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In this paper, not requiring that the Hermitian part of the complex symmetric linear system must be Hermitian positive definite, a class of splitting methods is established by the modified positive/negative-stable splitting (PNS) of the coefficient matrix and is called the MPNS method. Theoretical analysis shows that the MPNS method is absolutely convergent under proper conditions. Some useful properties of the corresponding MPNS-preconditioned matrix are obtained. Numerical experiments are reported to illustrate the efficiency of both the MPNS method and the MPNS preconditioner. [ABSTRACT FROM AUTHOR]

In this paper, a high-accuracy conservative difference scheme is presented to solve the initial-boundary value problem of the Zakharov equations, which preserves the original conservative properties. The proposed scheme is based on finite difference method. The scheme is second-order accuracy in time and fourth-order accuracy in space. A detailed numerical analysis of the scheme is presented including a convergence analysis result. Numerical examples are given to confirm the proposed scheme is efficient, reliable and of high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the superconvergence properties of the local discontinuous Galerkin (LDG) method applied to the two-dimensional sine-Gordon nonlinear hyperbolic equation on Cartesian grids. We perform a local error analysis and show that the actual error can be split into an O ( h p + 1 ) leading component and a higher-order component, when tensor product polynomials of degree at most p are used. We further prove that the leading term of the LDG error is spanned by two ( p + 1 ) -degree Radau polynomials in the x and y directions, respectively. Thus, the LDG solution is O ( h p + 2 ) superconvergent at Radau points obtained as a tensor product of the roots of ( p + 1 ) -degree right Radau polynomial. Computational results indicate that our superconvergence results hold globally. We use these results to construct simple, efficient, and asymptotically exact a posteriori LDG error estimates. The proposed error estimates are computationally simple and are obtained by solving local steady problems with no boundary conditions on each element. Finally, we present several numerical examples to validate the superconvergence results and the asymptotic exactness of our a posteriori error estimates under mesh refinement. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a boundary data identification for an electromagnetic problem by means of the potential field method (the A - ϕ method). One part of the boundary is over-determined. The other part of the boundary is unreachable and has to be determined as a part of the problem. We design a constructive algorithm by the A - ϕ formulation to solve this problem. The numerical scheme is based on the steepest descent method (SDM) for the minimization of a regularized cost functional, having its derivative determined via an adjoint method. We analyze the properties of the cost functional and prove the convergence of the minimization process. The method is supported by several numerical experiments. [ABSTRACT FROM AUTHOR]

This paper concerns a non-monotone algorithm for minimizing differentiable functions on closed sets. A general numerical scheme is proposed which combines a regularization/trust-region framework with a non-monotone strategy. Global convergence to stationary points is proved under usual assumptions. Numerical experiments for a particular version of the general algorithm are reported. In addition, a promising numerical scheme for medium/large-scale orthogonal Procrustes problem is also proposed and numerically illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we provide a local convergence analysis of Newton, Halley and Chebyshev iterative methods considered as methods for simultaneous determination of all multiple zeros of a polynomial f over an arbitrary normed field K . Convergence theorems with a priori and a posteriori error estimates for each of the proposed methods are established. The obtained results for Newton and Chebyshev methods are new even in the case of simple zeros. Three numerical examples are given to compare the convergence properties of the considered methods and to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a numerical method preserving positivity for stochastic age-dependent population equations. We use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution. It is proved that the Balanced Implicit Method (BIM) preserves positivity and converges with strong order 1/2 under given conditions. Finally, two examples are simulated to verify the positivity and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Recovering the low-rank, sparse components of a given matrix is a challenging problem that arises in many real applications. Existing traditional approaches aimed at solving this problem are usually recast as a general approximation problem of a low-rank matrix. These approaches are based on the nuclear norm of the matrix, and thus in practice the rank may not be well approximated. This paper presents a new approach to solve this problem that is based on a new norm of a matrix, called the truncated nuclear norm (TNN). An efficient iterative scheme developed under the linearized alternating direction method multiple framework is proposed, where two novel iterative algorithms are designed to recover the sparse and low-rank components of matrix. More importantly, the convergence of the linearized alternating direction method multiple on our matrix recovering model is discussed and proved mathematically. To validate the effectiveness of the proposed methods, a series of comparative trials are performed on a variety of synthetic data sets. More specifically, the new methods are used to deal with problems associated with background subtraction (foreground object detection), and removing shadows and peculiarities from images of faces. Our experimental results illustrate that our new frameworks are more effective and accurate when compared with other methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with high-fidelity modeling of signal propagation in corrugated coaxial cables. Taking advantage of the axisymmetry, we reduce the 3-D problem to a 2-D problem by solving a time dependent Maxwell’s equations in cylindrical coordinates. We develop a nodal discontinuous Galerkin method for solving our model equations. Stability and error analysis are proved for the semi-discrete scheme. Extensive numerical results are provided to demonstrate that our algorithm not only converges as our theoretical analysis predicts, but also is very effective in solving various signal propagation problems in practical corrugated coaxial cables. [ABSTRACT FROM AUTHOR]

