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Abstract This paper was dealt with buckling and post-buckling behavior of short thin-walled Z-columns made of a carbon-epoxy laminate, subjected to eccentric compressive load. The buckling mode and the buckling load of real structures versus load eccentricity were discussed. The study involved both experimental tests were carried out on real laminated structures and numerical simulations by the finite element method. The buckling load of real structures was determined by approximation methods on the basis of experimental and numerical post-buckling equilibrium paths of the structure. Additionally, in numerical simulations, the bifurcation load value was determined by solving an eigen problem. In all cases, experimental findings and numerical results show high agreement. The study determined the quantitative influence of the direction and value of compressive load eccentricity on the buckling load and rigidity of the structure in the post-buckling state. [ABSTRACT FROM AUTHOR]

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to propose a new three-node triangular element in the framework of the numerical manifold method (NMM), which is designated by Trig3-MLScns.Design/methodology/approach The formulation uses the improved parametric shape functions of classical triangular elements (Trig3-0) to construct the partition of unity (PU) and the moving least square (MLS) interpolation method to construct the local approximation function.Findings Compared with the classical three-node element (Trig3-0), the Trig3-MLScns element has a higher order of approximations, much better accuracy and continuous nodal stress. Moreover, the linear dependence problem associated with many PU-based methods with high-order approximations is eliminated in the present element. A number of numerical examples indicate the high accuracy and robustness of the Trig3-MLScns element.Originality/value The proposed element inherits the individual merits of the NMM and the MLS. [ABSTRACT FROM AUTHOR]

In this paper, we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numerical results to assess the validity of the theoretical estimates. [ABSTRACT FROM AUTHOR]

In this paper a method based on Sinc approximation is developed for the numerical solution of a nonlinear fractional pantograph equation. In order to use Sinc approximation, the problem needs to have an analytic solution. So we investigated the existence and uniqueness of analytic solutions in the proposed domain. Single and double exponential transformations are used to approximate the solution. Some test problems are given to demonstrate the efficiency and applicability of the methods. The results are compared with some other existing numerical methods to show the performance and good accuracy of the methods. The numerical orders of convergence show that the method has exponential rate of convergence. [ABSTRACT FROM AUTHOR]

Although numerical methods of nonlinear stochastic differential delay equations (SDDEs) have been discussed by several authors, there is so far little work on the numerical approximation of SDDE with coefficients of polynomial growth. The main aim of the paper is to investigate convergence in probability of the Euler-Maruyama (EM) approximate solution for SDDE with one-sided polynomial growing drift coefficient and polynomial growing diffusion coefficient. Moreover, we prove the existence-and-uniqueness of almost surely exponentially stable global solution for this nonlinear stochastic delay system. Finally, a computer simulation confirms the efficiency of our numerical method. [ABSTRACT FROM AUTHOR]

Coupling multiphysical systems by means of a co-simulation, the data between the subsystems are interchanged at a discrete macro time grid, also denoted as communication time grid. Between the communication points the coupling variables are approximated so that the numerical solvers in the subsystems can calculate the differential equations. Classical approximation techniques based on extrapolation entail a discontinuity in the equations in each macro time step which can slow down the numerical time integration. In the paper at hand a C0-continuous technique for approximating the coupling variables is reconsidered and the numerical stability and the local error of the method are compared to the classical Lagrange approximation approach. Further, the method is enhanced to a C1-continuous (continuous and differentiable) approximation technique. Both methods are investigated in combination with different numerical coupling approaches (sequential Gauss-Seidel scheme, parallel Jacobi scheme, force/displacement coupling, displacement/displacement coupling) which are commonly applied for co-simulation in technical applications. It is shown that the C1-continuous approximation technique yields a similar numerical stability and a similar local error as the Lagrange approach which results in a comparable or even better overall performance (taking into account the advantage of continuity at the numerical calculation of the subsystem differential equations). Applying the C0-continuous approach, a similar numerical stability is obtained. However, the order of the local error is significantly lower than for the C1-continuous method and the Lagrange approach. [ABSTRACT FROM AUTHOR]

