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Abstract In the paper, we present an efficient two grid method for the miscible displacement problem which discretized by mixed finite element methods for the pressure equation and concentration equation at the same time, and then analyzed the error estimate of the two-gird algorithm. At last, the numerical experiment presented confirmed the theoretical results. Compared with the standard mixed finite element methods, this two-grid scheme based on the mixed methods can keep the same convergence order and cost much less work. [ABSTRACT FROM AUTHOR]

Abstract This paper establishes a spectral conjugate gradient method for solving unconstrained optimization problems, where the conjugate parameter and the spectral parameter satisfy a restrictive relationship. The search direction is sufficient descent without restarts in per-iteration. Moreover, this feature is independent of any line searches. Under the standard Wolfe line searches, the global convergence of the proposed method is proved when | β k | ≤ β k F R holds. The preliminary numerical results are presented to show effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract With the explosive growth of data-intensive mobile, social, commercial and industrial applications, geo-distributed cloud becomes the main trend of cloud computing due to its advantages of higher flexible scalability, stronger stability, lower latency, and more diverse services. Due to the limited network bandwidth, communication across geographic data centers typically suffers from wide-area latencies, which significantly deteriorates system performance. Data locality is an effective way to solve this problem. In order to provide flexible cloud computing services for data-intensive applications, combining with the advantage of geo-distributed cloud computing paradigm, this paper proposed a data locality optimization method based on data migration (DLO-Migrate) and a data locality optimization algorithm based on hotspots prediction (DLO-Predict) to reduce data access delay in geo-distributed cloud environment. In DLO-Migrate method, tasks are assigned according to node locality, and access data of non-node-locality tasks are migrated in advance by using the idle network bandwidth. In DLO-Predict algorithm, from cloud-level data locality perspective, hot files are predicted and synchronized periodically among data centers of the geo-distributed cloud during information interaction. Extensive experimental results show that, compared with baseline algorithms, our proposed algorithms can improve data locality of geo-distributed cloud and reduce job completion time substantially. [ABSTRACT FROM AUTHOR]

Abstract In scientific research and engineering practice, many optimization problems can be abstracted into many-objective optimizations. The key to solving many-objective optimizations is the way to design an effective algorithm to balance exploration and exploitation. This paper proposes a hybrid many-objective optimization algorithm, which consists of evolutionary membrane algorithm and chemical reaction optimization algorithm. In the proposed algorithm, object represents a candidate solution of many-objective optimization problem. The reaction rule will be applied by the four operators to evolve the objects. In addition, superior objects are selected based on corner solution search for balancing convergence and diversity of the solutions in the high-dimensional objective space. In the simulation, the proposed algorithm compared to some state-of-the-art algorithms, including MaOEA-CS, MOEA/D, MOEA/DD, RVEA and NSGA-III, to all benchmark functions for CEC2018 Competition on Evolutionary Many-Objective Optimization. Experimental results empirically demonstrate that the proposed algorithm has a beneficial adaptation ability in terms of both convergence enhancement and diversity maintenance. [ABSTRACT FROM AUTHOR]

Abstract PageRank problem is the cornerstone of Google search engine and is usually stated as solving a huge linear system. Moreover, when the damping factor approaches 1, the spectrum properties of this system deteriorate rapidly and this system becomes difficult to solve. In this paper, we demonstrate that the coefficient matrix of this system can be transferred into a block form by partitioning its rows into special sets. In particular, the off-diagonal part of the block coefficient matrix can be compressed by a simple low-rank factorization, which can be beneficial for solving the PageRank problem. Hence, a matrix partition method is proposed to discover the special sets of rows for supporting the low-rank factorization. Then a preconditioner based on the low-rank factorization is proposed for solving difficult PageRank problems. Numerical experiments are presented to support the discussions and to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract This paper derives a superconvergence result for the modified weak Galerkin (MWG) finite element method of the second order elliptic problem. The convergence rate of the MWG approximation is improved by 30% after applying a low cost L 2 projection post-processing technique. These superconvergence phenomena are proved theoretically and confirmed numerically. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the convergence of numerical scheme for combined nonlinear radiation–conduction heat transfer system in a gray, absorbing and non-scattering two-dimensional medium. The radiative transfer equation is solved using a Discontinuous Galerkin method with upwind fluxes. The conductive equation is discretized using the finite element method. Moreover, the Crank–Nicolson scheme is applied for time discretization of the semi-discrete nonlinear coupled system. Existence and uniqueness of the solution for the continuous and full discrete system are presented. The convergence proof follows from the application of a discrete fixed-point theorem, involving only the temperature fields at each time step. The order of approximation error, stability, and order of convergence are investigated. Finally, the theoretical stability and convergence results are supported with numerical examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper a transformation of the pseudo-integral into another pseudo-integral is considered. Using the transformed pseudo-integral, monotone convergence theorems for the pseudo-integral are obtained. Based on the reverse Fatou's lemma for the pseudo-integral, the dominated convergence-type theorem is proven. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the construction and convergence analysis of two B-spline collocation methods for a class of nonlinear derivative dependent singular boundary value problems (DDSBVP). The first method is based on uniform mesh, while the second method is based on non-uniform mesh. For the second method, we use a grading function to construct the non-uniform grid. We prove that the method based on uniform mesh is of second-order accuracy and the method based on non-uniform mesh is of fourth-order accuracy. Three nonlinear examples with derivative dependent source functions are considered to verify the performance and theoretical rate of convergence of present methods. Moreover, we consider some special cases of the problem under consideration in order to compare our methods with other existing methods. It is shown that our second method based on cubic B-spline basis functions has the same order of convergence as quartic B-spline collocation method [1]. Moreover, our methods yield more accurate results and are computationally attractive than the methods developed in [1–8]. The proposed methods are applied on three real-life problems, the first problem describes the distribution of radial stress on a rotationally shallow membrane cap, the second problem arises in the study of thermal explosion in cylindrical vessel and the third problem arises in astronomy. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose a new approximate method, namely the discrete Adomian decomposition method (DADM), to approximate the solution of a strongly nonlinear singular boundary value problems describing the electrohydrodynamic flow of a fluid in an iron drag configuration in a circular cylindrical conduit. Convergence of the new method is analyzed. The velocity field of electrohydrodynamic flow of a fluid is determined. The influence of the Hartmann electric number and the strength of nonlinearity on the velocity profile is investigated. It is observed that the velocity field increases with the increase in the Hartmann electric number and decreases with the increase in the strength of nonlinearity. The results obtained by the proposed method are compared with results given in the literature. [ABSTRACT FROM AUTHOR]