In this paper, we propose two systematic strategies to recover the gradient on the boundary of a domain. The recovered gradient has comparable superconvergent property on the boundary as that in the interior of the domain. This superconvergence property has been validated by several numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of population density in PSO, and accordingly, we discuss the relationship between the search capability of PSO and the population density. From related numerical experiments, we find that the search capability of PSO becomes saturated when the population density exceeds a certain value. Accordingly, we propose a strategy that divides the particles into two parts for different functions. Thus, we propose an approach called multi-function global particle swarm optimization (MFPSO) on the basis of this strategy. Further, we carry out a series of numerical experiments to verify that MFPSO has high global convergence capability, high convergence speed, and highly reliable performance when it is used to solve complex problems. [ABSTRACT FROM AUTHOR]

In this paper, numerical methods to compute the Karcher means on the n -order rotation group SO( n ) are considered. First, after recalling Karcher means as solutions of a kind of minimization problems on SO( n ), a super-linearly convergent numerical method, namely conjugate gradient method, has been used to deal with them. By the geometric structure of SO( n ), the proposed algorithm is structure preserving. Then, a variety of numerical experiments are presented to demonstrate the performance and efficiency of the proposed algorithm by comparing with a recent structure preserving method. [ABSTRACT FROM AUTHOR]

In this paper, we derive a high order numerical scheme for variable order fractional ordinary differential equation by establishing a second order numerical approximation to variable order Riemann–Liouville fractional derivative. The scheme is strictly proved to be stable and convergent with second order accuracy, which is higher than some recently derived schemes. Finally, some numerical examples are presented to demonstrate the theoretical analysis and verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified Newton–Traub composition with increasing order of convergence for solving systems of nonlinear equations. The idea is based on the recent development by Sharma et al. (2015). Analysis of convergence shows that the presented method has sixth order of convergence. Computational efficiency of the new method is considered and compared with some well-known existing methods. Numerical tests are performed on some problems of different nature, which confirm robust and efficient convergence behavior of the proposed method. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems. The basins of attraction of existing methods and the presented method are given to demonstrate their performance. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze a unified model of two-step iterative method for solving a system of nonlinear equations. We prove that the unified model achieves fourth order convergence. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods. From the comparison with some known methods it is observed that the present methods are of practical utility. [ABSTRACT FROM AUTHOR]

In this paper, we propose a partitioned PSB method for solving partially separable unconstrained optimization problems. By using a projection technique, we construct a sufficient descent direction. Under appropriate conditions, we show that the partitioned PSB method with projected direction is globally and superlinearly convergent for uniformly convex problems. In particular, the unit step length is accepted after finitely many iterations. Finally, some numerical results are presented, which show that the partitioned PSB method is effective and competitive. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new global optimization method and study its global convergence property through theoretical and experimental approaches. The proposed method is named as multivariant optimization algorithm (MOA) because the intelligent searchers, which are called as atoms, not only are divided into multiple subgroups but also are variant in responsibility. That is, global atoms explore the whole solution space in the hope of finding potential areas where local atoms start the local exploitation. The proposed method is characterized by two important features. On one hand, global atoms do the global exploration in each loop to jump out from local traps. On the other hand, global and local atoms conduct the global exploration and the local exploitation according to their own responsibility, respectively. These features contribute to increasing the chance of converging to the global best. To study the convergence property of MOA, we carried out the convergence analysis, numerical optimization experiments and the shortest path planning experiments. And the results demonstrate that MOA is globally convergent and superior to the compared methods in the global convergence accuracy and probability in solving complex challenging problems which have one or more features such as deceptiveness, randomly located optimum, asymmetry or multiple traps. [ABSTRACT FROM AUTHOR]