This paper demonstrates the capability of our previously published undoped Double-Gate (DG) MOSFET explicit and analytical compact model to also forecast the effect of the volume inversion (VI) on the intrinsic capacitances. For that purpose, we present simulation results for these capacitances. We show now that the model presents an accurate dependence on the silicon layer thickness, consistent with two-dimensional numerical simulations, for both thin and thick silicon films. As opposed to our previous work, here we test the capacitance model for three different film thicknesses and also show that the transition from VI regime to dual gate behaviour is well simulated. We demonstrate in this paper that even if the current drive and transconductance are enhanced in VI regime, our results show that intrinsic capacitances are higher as well, which may limit the high-speed (delay time) behaviour of DG MOSFETs under VI regime. The good agreement between the numerical simulations and our model shows the high potential of our complete DG MOSFET model. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Numerical ocean modelling is computationally very demanding. Traditionally, the hydrostatic approximation has been applied to reduce the computational burden. This approximation is valid in large scale studies with coarse grid resolution. With faster computers and gradually smaller grid sizes, we may expect that more studies will be performed with non-hydrostatic ocean models. In recent papers several methods for including non-hydrostatic pressure in σ-coordinate models have been suggested. In this paper the sensitivity of the non-hydrostatic pressure field, the velocity fields, and the density fields to changes in the method for computing non-hydrostatic pressure in σ-coordinate ocean models is addressed. The first test case used involves the propagation and breaking of an internal wave at an incline in a tank. The other test case concerns tidally driven flow over a sill in a stratified fjord. The results from our numerical exercises suggest that the velocity and density fields are very robust to the model choices investigated here. The differences between the model results are of the same order as the uncertainty due to the internal pressure gradient error, and they are smaller than an estimate of the uncertainty due to subgrid scale closure. [Copyright &y& Elsevier]

SUMMARY The multiport scattering (S-) parameter matrix is increasingly utilized to compose models of large bit-width interconnect systems with broadband characteristics (frequency range of zero to tens of gigahertz) to perform increasingly accurate signal-integrity and power-integrity simulations. The search for an optimal solution space often requires generation of S-parameter models of interconnect systems for various signal/ground pin mappings, a process that can be computationally costly if the structure is electromagnetically solved for each distinct pin mapping. To expedite this model-generation process, we propose a method in which an N-port structure is electromagnetically solved only once to yield an N × N S-matrix; then, a linear system is formulated and solved to yield an ( N − M) × ( N − M) post-suppressed S-matrix (where M is the number of suppressed ports). This approach results in significant computational savings through elimination of electromagnetic field-solver runs for each distinct pin mapping. Included in this paper is a discussion about the limitations of this technique and several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we propose a numerical procedure for the prediction of capillary forces in polydisperse granular assemblies at a degree of moisture content that corresponds to the so-called pendular regime. The capillary force model is adopted within the Laplace-Young framework with a toroidal approximation of the liquid bridge geometry. Governing equations are first derived in a form that highlights the role of intrinsic parameters such as inter-particle separation distance, ratio of particle radii and liquid volume. A proper scaling of these equations is adopted so that the solution applies to any particle pair configuration. Numerical integration algorithms are provided in a way that facilitates implementations in macroscopic procedures for computer simulations. A qualitative evaluation is undertaken to highlight model predictions of the effects on capillary force of various intrinsic parameters that characterise the particle pair and liquid bridge. The model is validated against the experimental results provided by Willet et al. (Langmuir 16:9396-9405, ) for a wide range of liquid volumes and particle-pair polydispersity. [ABSTRACT FROM AUTHOR]

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures. [ABSTRACT FROM AUTHOR]

Abstract: A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the density and velocity orientation. Short-range repulsion is included through a singular pressure which becomes infinite at the jamming density. The singular limit of infinite pressure stiffness leads to phase transitions from compressible to incompressible dynamics. The paper proposes an Asymptotic-Preserving scheme which takes care of the singular pressure while preventing the breakdown of the Courant–Friedrichs–Lewy (CFL) stability condition near congestion. It relies on a relaxation approximation of the system and an elliptic formulation of the pressure equation. Numerical simulations of impinging clusters show the efficiency of the scheme to treat congestions. A two-fluid variant of the model provides a model of path formation in crowds. [Copyright &y& Elsevier]

Abstract: Various ad hoc methods have been proposed for solving population balance equations (PBEs). Relatively little discussion has taken place to generalize these discretization approaches. In this paper, a flexible method is presented for the discrete solution of PBEs. The method is a generalization of similar techniques. The approach allows for complete control of the discretization and order of approximation of the solution. A simple error analysis of the method is provided. Simulations were performed for pure random breakage, constant kernel aggregation, additive kernel aggregation, combined random breakage/constant kernel aggregation, and free-molecular Brownian coagulation. The numerical results are compared to exact solutions and simulated results from the literature. It was found that increasing the quadrature order within the sections is a more efficient means to increase accuracy as opposed to finer discretization. [Copyright &y& Elsevier]

Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors. [Copyright &y& Elsevier]

Abstract: In this paper we revisit a strain-adaptive bone remodelling problem, assuming that the rate of the apparent density at a particular location is described as a local objective function and depending on a particular stimulus at that location. Normally, continuum mathematical descriptions of adaptive bone remodelling can lead to discontinuous solutions on the global apparent density distribution. To improve this numerical solution, in this work, as the main novelty, we include the diffusion of the bone remodelling into the model. The variational problem is written as a coupled system of a nonlinear variational equation for the displacement field and a parabolic elliptic variational inequality for the apparent density. An existence and uniqueness result is stated. Then, a fully discrete problem is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. A priori error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is deduced. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation and the behaviour of the solution. [Copyright &y& Elsevier]

