Adomian decomposition method with Green’s function for sixth-order boundary value problems

In this paper, the Adomian decomposition method with Green’s function is applied to solve linear and nonlinear sixth-order boundary value problems. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.     

Non-linear singular systems using RK–Butcher algorithms

The Runge–Kutta (RK)–Butcher algorithm is used to study time-invariant and time-varying non-linear singular systems. The results (discrete solutions) obtained using the RK method based on the arithmetic mean (RKAM), single-term Walsh series (STWS) and RK–Butcher algorithms are compared with the exact solutions of the non-linear singular systems for the time-invariant and time-varying cases. It is found that the solution obtained using the RK–Butcher algorithm is closer to the exact solutions of the non-linear singular systems. Stability regions for the RKAM, STWS and RK–Butcher algorithms are presented. Error graphs for discrete and exact solutions are presented in a graphical form to highlight the efficiency of this method. The RK–Butcher algorithm can easily be implemented using a digital computer and the solution can be obtained for any length of time for both time-invariant and time-varying cases for these non-linear singular systems, which is an added advantage of this algorithm.     

Partitioned strong coupling algorithms for fluid–structure interaction

Numerical simulation of fluid–structure interaction is often attempted in the context of partitioned methods, where already existing solvers for fluid or structure alone are used jointly. Mostly this is done by exchanging information from time step to time step in an alternating fashion. These weak coupling methods are explicit and hence suffer from possible instabilities. Therefore often strong coupling––where equilibrium is satisfied jointly between fluid and structure in each time step––is desired; the simplest computational procedure is similar to the time stepping an alternating iteration. We show why also this approach may experience difficulties, and how they may be circumvented with block-Newton methods, still in the partitioned framework, by only using the solvers of the subproblems fluid and structure.     

RK–Butcher algorithms for singular system-based electronic circuit

In this paper, a new method of analysis for a singular system-based electronic circuits using the Runge–Kutta (RK)–Butcher algorithm is presented for linear time-invariant and time-varying cases. The discrete solutions obtained using the RK–Butcher algorithms are compared with the exact solutions of the electronic circuit problem and are found to be very accurate. Stability regions for the Single term walsh series method and the RK–Butcher algorithms are presented. Error graphs for inductor currents and capacitor voltages are presented in a graphical form to show the efficiency of this method. This RK–Butcher algorithm can be easily implemented in a digital computer and the solution can be obtained for any length of time.     

Dual–primal proximal point algorithms for extended convex programming

This paper presents a class of dual–primal proximal point algorithms (PPAs) for extended convex programming with linear constraints. By choosing appropriate proximal regularization matrices, the application of the general PPA to the equivalent variational inequality of the extended convex programming with linear constraints can result in easy proximal subproblems. In theory, the sequence generated by the general PPA may fail to converge since the proximal regularization matrix is asymmetric sometimes. So we construct descent directions derived from the solution obtained by the general PPA. Different step lengths and descent directions are chosen with the negligible additional computational load. The global convergence of the new algorithms is proved easily based on the fact that the sequences generated are Fejér monotone. Furthermore, we provide a simple proof for the O(1/t) convergence rate of these algorithms.     

Distributed leaderless consensus algorithms for networked Euler–Lagrange systems

This article proposes and analyses distributed, leaderless, model-independent consensus algorithms for networked Euler–Lagrange systems. We propose a fundamental consensus algorithm, a consensus algorithm accounting for actuator saturation, and a consensus algorithm accounting for unavailability of measurements of generalised coordinate derivatives, for systems modelled by Euler–Lagrange equations. Due to the fact that the closed-loop interconnected Euler–Lagrange equations using these algorithms are non-autonomous, Matrosov's theorem is used for convergence analysis. It is shown that consensus is reached on the generalised coordinates and their derivatives of the networked Euler–Lagrange systems as long as the undirected communication topology is connected. Simulation results show the effectiveness of the proposed algorithms.     

Finite-dimensional recurrent algorithms for optimal nonlinear logical–dynamical filtering

The problem of the most accurate estimation of the current state of a multimode nonlinear dynamic observation system with discrete time based on indirect measurements of this state is considered. The general case when a mode indicator is available and the measurement errors depend on the plant disturbances is investigated. A comparative analysis of two known approaches is performed—the conventional absolutely optimal one based on the use of the posterior probability distribution, which requires the use of an unimplementable infinite-dimensional estimation algorithm, and a finitedimensional optimal approach, which produces the best structure of the difference equation of a low-order filter. More practical equations for the Gaussian approximations of these two optimal filters are obtained and compared. In the case of the absolutely optimal case, such an approximation is finitedimensional, but it differs from the approximation of the finite-dimensional optimal version in terms of its considerably larger dimension and the absence of parameters. The presence of parameters, which can be preliminarily calculated using the Monte-Carlo method, allows the Gaussian finite-dimensional optimal filter to produce more accurate estimates.     

On parallel push–relabel based algorithms for bipartite maximum matching

We study multithreaded push–relabel based algorithms for computing maximum cardinality matching in bipartite graphs. Matching is a fundamental combinatorial problem with applications in a wide variety of problems in science and engineering. We are motivated by its use in the context of sparse linear solvers for computing the maximum transversal of a matrix. Other applications can be found in many fields such as bioinformatics (Azad et al., 2010) [4], scheduling (Timmer and Jess, 1995) [27], and chemical structure analysis (John, 1995) [14]. We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a test set comprised of a wide range of real-world instances.     