In this paper, a fractional order variational model for estimating the optical flow is presented. In particular, the proposed model generalizes the integer order variational optical flow models. The fractional order derivative describes discontinuous information about texture and edges, and therefore a more suitable in estimating the optical flow. The proposed variational functional is a combination of a global model of Horn and Schunck and the classical model of Nagel and Enkelmann. This formulation yields a dense flow and preserves discontinuities in the flow field and also provides a significant robustness against outliers. The Grünwald–Letnikov derivative is used for solving complex fractional order partial differential equations. The corresponding linear system of equations is solved by an efficient numerical scheme. A detailed stability and convergence analysis is given in order to show the mathematical applicability of the numerical algorithm. Experimental results on various datasets verify the validity of the proposed model. [ABSTRACT FROM AUTHOR]

The problem of consistency of smoothed particle hydrodynamics (SPH) has demanded considerable attention in the past few years due to the ever increasing number of applications of the method in many areas of science and engineering. A loss of consistency leads to an inevitable loss of approximation accuracy. In this paper, we revisit the issue of SPH kernel and particle consistency and demonstrate that SPH has a limiting second-order convergence rate. Numerical experiments with suitably chosen test functions validate this conclusion. In particular, we find that when using the root mean square error as a model evaluation statistics, well-known corrective SPH schemes, which were thought to converge to second, or even higher order, are actually first-order accurate, or at best close to second order. We also find that observing the joint limit when N → ∞ , h → 0 , and n → ∞ , as was recently proposed by Zhu et al., where N is the total number of particles, h is the smoothing length, and n is the number of neighbor particles, standard SPH restores full C 0 particle consistency for both the estimates of the function and its derivatives and becomes insensitive to particle disorder. [ABSTRACT FROM AUTHOR]

It is well-known that one-step methods have order reduction if they are applied on stiff ODEs such as the example of Prothero–Robinson. In this paper we analyse the local error of Runge–Kutta and Rosenbrock–Wanner methods. We derive new order conditions and define with them B P R -consistency. We show that for strongly A -stable methods B P R -consistency implies B P R -convergence. Finally we analyse methods from literature, derive new B P R -consistent methods and present numerical examples. The numerical and analytical results show the influence of different properties of the methods and of different order conditions on the numerical error and on the numerical convergence order. [ABSTRACT FROM AUTHOR]

In this paper, a modified two-grid decoupling method for the mixed Navier–Stokes/Darcy model is proposed and analyzed. The solution on interface condition is approximated by the solution obtained on the fine grid. Stability and convergence of the method are proved. The convergence rate for the L 2 -norm of ∇ u and p is improved from O ( H 3 2 ) to O ( H 2 ) . The numerical results are consistent with the theoretical results and illustrate that the proposed method is quite efficient. [ABSTRACT FROM AUTHOR]

We present a simple and effective Chebyshev polynomial scheme (CPS) combined with the method of fundamental solutions (MFS) and the equilibrated collocation Trefftz method for the numerical solutions of inhomogeneous elliptic partial differential equations (PDEs). In this paper, CPS is applied in a two-step approach. First, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then the resulting homogeneous equation is solved by boundary type methods including the MFS and the equilibrated collocation Trefftz method. Numerical results for problems on various irregular domains show that our proposed scheme is highly accurate and efficient. [ABSTRACT FROM AUTHOR]

