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For an efficient force method of frame analysis, the formation of localized self-equilibrating systems is an important issue. Such systems can be constructed on minimal cycle basis of the graph model of the structure. In this paper, algorithms are presented for the formation of minimal cycle bases of graph products corresponding to sparse cycle adjacency matrices, leading to the formation of highly sparse flexibility matrices. The algorithms presented employ concepts from three graph products namely Cartesian, strong Cartesian and lexicographic products. Though the formulation for the first two products exist, however, efficient implementations are made in this paper. The formulation for the generation of minimal cycle basis is extended to the lexicographic product. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents an algorithm for use with the discrete element method to study possible strain-gradient effects in granular materials. The algorithm produces an intentionally non-uniform displacement pattern by applying external (body) forces to the particles within a simulated granular assembly. The paper describes a method for adjusting the external forces to attain the intended gross displacement pattern, but while allowing individual particles to be in equilibrium among neighbouring particles. The performance of the algorithm is tested in an example of quasi-static deformation, and the algorithm's performance is measured in three respects. The algorithm is shown to enforce the intended displacement pattern, to allow particles to equilibrate among neighbouring particles, and to produce a smooth distribution of the external forces among particles. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In a preceding paper we have presented a unified view of the identification methods dedicated to adaptive sequential systems. In this paper, we develop the resolution technique based on genetic simulation. We analyse the various parameters of such an approach, then, we propose a tool intended to demonstrate the interest of this new approach, and finally we present some differential identification experiments conducted with this tool. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There exist quite a number of published papers showing that BEM/FEM coupling in time domain is a robust procedure leading to great computer time savings for infinite domain analyses. However, in many cases, the procedures presented so far have considered only constant time interpolation for BEM tractions, otherwise one may have (mainly in bounded domains) strong oscillations which invalidate the results. In this paper, such a limitation is overcome by employing the linear θ method which consists, basically, of computing the response at the time tn+1 from the response previously computed at the time tn+θ, θ⩾ 1.0. This procedure is implicitly incorporated into the BEM algorithm in the coupled BEM/FEM process presented here, i.e. the response is calculated directly at time tn+1. Proceeding this way, it becomes possible to adopt the Newmark scheme in the FEM algorithm. Two examples are presented in order to validate the formulation. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper compares the parallel efficiency of three Gram–Schmidt orthonormalization algorithms: modified Gram–Schmidt, classical Gram–Schmidt, and iterated classical Gram–Schmidt. The paper shows how these algorithms can be implemented on a parallel computer, and how their communication overhead can be minimized. In addition, it briefly examines the numerical properties of these algorithms. Finally, it provides some guidelines for selecting the most appropriate algorithm. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The advance of powerful software for symbolic and numerical computations such as Mathematica sheds a new light on a paper by Golub and Welsch from 1969. Based on this paper the author describes a Mathematica procedure for determining the weights and abscissae of a Gauss quadrature rule with a user-defined weight function. After a brief description of the algorithm and its implementation examples demonstrate the usefulness of the procedure. The procedure is extremely useful if one has to compute many integrals with the same, possibly weakly singular, weight function. This might happen, for example, in the boundary element method. [ABSTRACT FROM AUTHOR]

PISO (pressure-implicit with splitting of operators) is an algorithm devised to solve the transient incompressible Navier-Stokes and energy equations. In that it uses separate equations for each of two pressure corrections, velocity components and transported scalars, PISO is known as a segregated solution procedure. Preconditioned, generalized conjugate gradient (GCG) methods in combination with schemes for vectorization and storage minimization are described in the paper for the purpose of solving both the symmetric and non-symmetric algebraic equation systems that result from the PISO algorithm. Of particular interest in the paper is a comparison of the present procedure with a procedure described by Chin et al. (1992) in which preconditioned conjugate gradient methods are used to solve the Jacobian matrix used in the Newton iteration of the fully coupled non-linear equations. The two methods are similar in that both techniques are based on a discretization using staggered control volumes with the power-law method for modelling advection-diffusion transport. [ABSTRACT FROM AUTHOR]

In a recent paper we presented a data structure to be used with multigrid techniques on non- homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance). [ABSTRACT FROM AUTHOR]

The generalized geometric programming algorithm GOP has been found to be one of the better algorithms for optimizing algebraic functions subject to algebraic constraints. The paper discusses two problems with the GOP algorithm presented by Avriel et al. (1980). The first problem is that, because of the way that constraint tolerances are checked, the checks may pass even when a constraint is violated beyond the acceptable tolerance. This problem can affect an acceleration technique suggested for the algorithm. This paper presents two possible solutions to this problem. The second problem is the algorithm's weakness in handling equality constraints. This problem seems to especially affect the `Phase I' part of the algorithm, which finds a feasible solution from a random starting point. While extensions have been made to get around this limitation, no discussion on why the original algorithm has problems with equality constraints has been made. This paper discusses why the problems exist. [ABSTRACT FROM AUTHOR]