Abstract The paper deals with a split-step θ -method for stochastic differential equations with piecewise continuous arguments (SEPCAs). The strong convergence of the method is proved under non-globally Lipschitz conditions. The exponential stability of the exact and numerical solutions is obtained. Some experiments are given to illustrate the conclusions. [ABSTRACT FROM AUTHOR]

Abstract The classical continuous Runge–Kutta methods are widely applied to compute the numerical solutions of delay differential equations without impulsive perturbations. However, the classical continuous Runge–Kutta methods cannot be applied directly to impulsive delay differential equations, because the exact solutions of the impulsive delay differential equations are not continuous. In this paper, impulsive continuous Runge–Kutta methods are constructed for impulsive delay differential equations with the variable delay based on the theory of continuous Runge–Kutta methods, convergence of the constructed numerical methods is studied and some numerical examples are given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose an iterative method based on reduced-space approximations for unconstrained optimization problems. The method works as follows: among iterations, samples are taken about the current solution by using, for instance, a Normal distribution; for all samples, gradients are computed (approximated) in order to build reduced-spaces onto which descent directions of cost functions are estimated. By using such directions, intermediate solutions are updated. The overall process is repeated until some stopping criterion is satisfied. The convergence of the proposed method is theoretically proven by using classic assumptions in the line search context. Experimental tests are performed by using well-known benchmark optimization problems and a non-linear data assimilation problem. The results reveal that, as the number of sample points increase, gradient norms go faster towards zero and even more, in the data assimilation context, error norms are decreased by several order of magnitudes with regard to prior errors when the assimilation step is performed by means of the proposed formulation. [ABSTRACT FROM AUTHOR]

Abstract Recently, Njeru and Guo presented an accelerated SOR-like (ASOR) method for solving the large and sparse augmented systems. In this paper, we establish an accelerated symmetric SOR-like (ASSOR) method, which is an extension of the ASOR method. Furthermore, the convergence properties of the ASSOR method for augmented systems are studied under suitable restrictions, and the functional equation between the iteration parameters and the eigenvalues of the relevant iteration matrix is established in detail. Finally, numerical examples show that the ASSOR is an efficient iteration method. [ABSTRACT FROM AUTHOR]

Abstract Nonnegative matrix factorization (NMF) has received intensive attention due to producing a parts-based representation of the data. However, because of the non-convexity of NMF models, these methods easily obtain a bad local solution. To alleviate this deficiency, this paper presents a novel NMF method by gradually including data points into NMF from easy to complex, namely self-paced learning (SPL), which is shown to be beneficial in avoiding a bad local solution. Furthermore, instead of using the conventional hard weighting scheme, we adopt the soft weighting strategy of SPL to further improve the performance of our model. An iterative updating algorithm is proposed to solve the optimization problem of our method. The convergence of the updating rules is also theoretically guaranteed. Experiments on both toy data and real-world benchmark datasets demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper we develop a numerical scheme for approximating interior jump discontinuity solutions of compressible Stokes flows with inflow jump datum. The scheme is based on a decomposition of the velocity vector into three parts: the jump part, an auxiliary one and the smoother one. The jump discontinuity is handled by constructing a vector function extending the density jump value of the normal vector on the interface to the whole domain. We show existence of the finite element solutions for the three parts, derive error estimates and also convergence rates based on the piecewise regularities. Numerical examples are given, confirming the derived convergence rates. [ABSTRACT FROM AUTHOR]