In Bai et al. (2013), a preconditioned modified HSS (PMHSS) method was proposed for a class of two-by-two block systems of linear equations. In this paper, the PMHSS method is modified by adding one more parameter in the iteration. Convergence of the modified PMHSS method is guaranteed. Theoretic analysis and numerical experiment show that the modification improves the PMHSS method. [ABSTRACT FROM AUTHOR]

In this paper, we present spectral methods in order to solve wave equation subject to a locally distributed nonlinear damping. Thanks to the efficiency and the accuracy of spectral method, we can check that discrete energy decreases to zero as time goes to infinity, uniformly with respect to the mesh size when the damping is supported in a suitable subset of the domain of consideration. We prove the convergence of the full Fourier–Galerkin discretization. Thus, we apply our schemes to illustrate the uniform discrete energy decay rates of the solution for a wide range of damping functions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and numerical analysis of solution to highly nonlinear stochastic differential equations with jumps. By the Itô formula, stochastic inequality and semi-martingale convergence theorem, we study the asymptotic stability in the p th moment and almost sure exponential stability of solutions under the local Lipschitz condition and nonlinear growth condition. On the other hand, we also show the convergence in probability of numerical schemes under nonlinear growth condition. Finally, an example is provided to illustrate the theory. [ABSTRACT FROM AUTHOR]

In this note we describe a strategy that improves the a priori error bounds for augmented mixed methods under appropriate hypotheses. This means that we can derive a priori error estimates for each one of the involved unknowns. Usually, the standard a priori error estimate is for the total error. Finally, a numerical example is included, that illustrates the theoretical results proven in this paper. [ABSTRACT FROM AUTHOR]

We develop an a posteriori error analysis for Helmholtz problem using the local discontinuous Galerkin (LDG for short) approach. For the sake of completeness, we give a description of the main a priori results of this method. Indeed, under some assumptions on regularity of the solution of an adjoint problem, we prove that: (a) the corresponding indefinite discrete scheme is well posed; (b) the approach is convergent, with the expected convergence rates as long as the meshsize h is small enough. We give precise information on how small h has to be in terms of the size of the wave number and its distance to the set of eigenvalues for the same boundary value problem for the Laplacian. After that, we present a reliable and efficient a posteriori error estimator with detailed information on the dependence of the constants on the wave number. We finish presenting extensive numerical experiments which illustrate the theoretical results proven in this paper and suggest that stability and convergence may occur under less restrictive assumptions than those taken in the present work. [ABSTRACT FROM AUTHOR]

In this paper, a series of new high-order numerical approximations to α th ( 0 < α < 1 ) order Caputo derivative is constructed by using r th degree interpolation approximation for the integral function, where r ≥ 4 is a positive integer. As a result, the new formulas can be viewed as the extensions of the existing jobs (Cao et al., 2015; Li et al., 2014), the convergence orders are O ( τ r + 1 − α ) , where τ is the time stepsize. Two test examples are given to demonstrate the efficiency of these schemes. Then we adopt the derived schemes to solve the Caputo type advection–diffusion equation with Dirichlet boundary conditions. The local truncation error of the derived difference scheme is O ( τ r + 1 − α + h 2 ) , where τ is the time stepsize, and h the space one. The stability and convergence of the proposed schemes for r = 4 are also considered. Without loss of generality, we only display the numerical examples for r = 4 , 5 , which support the numerical algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a numerical scheme based on the element-free Galerkin (EFG) method is proposed to find the numerical solutions of nonlinear sine-Gordon equation with Neumann boundary condition and generalized sinh-Gordon equation with Dirichlet boundary condition. In this scheme, a time stepping technique is used to approximate the time derivative terms of the given equations. Then, the penalty method is adopted to enforce the Dirichlet boundary condition and lastly, the EFG method is performed to establish the system of discrete equations. The convergence of the proposed scheme is derived theoretically and verified numerically by doing its error analysis. Numerical examples involving line and ring solitons are given to show the accuracy and efficiency of the scheme. The numerical results are in excellent agreement with the analytical solutions and/or previously reported numerical results. [ABSTRACT FROM AUTHOR]