In this work, the adhesive contact between a slightly wavy surface and a half-space has been investigated numerically. The surface traction was described by the Lennard-Jones potential with the Derjaguin's approximation. The deformation was first obtained by using the formula for the line contact and then, using the arc-length continuation algorithm, the relation between the contact half-width and the total force per asperity was obtained. The pull-off forces were then determined. The numerical simulation presented in this paper can be used to simulate all adhesive contacts ranging from the JKR contact to a rigid contact. [ABSTRACT FROM AUTHOR]

Abstract: Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell’s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart–Thomas–Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l 2 norm achieved for the lowest-order Raviart–Thomas–Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. [Copyright &y& Elsevier]

Abstract: This paper presents a theoretical analysis of possible jitter impact in application of numeric criterion for fast measurement of frequency by coincidence principle. The primary goal is the generation of a signal containing a known amount of each jitter components. This signal was used for testing signals with regular pulse trains. Initially, jitter components are analyzed and modeled individually. Next, sequences for combining different kinds of jitter are modeled, simulated and evaluated. Jitter model simulation in Matlab is utilized to show the independence of frequency measurement results on the total jitter present in the reference and desired pulse trains independently. A good agreement between previously introduced theory of fast measurement of frequency and simulation in jitter presence is verified; these results allows to engineers use the numeric criterion for fast measurement of frequency in spite to interactions among jitter components in various applications for frequency domain sensors. [Copyright &y& Elsevier]

Abstract: In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a nonconservative form of the two-dimensional shallow water equations, in eight velocity formulation and we build a numerical approximation, based on the Arbitrary lagrangian eulerian formulation, in order to compute the solution in the moving domain. [Copyright &y& Elsevier]

In this paper, we derive an algorithm to solve the linear quadratic (LQ) optimal regulator problems. The new approach is based on efficient Legendre and Chebyshev formulae at the Chebyshev-Gauss-Lobatto points. The technique enjoys advantages of both the Legendre and Chebyshev approximations near the end points. To show the numerical behavior of the proposed method, the simulation results of an example are presented. [ABSTRACT FROM AUTHOR]

We study the waiting-time distributions in cyclic polling models with renewal arrivals, general service and switch-over times, and exhaustive service at each of the queues. The assumption of renewal arrivals prohibits an exact analysis and reduces the available analytic results to heavy-traffic asymptotics, limiting results for large switch-over times and large numbers of queues, and some numerical algorithms. Motivated by this, the goal of this paper is to propose a new method for deriving simple closed-form approximations for the complete waiting-time distributions that work well for arbitrary load values. Extensive simulation results show that the approximations are highly accurate over a wide range of parameter settings. [ABSTRACT FROM AUTHOR]

Abstract: For the mechanical characterization of structural materials non-destructive tests combined with computer simulations and inverse analyses are more and more frequently and advantageously employed in various engineering fields. The contribution to such development presented in this paper can be outlined as follows. With reference to isotropic elastic–plastic material models, indentation test simulations are done preliminarily, once-for-all, by a conventional finite element forward operator. Results of these simulations are employed in a procedure which is centered on Proper Orthogonal Decomposition and Radial Basis Functions approximation and is used for fast interpolations which replace further finite element analyses in the parameter identification process. Comparative computational exercises are presented in order to point out the consequent significant reduction of computing times in test simulations and, hence, in the minimization of the discrepancy function by the Trust Region Algorithm, namely by a traditional first-order mathematical programming method. Such a parameter identification procedure may be carried out routinely and economically on small computers for in situ structural diagnoses. Both the force–penetration relationship (provided by an instrumented indenter) and the average imprint profile (achievable by laser profilometer) are considered as sources of measurable response quantities or experimental data. [Copyright &y& Elsevier]