Abstract Aggregation based algebraic multigrid is widely used to solve sparse linear systems, due to its potential to achieve asymptotic optimal convergence and cheap cost to set up. In this kind of method, it is vital to construct coarser grids based on aggregation. In this paper, we provide a new aggregation method based on coordinates partitioning recursively. The adjacent graph of the original coefficient matrix is partitioned into sub-graphs and each sub-graph is recursively partitioned until the minimal number of nodes over the sub-graphs on some level is small enough. In this way, a hierarchy of grids can be constructed from top to bottom, which is completely different from the classical schemes. The results from the solution of model partial differential equations with the preconditioned conjugate gradient iteration show that the new algorithm has better performance and is more robust than the widely used classical algorithms in most cases. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider the analytical and numerical solutions for a two-dimensional multi-term time-fractional diffusion and diffusion-wave equation. We derive the analytical solution for the equation using the method of separation of variables and properties of the multivariate Mittag-Leffler function. An implicit difference approximation is constructed. Stability and convergence analysis of the numerical scheme are proved by the energy method. Numerical examples are constructed to evaluate the working of the numerical scheme as compared to theoretical analysis. Highlights • A new two-dimensional multi-term time-fractional diffusion and diffusion. • Wave equation (2D-MT-TFD-DWE) is considered. • The analytical solution for the 2D-MT-TFD-DWE is derived. • A novel implicit difference method (IDM) for 2D-MT-TFD-DWE is proposed. • The stability and convergence of the IDM are proved by the energy method. • Numerical examples are given. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with bird-strike numerical simulations using the Smoothed Particle Hydrodynamics method to represent the bird model. A comparison between bird models with classical mesh-based particle distributions and bird models with initial particle distributions generated using a technique based on the Weighted Voronoi Tessellation algorithm is presented. The adopted iteration technique to fill the bird model with particles is described. Particle distributions generated using this new technique are assessed in comparison with reference bird models commonly used in the literature. Results of generic bird-strike simulations on a flat target structure indicate the superiority of the proposed bird models over the bird models with classical mesh-based particle distributions in terms of flow behavior, conservation of total energy, normal forces, pressures, and computational efficiency. [ABSTRACT FROM AUTHOR]

Abstract The problem of fast convergence to Nash equilibrium without steady state oscillation in static non-cooperative games with N players is considered in this paper. In this regard, players can generate their actions to achieve Nash equilibrium only by measuring their own payoff values, which means that the players do not need any information about the details of payoff function or other players' actions. Additionally, in contrast to the most classical extremum seeking algorithms, this algorithm can converge to Nash equilibria without steady state oscillation and faster, because the amplitude of excitation sinusoidal signal in the conventional extremum seeking is adjusted to converge to zero, so the deleterious effects of steady state oscillation will be eliminated. Moreover, since each player can possess a dynamic, the actions are filtered before applying to the payoff function, which can make this algorithm appealing to many applications such as mobile sensor networks. In addition, the details of convergence to Nash equilibria are provided. Finally, we illustrate the application of this algorithm to solve the formation control problem of non-holonomic unicycles, and evasion of jammer attacks on unmanned autonomous vehicles (UAVs), which clearly shows the effectiveness and superiority of this algorithm through simulation results. [ABSTRACT FROM AUTHOR]

Highlights • A new hybrid framework of adaptive-weighting active contour model is proposed. • The global term enhances the image contrast and accelerates the convergence rate. • The local term integrates fractional order differentiation and difference image information. • An adaptive weighting strategy and a termination criterion are employed. • Measures include the dice similarity coefficient and gray-leveled contrast. Abstract Segmenting intensity inhomogeneous images is a challenging task for both local and global methods. Some hybrid methods have great advantages over the traditional methods in inhomogeneous image segmentation. In this paper, a new hybrid method is presented, which incorporates image gradient, local environment and global information into a framework, called adaptive-weighting active contour model. The energy or level set functions in the framework mainly include two parts: a global term and local term. The global term aims to enhance the image contrast, and it can also accelerate the convergence rate when minimizing the energy function. The local term integrates fractional order differentiation, fractional order gradient magnitude, and difference image information into the well-known local Chan–Vese model, which has been shown to be effective and efficient in modeling the local information. The local term can also enhance low frequency information and improve the inhomogeneous image segmentation. An adaptive weighting strategy is proposed to balance the actions of the global and local terms automatically. When minimizing the level set functions, regularization can be imposed by applying Gaussian filtering to ensure smoothness in the evolution process. In addition, a corresponding stopping criterion is proposed to ensure the evolving curve automatically stops on true boundaries of objects. Dice similarity coefficient is employed as the comparative quantitative measures for the segmented results. Experiments on synthetic images as well as real images are performed to demonstrate the segmentation accuracy and computational efficiency of the presented hybrid method. [ABSTRACT FROM AUTHOR]