The study of hemodynamics in arterial models constructed from patient-specific medical images requires the solution of the incompressible flow equations in geometries characterized by complex branching tubular structures. The main challenge with this kind of geometries is that the convergence rate of the pressure Poisson solver is dominated by the graph depth of the computational grid. This paper presents a deflated preconditioned conjugate gradients (DPCG) algorithm for accelerating the pressure Poisson solver. A subspace deflation technique is used to approximate the lowest eigenvalues along the tubular domains. This methodology was tested with an idealized cylindrical model and three patient-specific models of cerebral arteries and aneurysms constructed from medical images. For these cases, the number of iterations decreased by up to a factor of 16, while the total CPU time was reduced by up to 4 times when compared with the standard PCG solver. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the numerical approximation of complex spatial patterns and rapidly evolving transients in chemotactic biological systems using parallel adaptive multiscale schemes and algorithms. Transport processes in such biological systems are typically modeled by coupled systems of nonlinear reaction–diffusion equations. For example, a model of this form has been proposed for studying chemotaxis in bacteria colonies. In the present study, we develop a variational formulation for this model leading to an approximate finite element scheme with adaptive time stepping and local adaptive mesh refinement/coarsening algorithms. The parallel adaptive solution algorithm is presented in detail and applied to investigate the effect of chemotaxis in spot formation behind concentric advancing concentrations fronts. Numerical results concerning the accuracy, efficiency, and performance of the algorithm are also presented. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To obtain a very fast solution for finite element models used in surgical simulations, low-order elements, such as the linear tetrahedron or the linear under-integrated hexahedron, must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately, the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper, we extend the average nodal pressure (ANP) tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing Total Lagrangian Explicit Dynamics algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared with the ANP element in case of models consisting of multiple materials. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Bioluminescence tomography (BLT) is employed to reconstruct internal bioluminescent source to reveal the molecular and cellular information. However, BLT faces many challenges such as quantitative reconstruction. In this paper, a reconstruction–oriented multigrid finite element algorithm is proposed to fully reconstruct the source density. A source permissible region is utilized to raise the numerical stability. The proposed algorithm transfers diffuse equation into liner relationship between the inner source and boundary information on a mesh. A tolerant algorithm for linearly constrained optimization algorithm can solve the box-constrained quadratic optimization problem. By setting a threshold as the average reconstruction densities, we can refine every possible source element and form next mesh until the reconstructed densities are accepted. Numerical simulation of homogeneous and heterogeneous phantom demonstrates the feasibility and potential of the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to bring forward and explore the issue of constitutive integrations in large deformation regime for anisotropic hyperelasto-plastic material models. Of particular interest is the appropriate treatment of cases with non-coaxiality of principal stress and its conjugate hyperelastic strain. The non-coaxiality can result from hyperelastic anisotropy, anisotropic flow directions or anisotropic yield function. In addition to discussing issues related to non-coaxiality, a constitutive integration algorithm is presented in some detail that is designed to be applicable to anisotropic non-coaxial (as well as to isotropic) hyperelastic–plastic solids. A numerical example is used to illustrate the problem. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The coupled equations for a propagating hydraulic fracture (HF) exhibit a multi-scale structure for which resolution on all length scales becomes computationally prohibitive. Asymptotic analysis is able to identify the dominant physical process active at the computational length scale. This paper describes a novel algorithm that uses weak-form tip asymptotics on a rectangular Eulerian mesh to solve the problem of a propagating HF. The location of the fracture front is determined within each tip element by matching the volume associated with the known asymptotic solution to the flux of fluid into the given element. Even if the fracture front is curved, the algorithm is able to capture the solution on a relatively coarse rectangular mesh by implementing a weak form of the tip asymptotic solution, based on averaging the volume over a tip element to determine the fracture widths at tip element centers. The fracture is divided into a ‘channel’ region made up of elements that are filled with fluid and a ‘tip’ region comprising partially filled elements. An iterative procedure is used to determine the fracture widths and fluid pressures in the channel region and the fracture font locations in the tip regions. The algorithm is tested by analyzing an HF propagating in a viscosity-dominated regime within an impermeable homogeneous elastic material for which a similarity solution is available. The numerical results show close agreement with the exact solution even though a relatively coarse mesh is used. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The adaptive variational multiscale method is an extension of the variational multiscale method where the fine-scale part of the solution is approximated by a sum of numerically computed solutions to localized subgrid problems. Furthermore, the crucial discretization parameters are chosen automatically by an adaptive algorithm based on a posteriori error estimates. This method has been developed for diffusion-dominated problems and applied to multiscale problems that arise in oil reservoir simulation. In this paper, we extend the method to convection–diffusion problems. We present a duality based a posteriori error representation formula and an adaptive algorithm that tunes the fine-scale mesh size and the patch sizes of the local problems. Numerical results show rapid convergence of the adaptive algorithm. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Given a set of normals in ℛ3, two algorithms are presented to compute the ‘most normal’ normal. The ‘most normal’ normal is the normal that minimizes the maximal angle with the given set of normals. A direct application is provided supposing a surface triangulation is available. The set of normals may represent either the face normals of the faces surrounding a point or the point normals of the points surrounding a point. The first algorithm is iterative and straightforward, and is inspired by the one proposed by Pirzadeh (AIAA Paper 94-0417, 1994). The second gives more insight into the complete problem as it provides the unique solution explicitly. It would correspond to the general extension of the algorithm presented by Kallinderis (AIAA-92-2721, 1992). Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm for analysis of periodic oscillations of forced elastic systems with geometric nonlinearity is presented in this paper. Modal decomposition of the solution, computation of periodic oscillations for every eigenmode and estimation of geometric nonlinearities using the method of initial deformations enable to construct a computational technique that can be very effective in computation of steady-state periodic motions of slightly damped structures under periodic forcing. It is shown that the developed algorithm can be successfully exploited for the calculation of structural response of a micromechanical cantilever. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The integration step size is the main algorithmic parameter in time integration analysis. Nowadays, for time integration with the complete records of digitized excitations, the integration steps cannot be set larger than the excitation steps. Considering the practical importance of this restriction, and with the aim of structural dynamic analysis with less computational cost, this paper intends to extend conventional time integration analyses to analyses, if needed, carried out with steps larger than the excitations steps. In view of few simplifying assumptions, and presenting a new theorem on responses convergence, a technique is developed and a computational procedure is set. Being based on convergence-oriented redefinition of digitized excitations, the implementation of the new procedure is simple and, though, sacrificing some accuracy, can considerably reduce the total computational cost. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, substructuring techniques for the analysis of frame structures by the force method are reviewed. An algorithm is presented for the formation of cycle basis of the graph model of a frame structure. A simple and efficient graph method is proposed for preserving the sparsity of the matrices involved for including the boundary conditions when algebraic and graph force methods are employed. Copyright © 2007 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]