Abstract: Computer modeling of radiation deep penetration problems is historically based on the discrete ordinates (S N) formulation. For efficiency reasons, besides accuracy, coarse-mesh spatial discretization is desirable. The spectral Green''s function (SGF) methods form a class of accurate coarse-mesh numerical methods as they use polynomial approximations only for the node-edge transverse leakage terms; the scattering source terms are treated analytically in the numerical algorithm. Therefore, algebraic work and the computational algorithms of the spectral nodal methods are rather complicated. To alleviate this negative feature, we offer in this paper a composite spatial grid SGF nodal method for the numerical solution of one-speed deep penetration S N problems with isotropic scattering in X,Y geometry. This method uses a rectangular coarse spatial grid, that is coincident with the material region distribution within the shielding structure. We first transverse integrate the S N equations separately in the x- and y-coordinate directions inside each material region, and then we introduce flat approximations for the transverse leakage terms. Furthermore, we use a fine spatial grid to discretize each set of “one-dimensional”S N nodal equations. As the spatial directions are coupled by the transverse leakage terms, we use an explicit alternate direction technique to converge the numerical solution. In order to verify the offered method''s accuracy, we present numerical results for typical model problems. Moreover, we compare the computing performance of this method with the conventional SGF-constant nodal method. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study and identify suitable outflow boundary conditions for the numerical simulation of viscous supersonic/hypersonic flow over blunt bodies, governed by the compressible Navier–Stokes equations, with an emphasis motivated primarily by the use of spectral methods without any filtering. The subsonic/supersonic composition of the outflow boundary requires a dual boundary treatment for well-posedness. All compatibility relations, modified to undertake the hyperbolic/parabolic behaviour of the governing equations, are used for the supersonic part of the outflow. Regarding the unknown downstream information in the subsonic region, different subsonic outflow conditions in the sense of the viscous blunt-body problem are examined. A verification procedure is conducted to make out the distinctive effect of each outflow condition on the solution. Detailed comparisons are performed to examine the accuracy and performance of the outflow conditions considered for two model geometries of different surface curvature variations. Numerical simulations indicate a noticeable influence of pressure from subsonic portion to supersonic portion of the boundary layer. It is demonstrated that two approaches for imposing subsonic outflow conditions namely (1) extrapolating all flow variables and (2) extrapolation of pressure along with using proper compatibility relations are more suitable than the others for accurate numerical simulation of viscous high-speed flows over blunt bodies using spectral collocation methods. [Copyright &y& Elsevier]

In this paper, we present a reliable algorithm to study the well-known model of nonlinear dispersive waves proposed by Boussinesq. We solve the Cauchy problem of Boussinesq equation using variational iteration method (VIM). The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that VIM is a powerful mathematical tool for solving nonlinear problems. [ABSTRACT FROM AUTHOR]

BCJR algorithm is an exact and efficient algorithm to compute the marginal posterior distributions of state variables and pairs of consecutive state variables of a trellis structure. Due to its overwhelming complexity, reduced complexity variations, such as the M-BCJR algorithm, have been developed. In this paper, we propose improvements upon the conventional M-BCJR algorithm based on modified active state selection criteria. We pro- pose selecting the active states based on estimates of the fixed-lag smoothed distributions of the state variables. We also present Gaussian approximation techniques for the low-complexity estimation of these fixed-lag smoothed distributions. The improved performance over the M-BCJR algorithm is shown via computer simulations. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach of-spline curve fitting to a set of ordered points, which is motivated by an insight that properly selected points called dominant points can play an important role in producing better curve approximation. The proposed approach takes four main steps: parameterization, dominant point selection, knot placement, and least-squares minimization. The approach is substantially different from the conventional approaches in knot placement and dominant point selection. In the knot placement, the knots are determined by averaging the parameter values of the dominant points, which basically transforms-spline curve fitting into the problem of dominant point selection. We describe the properties of the knot placement including the property of local modification useful for adaptive curve refinement. We also present an algorithm for dominant point selection based on the adaptive refinement paradigm. The approach adaptively refines a-spline curve by selecting fewer dominant points at flat regions but more at complex regions. For the same number of control points, the proposed approach can generate a-spline curve with less deviation than the conventional approaches. When adopted in error-bounded curve approximation, it can generate a-spline curve with far fewer control points while satisfying the desired shape fidelity. Some experimental results demonstrate its usefulness and quality. [Copyright &y& Elsevier]

The purpose of this paper is to derive a technique for accelerating the computation of cone-beam forward and backward projections that are the basic steps of tomographic reconstruction. The cone-beam geometry of C-arm systems is commonly described with projection matrices. Such matrices provide a continuous framework for analyzing the flow of operations needed to compute backprojection for analytical reconstruction, as well as the combination of forward and backward projections for iterative reconstruction. The proposed rectification technique resamples the original data to planes that are aligned with two of the reconstructed volume main axes, so that the original cone-beam geometry can be replaced by a simpler geometry, where succession of plane magnifications are involved only. Rectification generalizes previous independent results to the cone-beam backprojection of preprocessed data as well as to cone-beam iterative reconstruction. The memory access pattern of simple magnifications provides superior predictability and is, therefore, easier to optimize, independently of the choice of the interpolation technique. Rectification is also shown to provide control over interpolation errors through oversampling, allowing tradeoffs between computation speed and precision to be set. Experimental results are provided for linear and nearest neighbor interpolations, based on simulations, as well as phantom and patient data acquired on a digital C-arm system. [ABSTRACT FROM AUTHOR]

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a "double-self-focusing" synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality. Based on the variational approach, it obtains the approximately analytical solution of such Gaussian elliptical solitons. It also computes the stability of the solitons by numerical simulations. [ABSTRACT FROM AUTHOR]