Abstract Thin-walled structures are always subjected to a large range of extreme loading cases leading to obvious geometric nonlinearities in structural dynamic response, such as vibration with large amplitudes in aeronautics and astronautics field. Various dynamic reduced-order models have been investigated from detailed finite element models, to largely reduce the computational burden of the structural dynamic responses. However, to construct these low-order models, applying a series of nonlinear static simulations to the full-order model is necessary. This paper aims to develop a hybrid reduced-order modeling method by combining the dynamic and static reduced-order models together, to estimate the dynamic transient response caused by geometrically nonlinear finite element models. A few free-vibration modes of interest are selected to reduce basis vectors of dynamic reduced-order model. Based on Koiter asymptotic expansion theory, the constructed static reduced-order model is applied to the nonlinear static analyses. Therefore, not only does the proposed method make it possible to calculate the nonlinear dynamic response far more efficiently than full-order modeling methods, but computational burdens in construction of dynamic reduced-order model are also largely reduced compared to existing approaches. Various engineering numerical examples with hardening and/or softening nonlinearities are carefully tested to validate the good quality and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study the following attraction–repulsion Keller–Segel system u t = Δ u − ∇ ⋅ ( χ u ∇ v ) + ∇ ⋅ ( ξ u ∇ w ) , x ∈ Ω , t > 0 , v t = Δ v + α u − β v , x ∈ Ω , t > 0 , 0 = Δ w + γ u − δ w , x ∈ Ω , t > 0 , ∂ u ∂ ν = ∂ v ∂ ν = ∂ w ∂ ν = 0 , x ∈ ∂ Ω , t > 0 , u ( x , 0 ) = u 0 ( x ) , v ( x , 0 ) = v 0 ( x ) , x ∈ Ω , in a bounded domain Ω ⊂ R 2 with smooth boundary. The boundedness of solutions with arbitrarily large initial data has been proved in the case of ξ γ ≥ χ α (Jin and Wang, 2016). Under the additional assumption ξ γ β ≥ χ α δ , we show that the global classical solution will converge to the unique constant state ( u ̄ 0 , α β u ̄ 0 , γ δ u ̄ 0 ) as t → + ∞ . [ABSTRACT FROM AUTHOR]

Highlights • Flow condensation. • Heat transfer coefficient. • Two phase flow. • Experimental data. Abstract In this paper a new model is presented for heat transfer calculation during film condensation inside pipes. This new model has been verified by comparison with available experimental data of a total of 22 different fluids, including water, various refrigerants and organic substances, which condense inside horizontal, vertical and inclined tubes. The model is valid for a range of internal diameters ranging from 2 mm to 50 mm, reduced pressure values ranging from 0.0008 to 0.91, Pr values for the liquid portion of the condensate from 1 to 18, values of Reynolds number for the liquid portion between 68 and 84827, and for the portion of the steam between 900 and 594373, steam quality from 0.01 to 0.99 and mass flux rates in the ranges of 3–850 kg/(m2 s). The mean deviation found for the data analyzed for vertical and inclined tubes was 13.0%, while for the horizontal tube data the mean deviation was 11.8%. In all cases, the agreement of the proposed model for horizontal, vertical and inclined tubes is good enough to be considered satisfactory for practical design. [ABSTRACT FROM AUTHOR]

Highlights • A penalty finite element method for the steady MHD equations was given. • The solution of the penalty method convergence the solution of the steady MHD equations. • The stability analysis shows our method is stable. • The error estimate shows our method has an optimal convergence order. • The numerical results of the Hartmann flow was shown. Abstract In this paper, we give a penalty finite element method for the steady MHD equations. In this method, we decouple the MHD into two equations, one for the velocity and magnetic (u , B) , the other for the pressure p. We prove the existence of the penalty method and the optimal error estimate. Then, we give the penalty finite element method for the MHD equations. The stability analysis shows our method is stable, and the error estimate shows our method has an optimal convergence order. Finally, we give some numerical results of exact solution equation and Hartmann flow. The numerical results show that our penalty finite element method is effect. [ABSTRACT FROM AUTHOR]

• Software is presented for verifying Timoshenko beam finite elements. • A popular fiite element is shown to converge to the wrong answer. • An element modification sufficient for convergence is reviewed. Abstract The classic paper Han et al. Dynamics of transversely vibrating beams using four engineering theories , Journal of Sound and Vibration, 225, 1999, sets up the continuation problem that determines the exact vibrational frequencies and mode shapes of prismatic Timoshenko beams. This article presents a portable implementation of a solver for the problem. In order to reliably compute a complete set of modes, without redundancies, it is crucial to formulate the frequency equation as a continuation problem. The continuation problem is solved for a thickness parameter starting from zero thickness (the Euler beam), and increasing up to the finite thickness of interest. The continuation problem has a bifurcation point, at which a wave number variable passes from real to a purely imaginary value. For finite thickness, the continuation problem for all sufficiently high frequency modes crosses through this bifurcation. Han et al.[7] solve the continuation problem using an unspecified differential equation solver, and dummyTXdummy- do not discuss accuracy. Here a solution of the continuation problem using pseudoarclength continuation is presented. This article presents a description of how to compute this singularity exactly, and develops software that maintains full working precision. Furthermore the details of the computation of the mode shapes from the frequencies are presented for free-free, clamped-clamped and clamped-free boundary conditions. The source code is available under a MIT license from github in the TimoshenkoBeamEigenvalues repository. [ABSTRACT FROM AUTHOR]