The neutron transport equation in the integral form is of difficult solution and therefore, schemes for obtaining an equivalent differential formulation are used. In this paper is used the discrete ordinates method (S N method) in order to obtain the equivalent differential formulation. Inspired in the GLS method (Galerkin least square method) a variant of the GLS (Brooks and Hughes, 1982; Ern and Guermond, 2004; Johnson, 1990) method denoted GpLS (Galerkin partial least-square) is proposed for solving this equivalent differential formulation. The convergence rates as well as the robustness of GLS method are preserved by the GpLS method that possesses computational lower cost. Simulations comparing the convergence rates of GpLS method with other methods are presented, confirming the best performance of GpLS method. The numerical experiments were made using fixed source in multiplying medium, with the objective to test the robustness of GpLS method. All the numerical experiments presented confirm the good properties of approximation of GpLS method. [ABSTRACT FROM AUTHOR]

This paper deals with two new recursive numerical schemes for the solution of a class of doubly singular two-point boundary value problems with different types of boundary conditions. We first transform the original problem into an equivalent integral equation to overcome the singular behaviour at the origin and then establish recursive schemes by employing Homotopy perturbation method for the solution of the resultant equation. We establish the convergence results of the new numerical methods. Four numerical examples are considered to demonstrate the efficiency and accuracy of the proposed methods. The present methods are shown their advantage over some existing methods (Chawla and Katti, 1982; Pandey and Singh, 2007; Pandey and Singh, 2004; Caglar et al., 2009; Kumar and Aziz, 2004; Khuri and Sayfy, 2010) developed for the solution of singular two-point boundary value problems. Moreover, the new methods are used to obtain the approximate solutions of the singular boundary value problems arising in various physical problems. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive synchronization problem of Lü chaotic systems is investigated by using a novel hybrid controller. The proposed hybrid controller is composed of a single controller and impulsive controller. Using the impulsive theory and the novel hybrid controller, some sufficient conditions are derived for the synchronization of Lü chaotic systems. Numerical simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional single controller method and impulsive controller method. [ABSTRACT FROM AUTHOR]

In this paper, the preconditioned multisplitting USAOR method is established for solving the system of linear equations. The convergence and comparison results of the method are given when the coefficient matrices of the linear systems are H -matrices. The method for H -matrices is proved to be more efficient than the multisplitting USAOR method for M -matrices. Finally, a numerical example is given to illustrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

In this paper, we study the inviscid limit of the 3D chemotaxis-Navier–Stokes equations and establish the convergence rate of the inviscid limit for vanishing diffusion. [ABSTRACT FROM AUTHOR]

In this paper, a new mixed finite element scheme is proposed for the nonlinear Sobolev equation by employing the finite element pair Q 11 / Q 01 × Q 10 . Based on the combination of interpolation and projection skill as well as the mean-value technique, the τ -independent superclose results of the original variable u in H 1 -norm and the variable q → = − ( a ( u ) ∇ u t + b ( u ) ∇ u ) in L 2 -norm are deduced for the semi-discrete and linearized fully-discrete systems ( τ is the temporal partition parameter). What’s more, the new interpolated postprocessing operators are put forward and the corresponding global superconvergence results are obtained unconditionally, while previous literature always require certain time step conditions. Finally, some numerical results are provided to confirm our theoretical analysis, and show the efficiency of the method. [ABSTRACT FROM AUTHOR]

In order to solve large sparse saddle point problems (SPP) quickly and efficiently, Wang and Zhang recently studied the preconditioned accelerated Hermitian and skew-Hermitian splitting (PAHSS) methods. Through accelerating the PAHSS iteration algorithms by using parameterized Uzawa (PU) method, a preconditioned AHSS-PU alternating splitting iterative method (PAHSS-PU method) for solving saddle point problems is proposed in this paper. The convergence results of this new method are given under some suitable conditions. Moreover, we can obtain that if the parameters are suitable selected, then the PAHSS-PU algorithm will outperform the PAHSS algorithm and some Uzawa-type methods in the same precision condition. Numerical experiments are presented to illustrate the theoretical results and examine the numerical effectiveness of the PAHSS-PU method. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper we show that some of the methods presented in Neta et al. (2014) do not possess optimal eighth order of convergence. Such methods are especially those obtained by Hermite interpolation. One of the two methods based on Jarratt’s optimal fourth order method possesses the convergence of seventh order whereas the other possesses fourth order. The methods based on King’s and Ostrowski’s optimal fourth order methods have convergence order six. The theoretical results are also verified through numerical example. [ABSTRACT FROM AUTHOR]

