linear simplification method and by fractal interpolation to show original terrain reconstruction. In this paper, two-dimensional data of measured geographic profiles are taken as the study object, by using the DP method and the improved Douglas–Peucker (IDP) method to reduce data. Its aim is to retain spatial linear characteristics and variations, then take reduced data points as basic points and use the random fractal interpolation approach to add more data points up to the same as the original data points, in order to reconstruct the terrain, and compare the experimental data with the random point extraction method addressed in related literature. This paper uses tolerance calibration to generate different reduction rates and utilizes four types of evaluation factors, statistical measurement, image measurement, spectral analysis and elevation cumulative probability distribution graph, to make a quantitative analysis of profile variation. The study result indicates that real profile elevation data, manipulated with varied reduction approaches, then reconstructed by means of fractal interpolation can produce data points with a higher resolution than those originally observed, thereby the reconstructed profile gets more natural and real details. [Copyright &y& Elsevier]

Abstract: In this work we consider algorithms based on the singular value decomposition (SVD) to approximate Lyapunov and exponential dichotomy spectra of dynamical systems. We review existing contributions, and propose new algorithms of the continuous SVD method. We present implementation details for the continuous SVD method, and illustrate on several examples the behavior of continuous (and also discrete) SVD method. This paper is the companion paper of [L. Dieci, C. Elia, The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects, J. Diff. Equat., in press]. [Copyright &y& Elsevier]

Abstract: The paper presents control system design based on a non-linear model reference adaptive control law (MRAC) used for the vibration suppression of a smart piezoelectric mechanical structure. Numerical simulation of the proposed control system is performed based on the finite element (FE) model of the structure, modally reduced in order to meet the requirements of the control system design. First the MRAC problem is defined and a direct control algorithm described in the paper is suggested as a solution to the control problem. The basic MRAC algorithm is modified by augmenting the integral term of the control law in order to provide the robustness of the control system with respect to the stability. This approach provides preserving the boundness of the system states and adaptive gains, with small trackings error over large ranges of non-ideal conditions and uncertainties. The efficiency of the suggested control for the vibration suppression is tested and shown through a numerical simulation of the funnel-shaped piezoelectric structure. [Copyright &y& Elsevier]

We consider the problem of choosing the gate sizes or scale factors in a combinational logic circuit in order to minimize the total area, subject to simple RC timing constraints, and a minimum-allowed gate size. This problem is well known to be a geometric program (GP), and can be solved by using standard interior-point methods for small- and medium-size problems with up to several thousand gates. In this paper, we describe a new method for solving this problem that handles far larger circuits, up to a million gates, and is far faster. Numerical experiments show that our method can compute an adequately accurate solution within around 200 iterations; each iteration, in turn, consists of a few passes over the circuit. In particular, the complexity of our method, with a fixed number of iterations, is linear in the number of gates. A simple implementation of our algorithm can size a 10000 gate circuit in 25 s, a 100 000 gate circuit in 4 mm, and a million gate circuit in 40 mm, approximately. For the million gate circuit, the associated GP has three million variables and more than six million monomial terms in its constraints; as far as we know, these are the largest GPs ever solved. [ABSTRACT FROM AUTHOR]

Purpose - This paper sets out to perform a detailed numerical study of turbulent channel flow with strong temperature gradients using large-eddy simulations. Design/methodology/approach - A recently developed time-accurate algorithm based on a predictor-corrector time integration scheme is used in the simulations. Spatial discretization is performed on a collocated grid system using a flux interpolation technique. This interpolation technique avoids the pressure odd-even decoupling problem that is typically encountered in collocated grids. The eddy viscosity is calculated with the extension of the dynamic Smagorinsky model to variable-density flows. Findings - The mean velocity profile at the cold side deviates from the classical isothermal logarithmic law of the wall. Nonetheless, at the hot side, there is a better agreement between the present results and the isothermal law of the wall. Further, the numerical study predicts that the turbulence kinetic energy near the cold wall is higher than near the hot one. In other words heat addition tends to laminarize the channel flow. The temperature fluctuations were also higher in the vicinity of the cold wall, even though the peak of these fluctuations occurs at the side of the hot wall. Practical implications - The findings of the paper have applications in the design and analysis of convective heat transfer equipment such as heat exchangers and cooling systems of nuclear reactors. Originality/value - The paper presents the first numerical results for non-isothermal turbulent channel flow with high wall-temperature ratios (up to 9). These findings can be of interest to scientists carrying out research in turbulent flows. [ABSTRACT FROM AUTHOR]

Purpose - This paper seeks to develop an adaptive finite volume algorithm, and to present an extensive numerical analysis of it. Design/methodology/approach - The effectiveness of the developed algorithm is demonstrated through practical and computationally challenging problems. The algorithm is tested for a wide range of singularities. Findings - The convergence of the presented algorithm is independent of the regularity of the problems. It is shown that the our algorithm produces more accurate and well conditioned matrix systems. Research limitations/implications - Though the presented algorithm works for extreme singularities on rectangular meshes, it may not be as efficient if the underlying meshes are distorted, and it may not converge. Further research is under way for including the multi-point approximation technique into the algorithm. Practical implications - Almost all reservoir simulators use the two-point method, and this algorithm is based on this method. The algorithm can be easily incorporated into the reservoir simulators. The results show that such an implementation will greatly improve the computational efficiency of the simulators. The work is useful for computational scientists, and especially for the researchers in oil industries. The paper reports the numerical work with practical applications. Originality/value - The paper develops an adaptive finite volume algorithm. It is shown that adaptive meshes represent the underlying problem more accurately, and matrix systems associated with adaptive meshes are easier to solve compared with matrix systems associated with uniform meshes. [ABSTRACT FROM AUTHOR]