Highlights • A fixed-point algorithm is proposed to estimation the maximum of generalized correntropy (termed FP-GMC). • A sufficient condition is obtained for the convergence of the FP-GMC algorithm. • The sliding-window method and recursive method are applied to the FP-GMC algorithm for online signal processing. And, call these online algorithms as SW-GMC and RGMC, respectively. • A convex combination algorithm is proposed by adaptively combine two RGMC algorithms to improve the convergence rate of RGMC algorithm. And, call this combination algorithm as AC-RGMC. • The convergence rate of the AC-RGMC has been further increased by a simple and efficient weight control scheme. And, call this control algorithm as AC-RGMC-C. Abstract Compared with the MSE criterion, the generalized maximum correntropy (GMC) criterion shows a better robustness against impulsive noise. Some gradient based GMC adaptive algorithms have been derived and available for practice. But, the fixed-point algorithm on GMC has not yet been well studied in the literature. In this paper, we study a fixed-point GMC (FP-GMC) algorithm for linear regression, and derive a sufficient condition to guarantee the convergence of the FP-GMC. Also, we apply sliding-window and recursive methods to the FP-GMC to derive online algorithms for practice, these two called sliding-window GMC (SW-GMC) and recursive GMC (RGMC) algorithms, respectively. Since the solution of RGMC is not analyzable, we derive some approximations that fundamentally result in the poor convergence rate of the RGMC in non-stationary situations. To overcome this issue, we propose a novel robust filtering algorithm (termed adaptive convex combination of RGMC algorithms (AC-RGMC)), which relies on the convex combination of two RGMC algorithms with different memories. Moreover, by an efficient weight control method, the tracking performance of the AC-RGMC is further improved, and this new one is called AC-RGMC-C algorithm. The good performance of proposed algorithms are tested in plant identification scenarios with abrupt change under impulsive noise environment. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider stochastic Runge–Kutta methods for stochastic Hamiltonian partial differential equations and present some sufficient conditions for stochastic multi-symplecticity of stochastic Runge–Kutta methods. To present more clearly, we apply these ideas to three dimensional stochastic Maxwell equations driven by multiplicative noise, which play an important role in stochastic electromagnetism and statistical radiophysics areas. Theoretical analysis shows that the methods inherit the energy conservation law of the original system, and preserve the discrete stochastic multi-symplectic conservation law almost surely. [ABSTRACT FROM AUTHOR]

Abstract In this paper we introduce and analyze a mixed virtual element method (mixed-VEM) for a pseudostress-displacement formulation of the linear elasticity problem with non-homogeneous Dirichlet boundary conditions. We follow a previous work by some of the authors, and employ a mixed formulation that does not require symmetric tensor spaces in the finite element discretization. More precisely, the main unknowns here are given by the pseudostress and the displacement, whereas other physical quantities such as the stress, the strain tensor of small deformations, and the rotation, are computed through simple postprocessing formulae in terms of the pseudostress variable. We first recall the corresponding variational formulation, and then summarize the main mixed-VEM ingredients that are required for our discrete analysis. In particular, we utilize a well-known local projector onto a suitable polynomial subspace to define a calculable version of our discrete bilinear form, whose continuous version requires information of the variables on the interior of each element. Next, we show that the global discrete bilinear form satisfies the hypotheses required by the Babuška–Brezzi theory. In this way, we conclude the well-posedness of our mixed-VEM scheme and derive the associated a priori error estimates for the virtual solutions as well as for the fully computable projections of them. Furthermore, we also introduce a second element-by-element postprocessing formula for the pseudostress, which yields an optimally convergent approximation of this unknown with respect to the broken H (div) -norm. In addition, this postprocessing formula can also be applied to the postprocessed stress tensor. Finally, several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence are presented. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the backward problem introduced in [48] for Riesz–Feller fractional diffusion. To begin with, some basic properties of solution of the corresponding forward problem, such as the L p estimates, symmetry property and asymptotic estimates, are established by Fourier analysis technique. And then, under various a priori bound assumptions, we give the L 2 conditional stability estimates for the solution of backward problem and also its symmetry property. Moreover, in order to overcome the ill-posedness of the backward problem, we propose a new nonlocal regularization method (NLRM) to solve it. That is, the following nonlocal variational functional is introduced J (φ) = 1 2 ‖ u (φ (x) ; x , T) − f δ (x) ‖ 2 + β 2 ‖ [ P α 1 ⁎ φ ] (x) ‖ 2 , where β ∈ (0 , 1) is a regularization parameter, "⁎" denotes the convolution operation and P α 1 (x) is called a convolution kernel with parameter α 1 , which will be selected properly later. The minimizer of above variational problem is defined as the regularization solution, and the L 2 estimates, symmetry property of regularization solution are given. These results actually show the well-posedness of nonlocal variational problem. Our idea is essentially that using this well-posed problem to approximate the backward (ill-posed) problem. Thus, under an a posteriori parameter choice rule, we deduce various convergence rate estimates under different a-priori bound assumptions for the exact solution. Finally, several numerical examples are given to show that the proposed numerical methods are effective and adaptive for different a-priori information. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with nonlinear stochastic functional differential equations with piecewise continuous arguments (SFDEPCAs). Based on an adaptation to the underlying one-leg θ -methods for ODEs, a class of new one-parameter methods for nonlinear SFDEPCAs are introduced. The mean-square exponential stability criteria of analytical and numerical solutions are derived. Under the suitable conditions, it is proved that the one-parameter methods are convergent with strong order 1/2. Some numerical experiments are given to illustrate the theoretical results and computational advantages of the induced methods. Highlights • Stochastic one-leg θ -methods for nonlinear SFDEPCAs are proposed. • The mean-square exponential stability criteria of analytical and numerical solutions are derived. • It is proved under some conditions that stochastic one-leg θ -methods are convergent with strong order 1 2. • The numerical experiment shows that stochastic one-leg θ -methods have the greater computational advantages than stochastic split-step θ -methods. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the unconditional stability and convergence of characteristics type methods for the time-dependent incompressible MHD equations. For this purpose, we introduce a new characteristics time-discrete system. The optimal error estimates in L 2 and H 1 norms for the typical modified characteristics finite element method unconditionally can be deduced, while the whole previous works require certain time-step restrictions. Some numerical experiments document performance of the characteristics type methods for the time-dependent incompressible MHD equations. [ABSTRACT FROM AUTHOR]