In this paper, multiscale Galerkin method is presented to approximate the solutions of second-order boundary value problems of Fredholm integro-differential equation. The method is based on traditional Galerkin method and uses the multiscale orthonormal bases to discretize the equations. The proposed method is proved to be stable and have the optimal convergence order. Numerical examples are presented to confirm the theoretical results and show that the method is computationally stable, valid and accurate. [ABSTRACT FROM AUTHOR]

This paper proposes a new method for estimating the parameters of an autoregressive (AR) signal from observations corrupted by white noise. The feature of the new method is that the observation noise variance estimate is converted into the only solution of a nonlinear equation to yield unbiased estimate of the AR parameters. Moreover, a convergent Newton iterative algorithm with a deterministic initial point is presented for efficient implementation of the proposed new estimation method. As a result, the proposed new method can minimize the error of estimating the variance of the observation noise. Since more accurate estimates of this observation noise variance can be attained at earlier stages, the proposed method can achieve a good performance in estimating the AR signal parameters. Numerical results demonstrate that the proposed new algorithm is more effective in terms of accuracy and robustness against noise than conventional algorithms. [ABSTRACT FROM AUTHOR]

In this paper, mean-square convergence and mean-square stability of θ -Maruyama methods are studied for nonlinear stochastic differential delay equations (SDDEs) with variable lag. Under global Lipschitz conditions, the methods are proved to be mean-square convergent with order 1 2 , and exponential mean-square stability of SDDEs implies that of the methods for sufficiently small step size h > 0 . Further, the exponential mean-square stability properties of SDDEs and those of numerical methods are investigated under some non-global Lipschitz conditions on the drift term. It is shown in this setting that the θ -Maruyama method with θ = 1 can preserve the exponential mean-square stability for any step size. Additionally, the θ -Maruyama method with 1 2 ≤ θ ≤ 1 is asymptotically mean-square stable for any step size, provided that the underlying system with constant lag is exponentially mean-square stable. Applications of this work to some special problem classes show that the results are deeper or sharper than those in the literature. Finally, numerical experiments are included to demonstrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are collected using a microwave scattering facility which was built at the University of North Carolina at Charlotte. Our imaging problem is formulated as the inverse problem of the reconstruction of the spatially distributed dielectric constant ε r ( x ) , x ∈ R 3 , which is an unknown coefficient in Maxwell’s equations. On the first stage the globally convergent method of Beilina and Klibanov (2012) is applied to get a good first approximation for the exact solution. Results of this stage were presented in Thành et al. (2014). On the second stage the locally convergent adaptive finite element method of Beilina (2011) is applied to refine the solution obtained on the first stage. The two-stage numerical procedure results in accurate imaging of all three components of interest of targets: shapes, locations and refractive indices. In this paper we briefly describe methods and present new reconstruction results for both stages. [ABSTRACT FROM AUTHOR]

In this paper, a semilinear parabolic problem with an unknown time-dependent source function p ( t ) is studied. This missing parameter is reconstructed from a given measurement of the total energy/mass in the domain. The existence and uniqueness of a solution in suitable function spaces is established under minimal regularity assumptions on the data. A numerical time-discrete scheme to approximate the unique weak solution and the unknown source parameter is designed and convergence of the approximations is proved. Finally, the theoretically obtained results are supported by a numerical experiment. [ABSTRACT FROM AUTHOR]

