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This paper presents simple time domain fundamental solutions for the three-dimensional (3D) well known u–p formulation of saturated porous media, neglecting the compressibility of fluid and solid particles. At first, the corresponding boundary integral equations as well as the explicit Laplace transform domain fundamental solutions are obtained in terms of solid displacements and fluid pressure. Subsequently, the closed form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Finally, a set of numerical results are presented which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an improved procedure for imposing displacement boundary conditions in the direct stiffness method of the finite element analysis is presented. The proposed procedure neither changes the original order of the master stiffness matrix, nor does it require the rearrangement of the coefficient matrix. Consequently, it is easy to be implemented. Especially, the condition numbers of coefficient matrices of the improved procedure are remarkably reduced; hence the sensitivity of the solution to perturbations is considerably lowered. Numerical examples are used to demonstrate the validity of the proposed procedure. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The finite-element method (FEM) has become an applicable method to analyse the stress distribution of bioprosthetic valves. However, most of the stress analyses performed in the past have been on bioprosthetic aortic valves. No public reports are available on the numerical simulation of stress analysis for stentless quadrileaflet pericardial mitral valves up to date. This study applied FEM to investigate the mechanical behaviours of a modified stentless quadrileaflet pericardial mitral valve. The finite-element model includes the material non-linearity, large deformation and the contact condition of leaflets. The results showed that the deformed shapes of valve in the numerical simulation are quite similar to ones observed in the hydrodynamic experiment in vitro, the stress distribution is relatively uniform and the magnitudes of stresses are in a reasonable range. It can be concluded that the finite-element model in this paper is reasonable and feasible, and the numerical results can be used to evaluate the biomechanical performance of this valve. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. In this paper, an improved meshless collocation method is presented for use with either moving least square (MLS) or compactly supported radial basis functions (RBFs). A new technique referred to as an indirect derivative method is developed and compared with the direct derivative technique used for evaluation of second-order derivatives and higher-order derivatives of the MLS and RBF shape functions at the field point. As the derivatives are obtained from a local approximation (MLS or compact support RBFs), the new method is computationally economical and efficient. Neither the connectivity of mesh in the domain/boundary nor integrations with fundamental/particular solutions is required in this approach. The accuracy of the two techniques to determine the second-order derivative of shape function is assessed. The applications of meshless method to two-dimensional elastostatic and elastodynamic problems have been presented and comparisons have been made with benchmark analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The present work investigates the efficiency and the accuracy of a multigrid (MG) technique for solving the Navier–Stokes/Boussinesq equations. In order to improve convergence, an accelerated full multigrid (AFMG) method with the iterative red and black successive over-relaxation smoother (RBSOR) is utilized. The AFMG method consists in introducing an accelerated parameter Γ>0 in the standard full multigrid procedure (FMG). A well-known benchmark problem is used to demonstrate the effectiveness and the accuracy of the method. Solutions are compared with those of the literature and show excellent agreement. Results for Prandtl numbers Pr=12.5, 6.8, 0.71 and 0.025 are also presented in this paper. It is observed that the mean heat transfer rate is minimum for Pr=0.71 and maximum for Pr=0.025. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the implementation of Reissner's (J. Appl. Math. Phys. 1972; 23:795–804) strain–displacement relations for a planar beam using a variable order secant matrix (VOSM) technique. The secant matrices are formed using a Taylor expansion of the strain energy and hence the order of the secant and tangent matrices to be included in the nonlinear analysis can be varied depending upon the degree of nonlinearity involved in the problem. Nevertheless, a maximum of 24 matrices is sufficient to obtain predicted internal stress resultants to within 0.2% of the converged solution in all the problems tested. Using a three-noded isoparametric beam element, the accuracy of the VOSM method is demonstrated for the elastic postbuckling of arches. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes the a posteriori estimation of the error in the flux of a finite element approximation on a piece of the boundary of the domain. The estimate is obtained via a generalized Green's function corresponding to the quantity of interest on the boundary. We investigate the effects of smoothing the data corresponding to the quantity of interest and explore the effective domain of dependence of the quantity. We relate this approach to previous work by M. F. Wheeler, G. F. Carey, I. Babuska et al., and M. Larson et al. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