Abstract The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved. [ABSTRACT FROM AUTHOR]

Abstract The main goal of multi-objective optimization evolutionary algorithms (MOEAs) is to obtain a set of solutions with good diversity and convergence. However, how to concurrently improve the diversity and convergence is a difficult work. To address this problem, an updated strategy based on decomposition is used to maintain the diversity, and the convergence is enhanced by improving the search efficiency. In this paper, an improvement decomposition-based multi-objective evolutionary algorithm using multi-search strategy is aimed at improving the search efficiency. In this work, three search strategies are used to help crossover operators to carry out the local search and global search. This multi-search strategy selects sparse non-dominated solutions to carry out the exploration, and selects convergent solutions to implement the exploitation. In the experiments, the proposed algorithm is compared with seven efficient state-of-the-art algorithms, e.g., NSGAII, MOEA/D, MOEA-DVA, MOEA-IGD-NS, MOEA/D-PaS, RVEA and MPSOD, on twenty-two benchmark functions. Empirical results show that the proposed algorithm can find a set of solutions with better diversity and convergence than six compared algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a norm descent derivative-free algorithm for solving large-scale nonlinear symmetric equations without involving any information of the gradient or Jacobian matrix by using some approximate substitutions. The proposed algorithm is extended from an efficient three-term conjugate gradient method for solving unconstrained optimization problems, and inherits some nice properties such as simple structure, low storage requirements and symmetric property. Under some appropriate conditions, the global convergence is proved. Finally, the numerical experiments and comparisons show that the proposed algorithm is very effective for large-scale problems. [ABSTRACT FROM AUTHOR]

In this paper we consider 1D parabolic singularly perturbed systems of reaction–diffusion type which are coupled in the reaction term. The numerical scheme, used to approximate the exact solution, combines the fractional implicit Euler method and a splitting by components to discretize in time, and the classical central finite differences scheme to discretize in space. The use of the fractional Euler method combined with the splitting by components means that only tridiagonal linear systems must be solved to obtain the numerical solution. For simplicity, the analysis is presented in a complete form only in the case of systems which have two equations, but it can be easily extended to an arbitrary number of equations. If a special nonuniform mesh in space is used, the method is uniformly and unconditionally convergent, having first order in time and almost second order in space. Some numerical results are shown which corroborate in practice the theoretical ones. [ABSTRACT FROM AUTHOR]

In this paper, the generalized shift-splitting (GSS) preconditioner is implemented for solving a class of generalized saddle point problems which stem from the solution of complex symmetric linear systems. The GSS preconditioner is induced by the generalized shift-splitting iterative method. Theoretical analysis shows that the generalized shift-splitting iterative method is unconditionally convergent. Some numerical experiments are provided to show the effectiveness of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

Regarding the efficient previous method for approximation of one-dimensional functions integrals through Bernstein polynomials in Amirfakhrian (2011), this paper presents a development of this method for approximation of two-dimensional functions integrals for the first time. Then, by combining this approximation with Bernstein collocation method for numerical solution of two-dimensional nonlinear Fredholm integral equations, the kernels double integrals of integral equations will be approximated. Combination of two-dimensional functions numerical integration method with numerical solution of integral equations method (in both methods, Bernstein polynomials were used) will result in increase of convergence speed and accuracy of the method. The convergence analysis of the method is completely presented. Finally, numerical examples are presented to illustrate the efficiency and superiority of our method in comparing it with other methods. [ABSTRACT FROM AUTHOR]