Fixed point iterations are still the most common approach to dealing with a variety of numerical problems such as coupled problems (multi-physics, domain decomposition, …) or nonlinear problems (electronic structure, heat transfer, nonlinear mechanics, …). Methods to accelerate fixed point iteration convergence or more generally sequence convergence have been extensively studied since the 1960’s. For scalar sequences, the most popular and efficient acceleration method remains the Δ 2 of Aitken. Various vector acceleration algorithms are available in the literature, which often aim at being multi-dimensional generalizations of the Δ 2 method. In this paper, we propose and analyse a generic residual-based formulation for accelerating vector sequences. The question of the dynamic use of this residual-based transformation during the fixed point iterations for obtaining a new accelerated fixed point method is then raised. We show that two main classes of such iterative algorithms can be derived and that this approach is generic in that various existing acceleration algorithms for vector sequences are thereby recovered. In order to illustrate the interest of such algorithms, we apply them in the field of nonlinear mechanics on a simplified “point-wise” solver used to perform mechanical behaviour unit testings. The proposed test cases clearly demonstrate that accelerated fixed point iterations based on the elastic operator (quasi-Newton method) are very useful when the mechanical behaviour does not provide the so-called consistent tangent operator. Moreover, such accelerated algorithms also prove to be competitive with respect to the standard Newton–Raphson algorithm when available. [ABSTRACT FROM AUTHOR]

The Kaczmarz method is an iterative method for solving overcomplete linear systems of equations A x = b . The randomized version of the Kaczmarz method put forth by Strohmer and Vershynin iteratively projects onto a randomly chosen solution space given by a single row of the matrix A and converges linearly 1 in expectation to the solution of a consistent system. In this paper we analyze two block versions of the method each with a randomized projection, designed to converge in expectation to the least squares solution, often faster than the standard variants. Our approach utilizes both a row and column-paving of the matrix A to guarantee linear convergence when the matrix has consistent row norms (called nearly standardized), and a single column-paving when the row norms are unbounded. The proposed methods are an extension of the block Kaczmarz method analyzed by Needell and Tropp and the Randomized Extended Kaczmarz method of Zouzias and Freris. The contribution is thus two-fold; unlike the standard Kaczmarz method, our results demonstrate convergence to the least squares solution of inconsistent systems (both methods in the nearly standardized case and the second method in other cases). By using appropriate blocks of the matrix this convergence can be significantly accelerated, as is demonstrated by numerical experiments. [ABSTRACT FROM AUTHOR]

Vibro-acoustic analysis of a rail vehicle cabin is presented in this paper. Vehicle is modeled by an air cavity coupled to a flexible floor panel. Analytical procedure is employed to predict the structural-borne noise in the vehicle model generated by random excitation of the panel. In this study, natural frequencies of the coupled system are obtained and then the sound pressure field inside the cavity is analytically determined. In order to find dynamic responses of the coupled system in the time domain, Durbin's numerical Laplace transform inversion algorithm is employed. Convergence of the algorithm is verified and eventually a parametric study is carried out to investigate the effects of rail irregularity and vehicle speed on the time and frequency responses. [ABSTRACT FROM AUTHOR]

The paper is concerned with the exponential convergence for a class of shunting inhibitory cellular neural networks with oscillating coefficients in leakage terms. By employing the differential inequality techniques, we establish a novel result to ensure that all solutions of the addressed system converge exponentially to zero vector. Our approach handles particular cases which were not considered in some early relevant results. An example along with its numerical simulation is presented to demonstrate the validity of the proposed result. [ABSTRACT FROM AUTHOR]

Analytical solutions for tunnel design are widely used in practical engineering, as they allow a quick analysis of design issues such as estimation of support requirement. In recent years, several papers analyzing the behavior of rock masses that obey the conventional or generalized Hoek–Brown criterion have been published. This article presents a complementary analysis that includes a new normalization of the generalized Hoek–Brown failure criterion, complete solutions for associated and non-associated flow rules, with some new closed-form solutions in the latter case, and in-depth considerations regarding intermediate stresses and edge effects. The results obtained show full agreement with existing solutions in the literature, when possible, and with numerical finite element models in cases that had not been treated previously. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a discretized version of an elliptic optimal control problem which is presented by Stadler (2009). An alternating direction method is proposed to solve this problem and demonstrated as globally convergent. This class of methods is attractive due to its simplicity and thus is adequate for solving large-scale problems. The preliminary numerical results present the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]