As flow solvers have become more sophisticated, many now have the capability to handle meshes with general polyhedral elements, i.e. general elements. In response, researchers have begun to develop mesh generation strategies that exploit nonstandard element types. General elements have been employed locally in near-body extruded meshes to improve mesh quality and have also been used in solution adaptive mesh refinement algorithms. In this paper, we present two mesh generation strategies that employ general elements. We also discuss how a specific flow solver is formulated to work with general elements. We demonstrate our approach by presenting simulation results for two realistic configurations. We close with a discussion that highlights future research directions. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Simulation of multiphysics problems is a common task in applied research and industry. Often a multiphysics solver is built by connecting several single-physics solvers into a network. In this paper, we develop a basic adaptive methodology for such multiphysics solvers. The adaptive methodology is based on a posteriori error estimates that capture the influence of the discretization errors in the different solvers on a given functional output. These estimates are derived using duality-based techniques. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix–Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A fundamental-solution-less boundary element method, the scaled boundary finite-element method, has been developed recently for exterior wave problems. In this method, only the boundary is discretized yielding a reduction of the spatial dimension by one, but no fundamental solution is necessary. Seamless coupling with standard finite elements is straightforward. In this paper, the sparsity of the coefficient matrices of the scaled boundary finite-element equation is exploited in performing the partial Schur decomposition to reduce the required computer memory and time. The Gauss–Lobatto–Legendre shape functions with nodal quadrature are applied to the elements on boundary, which leads to lumped coefficient matrices and high-order elements. Numerical examples demonstrate that these advances, in combination with the Padé series solution for the dynamic stiffness matrix, increase significantly the computational efficiency of the scaled boundary finite-element method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper deals with the seismic response of a multilayered soil. It focuses on the influence of the uncertainty that may affect the soil height (SH). The soil under study is considered as a superposition of layers that extend horizontally to infinity. A tunnel, located inside this soil, is supposed to behave as a rigid inclusion; it represents a part of the Algiers subway. Its dynamical response is investigated under Boumerdes earthquake effect, 21 May 2003 (MW =6.5). The soil accelerations are collected at Keddara station (12 from the epicentre) as it corresponds to bedrock. As the study is devoted herein to SH wave propagation, the accelerations under study correspond to the EW horizontal direction. The SH below the tunnel is assumed to be a random variable. For this purpose, a log-normal distribution is adopted. The probabilistic seismic response of the soil is thus investigated. The mean and standard deviation of the tunnel displacement as well as of both the extreme ground acceleration and the transfer function are analysed. The present analysis is based on the boundary element method, which is adequate for the case of systems with infinite boundaries, while Green's functions are calculated using the thin layer method. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Canonical forms are recently employed in eigenproblems of structural mechanics to calculate the eigenvalues and eigenvectors. In this paper, such applications are extended to the static analysis of symmetric structures. In classical approaches the structure is decomposed into substructures and appropriate boundary conditions are then imposed. Here, a systematic method is developed which does not operate directly on the structural model, but rather on the matrices involved in the analysis of the structures. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper illustrates the use of simplified PN approximations as a tools of achieving verification of codes and simulations of radiative transfer in combustion systems. The main advantage of considering these models is the fact that the integro-differential equation for radiative transfer can be replaced by a set of differential equations which are independent of angle variable, compatible to the partial differential equations of flow and combustion, and easy to solve using standard numerical discretizations. Validation of these models is then performed by comparing predictions to measurements for a three-dimensional diffusion flame. The good agreement between measurements and predictions indicates that the simplified PN models can be used to incorporate radiation transfer in combustion systems at very low computational cost without relying on discrete ordinates or Monte Carlo methods. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Least-squares finite-element methods for Darcy flow offer several advantages relative to the mixed-Galerkin method: the avoidance of stability conditions between finite-element spaces, the efficiency of solving symmetric and positive definite systems, and the convenience of using standard, continuous nodal elements for all variables. However, conventional C0 implementations conserve mass only approximately and for this reason they have found limited acceptance in applications where locally conservative velocity fields are of primary interest. In this paper, we show that a properly formulated compatible least-squares method offers the same level of local conservation as a mixed method. The price paid for gaining favourable conservation properties is that one has to give up what is arguably the least important advantage attributed to least-squares finite-element methods: one can no longer use continuous nodal elements for all variables. As an added benefit, compatible least-squares methods inherit the best computational properties of both Galerkin and mixed-Galerkin methods and, in some cases, yield identical results, while offering the advantages of not having to deal with stability conditions and yielding positive definite discrete problems. Numerical results that illustrate our findings are provided. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The method proposed by J.C. Houbolt in 1950 is one of the pioneering methods of time integration. Nevertheless, especially due to its multi-step fashion and not having a well-defined starting procedure, the method has not met considerable acceptance. The conversion of the Houbolt method to a one-step method is reported in the literature. However, the resulting method still lacks an appropriate starting procedure for all practical cases. In this paper, a parameter-less unified starting procedure is proposed for time integration with the Houbolt method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A semi-analytical approach for evaluation of stresses and displacements in composite and sandwich laminates under cylindrical bending subjected to transverse load has been developed in this paper. Two dimensional (2D) partial differential equations (PDEs) of such a laminate are obtained by imposing plane-strain conditions of elasticity. The fundamental dependent variables are so selected in this formulation that they satisfy the continuity of displacements and transverse interlaminar stresses at the laminate interface through the thickness. The set of governing PDEs are transformed into a set of coupled first-order ordinary differential equations (ODEs) in thickness direction by assuming suitable global orthogonal trigonometric functions for the fundamental variables satisfying the boundary conditions. These ODEs are numerically integrated by a specially formulated ODE integrator algorithm involving transformation of a two-point boundary value problem (BVP) into a set of initial value problems (IVPs). Numerical studies on both composite and sandwich laminates for various aspect ratios are performed and presented. Accuracy of the present approach is demonstrated by comparing the results with the available elasticity solution. It is seen that the present results are in excellent agreement with the elasticity solutions. Some new results for sandwich laminates and for uniform loading condition are presented for future reference. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831–847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge–Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a numerical approach for examining a spherically symmetric advective–dispersive contaminant transport problem. The Taylor–Galerkin method that is based on an Euler time-integration scheme is used to solve the governing transport equation. A Fourier analysis shows that the Taylor–Galerkin method with a forward Euler time integration can generate an oscillation-free and non-diffusive solution for the pure advection equation when the Courant number satisfies the constraint Cr = 1. Such numerical advantages, however, do not extend to the advection–dispersion equation. Based on these observations, an operator-splitting Euler-integration-based Taylor–Galerkin scheme is developed to model the advection-dominated transport process for a problem that exhibits spherical symmetry. The spherically symmetric transport problem is solved using this approach and a conversion to a one-dimensional linear space with an associated co-ordinate transformation. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a systematic numerical analysis for a mixed nonlinear model of shock absorber under vibration excitation. The mixed nonlinear model is presented for attenuating vibration by considering the coupling of quadratic damping, viscosity damping, Coulomb damping and nonlinear spring forces. An approximate computational analytical solution for the dynamic transmissibility of the shock absorber was deduced by combining Fourier transforms and the harmonic balance method with deterministic excitation. The mathematical characteristics of the dynamic transmissibility were analyzed to illustrate the dynamic performance of the shock absorber. The results show multiple solutions, especially the low-frequency attenuation characteristics below the resonance frequency. The results provide a theoretical basis for the design of nonlinear shock absorbers. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The quadrilateral area co-ordinate (QAC) method is a new tool for developing quadrilateral finite element models. Compared with those traditional elements using isoparametric co-ordinates, models formulated by QAC method are less sensitive to mesh distortion. Furthermore, another advantage for QAC system is that the analytical expressions for element stiffness matrix can be obtained theoretically by basic formulae of QAC integrals, which are beneficial to finite element computation procedure. However, because of the relative complexity of the derivation process, no such explicit form of the stiffness matrix has been presented before. In this paper, the analytical element stiffness matrix of a recent 4-node quadrilateral membrane element, AGQ6-I, is given out for the first time. This element AGQ6-I, which was constructed by QAC method and generalized conforming conditions, successfully overcomes various locking problems and exhibits much better performances than many isoparametric models. And its formulations have also been introduced in shell analysis by other researchers. Numerical examples show that obvious higher computation efficiency can be achieved by presented explicit formulations. So the analytical form of the element stiffness matrix of element AGQ6-I possesses significance for its further applications. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an eigenvalue problem that involves uncertain-but-non-random parameters is discussed. A new method is developed to evaluate the reliable upper and lower bounds on frequencies of structures for these problems. In this method the matrix in the deviation amplitude interval is considered to be a perturbation around the nominal value of the interval matrix, and the upper and lower bounds to the maximum and minimum eigenvalues of this perturbation matrix are computed, respectively. Then based on the matrix perturbation theory, the eigenvalue bounds of the original interval eigenvalue problem can be obtained. Finally, two numerical examples are provided and the results show that the proposed method is reliable and efficient. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptively preconditioned iterative method for the solution of large-scale linear stochastic algebraic systems of equations with one random variable that arise from the stochastic finite element modelling of linear elastic problems. Firstly, a Rank-one posteriori preconditioner is introduced for a general linear system of equations. This concept is then developed into an effective adaptive preconditioning scheme for the iterative solution of the stochastic equations in the context of a modified Monte Carlo simulation approach. To limit the maximum number of base vectors used in the scheme, a simple selection criterion is proposed to update the base vectors. Finally, numerical experiments are conducted to assess the performance of the proposed adaptive preconditioning strategy, which indicates that the scheme with very few base vectors can improve the convergence of the standard Incomplete Cholesky preconditioning up to 50%. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix–vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When the direct current (DC) metallized thin film capacitor is fully charged the electromagnetic fields can be considered to have reached a steady state in which the governing equation is Laplace's equation. It is the computational analysis of the electrostatic state that is considered in this paper. The capacitor is modelled as a stack made up of infinitesimally thin layers of metal on polymer. An integral equation method from the BEMLAP package (www.boundary-element-method.com (Introduction to the Boundary Element Method for Scientists and Engineers: The BEMLAP Fortran Library for Laplace Problems)) for modelling the electric field, based on the methods described in Kirkup (Fortran codes for computing the discrete Helmholtz integral operators; Adv. Comput. Math. 1998; 9:391–409). The method is applied to a typical capacitor structure and encouraging results are obtained. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the preliminary results of an extensive numerical parametric study on seismic behaviour of two-dimensional semi-sine-shaped valleys subjected to vertically propagating incident in-plane compression and shear waves. The medium is assumed to have a linear elastic constitutive behaviour. All calculations are executed in time-domain using the direct boundary element method. Clear perspectives of the amplification patterns of the valley are presented by investigation of the frequency-domain responses. It is shown that wavelength, site geometry and in a less order of importance, wave type and material parameters, are the independent key parameters governing the valley's amplification pattern. Some simple rules are obtained which could be used in seismic microzonation and seismic design of structures founded inside the valley. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Free-surface boundary is not only unknown in a priori but also the boundary conditions are overspecified. In this paper, the Laplace problem with overspecified boundary conditions on the free surface is solved by using the hypersingular equation instead of singular equation used conventionally in boundary element method. The free surface can be determined using an iterative procedure starting from an initial guess. By introducing the hypersingular equation, the convergence rate of free surface can be accelerated. Finally, numerical examples including rectangular dams and canals were demonstrated and were compared with others to show the validity of the present method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a stabilized space–time Petrov–Galerkin finite element model of coastal ocean circulation is derived. Continuous linear interpolation in space and time is employed and a spatial unstructured mesh of triangular elements is used. To simulate the hydro-thermodynamical ocean behaviour a gravity reduced model is proposed. This model solves the motion and continuity hydrodynamic equations coupled with the advection–diffusion transport equation for temperature which governs the heat exchanges in the upper layer. The model is used to evaluate the main dynamical features of the coastal waters of the Rio de Janeiro State, namely: cold plumes, coastal jets and the influence of the warmer water bays. Numerical experiments are performed to highlight the typical observed events of coastal upwelling phenomena and their interaction with the existing coastal bays and the offshore conditions. Such experiments deal with a series of idealized northeast wind field forcing patterns, showing the solutions dependence on the horizontal structure of the wind fields in relation to the coastline configuration. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier–Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171–186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199–210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present the construction and computational assessment of an hp-version discontinuous Galerkin finite element method (DGFEM) for the numerical solution of the Navier–Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, which ensures that the incompressibility constraint is automatically satisfied, we reduce the system of Navier–Stokes equations to a single fourth-order nonlinear partial differential equation. We introduce a discretization of this fourth-order nonlinear partial differential equation based on a combination of the symmetric DGFEM for the biharmonic part of the equation and a DGFEM with jump-penalty terms for the hyperbolic part of the problem, and then we solve the resulting nonlinear problem using Newton's method. Numerical examples, including the solution of the 2D lid-driven cavity flow problem, are presented to demonstrate the convergence and accuracy of the method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A computational modelling for the prediction of the hydrodynamic performance of a centrifugal pump in cavitating flows is presented in this paper. The cavitation model is implemented in a viscous Reynolds-averaged Navier–Stokes solver. The cavity interface and shape are determined using an iterative procedure matching the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient on the wall, is taken into account in updating the cavity shape iteratively. Numerical validation of the present cavitation model and algorithms is performed on different headform/cylinder bodies for a range of cavitation numbers through comparing with the experimental data. Flow characteristics trends associated with off-design flow and twin cavities in the blade channel are observed using the presented cavitation prediction. The rapid drop in head coefficient at low cavitation number is captured for two different flow coefficients. Local flow field solution illustrates the principle physical mechanisms associated with the onset of breakdown. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The method of generalized displacements (GDC) is a path-following algorithm for non-linear mechanics, capable to overcome both limit and snap-back points. It was proposed as a consistent alternative to most existing techniques, such as the arc-length family of algorithms. Although it is a reliable algorithm, it has not been as widely used as the arc-length methods, possibly because it has been seen as belonging to a different category. This paper shows that the GDC method can be seen as an orthogonal arc-length method, with an interesting constraint equation which leads to its appealing features. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Collocation methods based on radial basis functions can be used to provide accurate solutions to deterministic problems. For stochastic problems, accurate solutions may not be desirable if they are too sensitive to random inputs. In this paper, four methods are used to solve stochastic Poisson problems by expressing solutions in terms of source terms and boundary conditions. Comparison among the methods reveals that the method based on fundamental solutions performs better than other methods. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present a robust and efficient technique for surface meshing based on Stereolithography (STL) surface definition. Ridges are correctly identified using checks on dihedral angle and comparisons of the ratio of triangle edge lengths. Robust edge swapping, splitting and contraction are performed with stringent element validity checks. The improved remeshing technique is applied directly to CAD models and it is also used to improve surface triangulations which are reconstructed from sectional contours extracted from medical images. All the application examples, including the circulatory system and the urinary system, demonstrate that the enhanced remeshing procedure is robust and efficient for surface grid generation. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new method for computing eigenvector derivatives with distinct and repeated eigenvalues for the real symmetric eigensystems is presented. Its main idea is to extend the governing equations of particular solutions for eigenvector derivatives. The extension is completed by requiring the solution to be mass orthogonal with respect to the distinct or repeated modes and adjusting the corresponding coefficients so that the coefficient matrix of the extended system is non-singular and has smaller condition number. Numerical examples are included to demonstrate the validity of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, some finite difference schemes I, II, III and IV, are investigated and compared in solving a kind of mixed problem of generalized Korteweg-de Vries (GKdV) equations especially the relative errors. Both the numerical dispersion and the numerical dissipation are analysed for the constructed difference scheme I. The stability is also obtained for scheme I and the constructed predictor-corrector scheme IV by using a linearized stability method. Other two schemes, II and III, are also included in the comparison among these four schemes for the numerical analysis of different GKdV equations. The results enable one to consider the relative error when dealing with these kinds of GKdV equations. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an approach which allows the solution of elastic problems concerning a half-space (half-plane) with cavities by the boundary integral equation methods using Neumann's series. To evaluate the series terms at singular points, the regular representations of singular integrals for the external problems were proven and the regular recurrent relationships for the series terms, which can be calculated by any known quadrature rule, are obtained. The numerical proposed procedure was tested by comparison with known theoretical solution and the method convergence was studied for various depths of a buried cavity. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper describes the application of the primal-dual theory of limit and shakedown analysis in safety assessment and design of pressure components according to the new European approach to design by analysis. Two methods, the static and kinematic one, and their combination, the primal-dual method, are discussed. A numerical example is presented to show the robustness of the primal-dual method compared with two other methods recently used in two European projects on safety assessment and design. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A novel mathematical model for accurately calculating the currents flowing along the conductors of grounding system below high voltage a.c. substations and nearby floating metallic structure buried in horizontal multilayer earth model has been developed in this paper. Not only the mutual conductive and capacitive coupling influences of leakage currents, but also mutual inductive coupling influence of network currents flowing along the conductors of grounding system and nearby floating metallic structure in the horizontal multilayer earth model have been considered in this model, and only propagation effect of electromagnetic wave within limited area of the substation has been neglected. The quasi-static complex image method and closed form of Green's function are introduced into this model to accelerate the calculation. The model is then implemented in a computer program, which can be used to calculate currents distribution along the conductors of any configuration of grounding system, and with or without floating metallic structure under some hundreds of kHz frequency harmonic wave. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The Crank–Nicholson method is a widely used method to obtain numerical approximations to the diffusion equation due to its accuracy and unconditional stability. When the diffusion coefficient is not a constant, the general approach is to obtain a discretization for the PDE in the same manner as the case for constant coefficients. In this paper, we show that the manner of this discretization may impact the stability of the resulting method and could lead to instability of the numerical solution. It is shown that the classical Crank–Nicholson method will fail to be unconditionally stable if the diffusion coefficient is computed at the time gridpoints instead of at the midpoints of the temporal subinterval. A numerical example is presented and compared with the exact analytical solution to examine its divergence. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a new lattice Boltzmann (LB) method for the study of shock wave propagation in elastic solids. The method, which implements a flux-corrected transport (FCT) algorithm, contains three stages: collision, streaming, and correction. In the collision stage, distribution functions are updated. In the streaming stage, the distribution functions are shifted between lattice points. Generally, a partial differential equation (PDE) is solved in the streaming stage, and finite element methods are employed to support the use of unstructured meshes in the LB method. The FCT algorithm is used in the correction stage to revise the distribution functions at lattice points, so fluctuations behind shock wave fronts can be eliminated efficiently. In this method, schemes for shock wave reflection at fixed and free boundaries are developed based on the bounce-back technique. A similar technique is used to treat wave reflection and transmission at material interfaces of composites. Several one-dimensional examples show that this LB-FCT method can provide ideal depictions of shock wave propagation in structures, especially composite structures. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a method for finding the eigenvalues of some equations, or the zeros of analytic functions. There are two steps in the method. In the first step, integration along the edges of rectangle for an analytic function is performed. From the result of integration, one can know whether the zero exists in the rectangle or not. If the zero of an analytic function exists in the rectangle, we can perform the second step. In the second step, the zero is obtained by iteration. Therefore, the method is called a region searching method. Particular advantage of the suggested method is that the process for finding zero can be visualized. For example, one can clearly indicate the rectangles, which contain the zeros of an analytic function. Three numerical examples are presented. The obtained results are satisfactory even for a complicated case, for example, for finding eigenvalues of a composed wedge of dissimilar materials. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that the recently developed high performance divide and conquer algorithm for solving linear recurrence systems with constant coefficients together with the new BLAS-based algorithm for narrow-banded triangular Toeplitz matrix–vector multiplication, allow to evaluate linear recursive filters efficiently on distributed memory parallel computers. We apply the BSP model of parallel computing to predict the behaviour of the algorithm and to find the optimal values of the method's parameters. The results of experiments performed on a cluster of twelve dual-processor Itanium 2 computers and Cray X1 are also presented and discussed. The algorithm allows to utilize up to 30% of the peak performance of 24 Itanium processors, while a simple scalar algorithm can only utilize about 4% of the peak performance of a single processor. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The differential quadrature method based on spline functions (SDQM), considered as a piecewise polynomials of any degree, is proposed in the paper. The conditions for the determination of the interpolation function are presented. The symbolic computing has been employed to determine the weighting coefficients for the SDQM. The method has been examined in the vibration analysis of a plate. Effects of the spline degree, the number of nodes, the grid point distribution and two types of end conditions on the accuracy and convergence have been investigated in the example. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper reviews several novel and older methods for coupling mesh-free particle methods, particularly the element-free Galerkin (EFG) method and the smooth particle hydrodynamics (SPH), with finite elements (FEs). We study master–slave couplings where particles are fixed across the FE boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent of the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study those matrices which can be written as the sum of two Kronecker products. Special decompositions are proposed. Applications are extended to the eigensolution of problems from structural mechanics. It is also shown how the analysis of structures can be performed without finding the inverse of the structural matrices. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A simplified method for analysing lateral response of suspension bridges under wind loads is proposed in this paper. The geometric non-linearity in the deflection theory and the three components of displacement-dependent wind loads are taken into account in the method. The analytical formulas for calculating the torsional, vertical, and lateral responses of suspension bridges under wind loads are derived. An iterative procedure, which has a high convergence rate for solving the problem, is developed. The proposed method is sufficient and simple to use. Wind-induced lateral response analysis of a long-span suspension bridge demonstrates the proposed method's efficiency and accuracy. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a meshfree interpolating moving least squares (IMLS) method based on singular weights for the solution of partial differential equations. Due to the specific singular choice of weight functions, which is needed to guarantee the interpolation, there arises a problem of finding the inverse of the occurring singular matrix. The inverse is carried out using a regularization of weight functions. It turns out that a stable inverse is obtained by considering the vanishing regularization parameter. Moreover, the use of this perturbation technique allows the correct evaluation of all necessary derivatives in interpolation points at a reasonable cost. Unlike standard kernel functions used in EFGM, RKPM, etc., the singular kernel functions lead to really interpolating functions which satisfy the Kronecker-delta property. They can be used for enforcement of Dirichlet boundary conditions when solving boundary value problems. Solution to a model BVP as well as an experimental convergence study of the method to analytical solutions, confirming the mathematical derivations, are given. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new 3-node, 18-DOF triangular layered plate element is developed in this paper for the geometric and material non-linear analysis of isotropic plates and reinforced concrete slabs under service loads. The proposed model is a combination of Allman's 3-node, 9-DOF triangular membrane element with drilling degrees of freedom and the refined non-conforming 3-node, 9-DOF triangular plate-bending element RT9 in order to account for the coupling effects between membrane and bending actions. The element is modelled as a layered system of concrete and equivalent smeared steel reinforcement layers, and perfect bond is assumed between the concrete layers and the smeared steel layers. The maximum normal stress criterion is employed to detect cracking of the concrete, and a smeared fixed crack model is assumed. Both geometric non-linearity with large displacements but moderate rotations and material non-linearity, which incorporates tension, compression, concrete cracking and tension stiffening, are included in the model. An updated Lagrangian approach is employed as a solution strategy for the non-linear finite element analysis and a numerical example of reinforced concrete slab is given to demonstrate the efficacy of this robust element. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]