In the current paper, we present a direct numerical scheme to approximate a second-kind nonlinear Volterra integral equations (NVIEs). The scheme is based upon shifted Chebyshev polynomials and its operational matrices which eventually leads to the sparsity of the coefficients matrix of obtained system. The main idea of the proposed approach is based on a useful property of Chebyshev polynomials that yields to construct a new operational vector. This vector eliminates any requirement of using projection methods and also enhances the accuracy vs. other methods applied projection methods. The constructive technique and the convergence analysis of this approach under the L w 2 -norm are also described. Numerical experiments and comparisons confirm the applicability and the validity of the presented scheme. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the asymptotic behavior of solutions to the linear spatially homogeneous Boltzmann equation for hard potentials without angular cutoff. We obtain an optimal rate of exponential convergence towards equilibrium in a L 1-space with a polynomial weight. Our strategy is taking advantage of a spectral gap estimate in the Hilbert space L 2 (μ − 1 2 ) and a quantitative spectral mapping theorem developed by Gualdani et al. (2017). [ABSTRACT FROM AUTHOR]

Abstract The restricted version of the overlapping Schur complement (SchurRAS) preconditioner was introduced by Li and Saad (2006) for the solution of linear system A x = b , and numerical results have shown that the SchurRAS method outperforms the restricted additive Schwarz (RAS) method both in terms of iteration count and CPU time. In this paper, based on meticulous derivation, we give an algebraic representation of the SchurRAS preconditioner, and prove that the SchurRAS method is convergent under the condition that A is an M -matrix and it converges faster than the RAS method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the adaptive fashion of the Ciarlet–Raviart mixed method for biharmonic equation/eigenvalue problem with simply supported boundary condition in R d. We propose an a posteriori error indicator of the Ciarlet–Raviart approximate solution for the biharmonic equation and an a posteriori error indicator of the Ciarlet–Raviart approximate eigenfuction, and prove the reliability and efficiency of the indicators. We also give an a posteriori error indicator for the approximate eigenvalue and prove its reliability. We design an adaptive Ciarlet–Raviart mixed method with piecewise polynomials of degree less than or equal to m , and numerical experiments show that numerical eigenvalues obtained by the method can achieve the optimal convergence order O (d o f − 2 m d ) (d = 2 , m = 2 , 3 ; d = 3 , m = 3). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider a semi-explicit form of Volterra integro-differential-algebraic equations (IDAEs) and investigate the existence and uniqueness of solution of these systems by using differentiability index. Numerical method based on discontinuous piecewise polynomial approximation is proposed for the solution of the semi-explicit IDAEs and global convergence results are established. The performance of the numerical scheme is illustrated by means of some test problems. [ABSTRACT FROM AUTHOR]

Abstract Active noise control (ANC) is the most popular method for attenuating acoustic primary noise or disturbances by generating controllable secondary sources by which the output noise can be cancelled with the same amplitude but with opposite sign/sense. Most available ANC uses the secondary path modelling including filtered x least mean square (FxLMS) algorithm. The modelling requirement of the secondary path increases the complexity of the system implementation and decreases the control system performance. Recently several new ANC algorithms have been developed; in which there is no requirement for the modelling of the secondary path transfer function. In this regard, the aim of this paper is concerned about a narrowband feedforward ANC system in systems like air intake duct system and its novelty is to introduce all-pass filtered x LMS (APFxLMS) algorithm which do not require an estimation of the secondary path. Here first-order all pass filters with single parameter is used to improve the convergence of the LMS algorithm. The performance evaluation in terms of convergence speed of the proposed algorithm is validated with standard ANC without secondary path modelling. The results also show that the proposed method outperforms other LMS algorithm without secondary path modelling. The proposed narrowband LMS algorithm would benefit in the design of efficient feedforward ANC system that can realize noise control in air intake duct applications. [ABSTRACT FROM AUTHOR]

The Gravitational Search Algorithm (GSA) has excellent performance in solving various optimization problems. However, it has been demonstrated that GSA tends to trap into local optima and are easy to lose diversity in the late evolution process. In this paper, a new hybrid algorithm based on self-adaptive Gravitational Search Algorithm (GSA) and Differential Evolution (DE) is proposed for solving single objective optimization, named SGSADE. Firstly, a self-adaptive mechanism based on GSA is proposed for improving the convergence speed and balancing exploration and exploitation. Secondly, the diversity of the population is maintained in the evolution process by using crossover and mutation operation from DE. Besides, to improve the performance of the algorithm, a new perturbation based on Levy flight theory is embedded to enhance exploitation capacity. The simulated results of SGSADE on 2017 CEC benchmark functions show that the SGSADE outperforms the state-of-the-art variant algorithms of the GSA. [ABSTRACT FROM AUTHOR]