Preprocessing for 2D FE–BE domain decomposition methods

The non-overlapping Domain Decomposition (DD) method is a powerful tool for the coupling of Finite Element (FE) and Boundary Element (BE) methods. Moreover it provides a natural basis for constructing efficient parallel solvers. However, both, the efficiency and the robustness of DD–solvers depends heavily on the underlying decomposition of the domain of interest into subdomains. In this paper, we introduce the Adaptive Domain Decomposition Preprocessor ADDPre which realizes an automatic decomposition of the computational domain into p subdomains, where p is the number of processors to be used. We discuss the codes being involved, the algorithms which they are based on and the data–formats being used for describing the decomposition of the problem. Numerical examples, demonstrating the performance of the preprocessor are presented. Received: 20 January 1999 / Accepted: 12 May 1999     

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

In partitioned fluid–structure interaction simulations, the flow equations and the structural equations are solved separately. As a result, a coupling algorithm is needed to enforce the equilibrium on the fluid–structure interface in cases with strong interaction. This coupling algorithm performs coupling iterations between the solver of the flow equations and the solver of the structural equations. Current coupling algorithms couple one flow solver with one structural solver. Here, a new class of multi-solver quasi-Newton coupling algorithms for unsteady fluid–structure interaction simulations is presented. More than one flow solver and more than one structural solver are used for a single simulation. The numerical experiments demonstrate that the duration of a simulation decreases as the number of solvers is increased.     

Optimal controls of multidimensional modified Swift–Hohenberg equation

In this paper, we deal with the optimal control problem governed by multidimensional modified Swift–Hohenberg equation. After showing the relationship between the control problem and its approximation, we derive the optimality conditions for an optimal control of our original problem by using one of the approximate problems.     

Thermodynamic modeling of B–Mo–Nb ternary system with modified B–Nb description

Based on a critical evaluation of the literature data, the B–Mo–Nb ternary system has been assessed by means of the CALPHAD (CALculation of PHAse Diagrams) technique. There is no ternary compound reported in this system. According to their crystal structures, the substitutional solution is adopted to model the ternary liquid, and the sublattice models are used to describe the Mo₂B, αMoB, (Mo,Nb)B, (Mo,Nb)B₂, Mo₂B₅, MoB₄, Nb₃B₂, Nb₅B₆, Nb₃B₄, Nb₂B₃, (Mo,Nb) and (B) phases. The modeling covers the whole composition and temperature ranges. Due to the same crystal structure, the sublattice model of the NbB phase in the B–Nb binary system is adjusted as (Me,Va)_0.5(B,Va)_0.5, in order to be consistent with the βMoB phase in the B–Mo binary system. The obtained thermodynamic parameters of the B–Mo–Nb system are demonstrated to be self-consistent and reasonable by adequately comparing the calculated and reported thermodynamic information and phase diagram. Based on the present thermodynamic parameters, the liquidus projection and reaction scheme of B–Mo–Nb system are presented.     

FPGA implementation of time–frequency analysis algorithms for laser welding monitoring

The on-line monitoring and detection of defects in laser welding is a basic manufacturing requirement in several applicative contexts, as vehicle assembly in automotive production. This work presents the FPGA implementation of time–frequency analysis algorithms as an effective solution compared with pure software implementation based on different modern processors. In particular the proposed FPGA based approach not only satisfies the processing constraints of the considered application, but still offers a high degree of flexibility and modularity.     

Orthonormal Bernoulli polynomials for space–time fractal-fractional modified Benjamin–Bona–Mahony type equations

Engineering with Computers - In this study, a new fractal-fractional (FF) derivative is defined by coupling the local conformable derivative and non-local Caputo fractional derivative. Using the...     

On linear stability of predictor–corrector algorithms for fractional differential equations

This paper deals with the numerical approximation of differential equations of fractional order by means of predictor–corrector algorithms. A linear stability analysis is performed and the stability regions of different methods are compared. Furthermore the effects on stability of multiple corrector iterations are verified.     

A modified predictor-corrector scheme for the Klein–Gordon equation

A numerical method based on a three-time level finite-difference scheme has been proposed for the solution of the two forms of the Klein–Gordon equation. The method, which is analysed for local truncation error and stability, leads to the solution of a nonlinear system. To avoid solving it, a predictor-corrector scheme using as predictor a second-order explicit scheme is proposed. The procedure of the corrector is modified by considering, as known, the already evaluated corrected values instead of the predictor ones. This modified scheme is applied to problems possessing periodic, kinks and soliton waves. The accuracy as well as the long-time behaviour of the proposed scheme is discussed and comparisons with the relevant known in the bibliography schemes are given.     

Real-time 2D–3D filtering using order statistics based algorithms

The paper presents a review of the author’s own results obtained in the last several years. Some examples of real-time processing of 2D and 3D images are described. In particular, we discuss the noise model and objective criteria that can be applied to characterize the performance of the processing algorithms. Several proposed algorithms based on RM approach are compared with other known ones, demonstrating the advantages in noise suppressing and preservation of fine image details and edges. A number of 2D and 3D image denoising filters are implemented on DSP, realizing real-time mode in the image processing. The performances of the proposed processing algorithms and the known ones are discussed and evaluated here.