Highlights • The ADP algorithm of actor-critic networks is used to deal with the decentralized reliable guaranteed cost control problem of large-scale nonlinear systems with mismatched interconnection and time-varying actuator fault. • A novel relationship of the control policy between isolated system and original system with interconnection and actuator faults, is constructed. • The considered reliable guaranteed cost control problem is transformed into design an optimal control strategy of the isolated system. Abstract In this paper, the decentralized reliable guaranteed cost control problem of large-scale nonlinear systems with mismatched interconnection and time-varying actuator fault is investigated. The unknown actuator fault is assumed to be with known upper bounds. Under the case that the interconnection term is unknown and mismatched, the guaranteed cost control problem for a class of large-scale nonlinear systems can be transformed into design an optimal control strategy of the isolated system, which is necessary to solve the HJB (Hamilton–Jacobi–Bellman) equations by using adaptive dynamic programming (ADP) of actor-critic networks. The convergence property of the neural network weights and the stability of the closed-loop system have been strictly proved even if time-varying actuator faults and unknown interconnection coexist. Finally, simulation examples are given to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract Full waveform inversion (FWI) consists in finding an accurate optimal model of the subsurface from local measurements of the seismic wavefield. This aim is achieved by minimizing the difference between the observed and predicted data, starting from an initial estimation of the subsurface parameters. One challenge for FWI is its intensive large-scale wavefield simulations, which seriously restricts its wide applications. Additionally, due to the ill-posedness of FWI problem, when the nonlinear conjugate gradient method is employed, the current gradient often lies in the space spanned by the previous directions, resulting in very slow convergence. In this paper, a limited memory version conjugate gradient method equipped with the scalable HSS-structured multifrontal solver is applied to efficiently solve the FWI problem. A hierarchically preconditioned scheme is considered to enhance the robustness of the inversion algorithm. Numerical experiments including 2D and 3D are illustrated to show the performances of this high efficient inversion algorithm. Highlights • Multiforntal solver with HSS compression is employed to efficiently solve forward problems. • Nonlinear CG method guaranteed descent is accelerated with limited memory technique. • Numerical performances for this limited memory version CG method are conducted for 2D and 3D FWI problems. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an improved understanding of the interaction of hybrid optimization method with variable low-thrust trajectory optimization requirements. To analyze fuel-optimal bang-bang control problem, a new version of homotopic algorithm, termed robust homotopic method, is investigated with the prospect of improving the efficiency and automation of the homotopic approach to achieve a high-level of robustness, and consequently enlarge its range of application. Such desired characteristics are promoted via a combination of several techniques. As an effective approach, a modified methodology of the switching detection process is presented for the bang-bang optimal-control problem. Moreover, the value of unknown costates and switching functions are mapped to new normalized intervals throughout the computational process. As a result, the optimal solution is rapidly designed to obtain the global robust-convergence to satisfy all constraints without any ambiguity. The fitting process of all iterations robustly find the unknown variables with the percent of converged solutions to maximum, and the penalty terms are quickly satisfied with predetermined high-accuracy, from the energy-optimal to the fuel-optimal solution, especially close to zero point as a critical point. Accordingly, two advanced interplanetary trajectories are optimized using two dynamic modeling approaches for the instantaneous and constant maximal thrust magnitude as a way to analyze and substantiate the robustness of the proposed algorithm. Results and performances are compared with existing solutions of the same mission problem. [ABSTRACT FROM AUTHOR]

Highlights • Obtain the optimal solution of far rapid cooperative rendezvous in general case. • Design QPSO-SQP and proving the advance of QPSO-SQP. • Solve the complex optimal control problem with 29 variables. Abstract Focused on far-distance rapid cooperative rendezvous between two spacecraft under continuous large thrust, this paper presents a series of artificial intelligence algorithms for fuel and time optimization. The process of far-distance rapid cooperative rendezvous was optimized by a type of hybrid algorithm-integrated Quantum-behaved Particle Swarm Optimization (QPSO) and Sequential Quadratic Programming (SQP). The convergent co-state vectors were obtained by QPSO and subsequently set as the initial values of SQP to search for the exact solutions in a smaller area. Applications of non-coplanar cooperative rendezvous are provided to demonstrate that the QPSO-SQP algorithm has better performance than other popular algorithms in less time consumption, faster convergence rate and highly stable solutions. [ABSTRACT FROM AUTHOR]

This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. The methods have high order of convergence but only using first order derivatives. Moreover only one LU decomposition is required in each iteration. In particular, the methods are real alternatives to the classical Newton method. We present a local convergence analysis based on hypotheses only on the first derivative. These types of local results were usually proved based on hypotheses on the derivative of order higher than two although only the first derivative appears in these types of methods (Bermúdez et al., 2012; Petkovic et al., 2013; Traub, 1964). We apply these methods to an equation related to the nonlinear complementarity problem. Finally, we find the most efficient method in the family for this problem and we perform a theoretical and a numerical study for it. [ABSTRACT FROM AUTHOR]