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 new algorithm to map a given mesh over a source surface onto a target surface. This projection is determined by means of a least-squares approximation of a transformation defined between the loops of boundary nodes of the cap surfaces in the parametric spaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped to the target surface according to its parameterization. Therefore, in contrast with the usual techniques, the developed algorithm does not require solving any root finding problem to ensure that the projected nodes are on the target surface. Finally, this projection algorithm is extended to three-dimensional cases and included in a sweep meshing tool in order to generate the inner layers of elements in the physical space. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new principle of geometric design for blade's surface of an impeller is established. This is a thorough mathematical investigation of a shape control problem for the optimal design of an impeller's blade while 3D rotating Navier–Stokes equations are as the state equations in the control problem. The objective is to design the blade such that the viscous drag is minimized. Establishing a new curvilinear coordinate system, we depart from a standard domain transformation commonly used in the engineering literature and utilizing it we rephrase the design problem in one on a fixed domain. Certain advantages of our approach as no need for mesh regeneration and node redistribution and 3D mesh quality improvement are evident. Furthermore, in new coordinate system, it is easy to obtain gradient of optimal functional with respect to the surface of blade and to derive Euler–Lagrange equations for optimal solution which is an elliptic boundary value problem of fourth order. Moreover, we give the conjugate gradient algorithm for the control problem. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyse some local and parallel covolume algorithms for second-order elliptic problems. We first prove some local a priori error estimates for covolume method. With these results, we shall apply the two-grid strategy to covolume approximation to give two novel covolume algorithms, and show that the convergence rates of these algorithms are optimal in piecewise H1-norm. Numerical results confirming the theory are also provided. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The problem of the buckling of finite length externally constrained thin circular cylinders is solved to yield a generalized eigenvalue problem with constraint conditions. The solution is based on an inverse iteration procedure in which the non-linear complementary equation is solved by a non-smooth version of Newton's method that saves computer time and space when compared to a linear complementary algorithm. The numerical results show that the method proposed is effective and that the critical buckling load of the constrained cylinder is almost independent of the length of the cylinder, unlike the critical load of free (unconstrained) thin cylinders. In the direction of its axis, the shell is discretized by finite strips which circumferentially use straight bar and beam displacement functions. It is proved that when the widths of the strips approach zero, the geometrical relationships used in this paper approach those of Koiter–Sanders cylindrical shell theory. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a finite element solution algorithm for the numerical solution of large size three-dimensional flow problems on a personal computer. To demonstrate the algorithm, the Stokes equations in velocity–vorticity form are solved for a lid-driven cubical cavity problem. The Galerkin's weighted residual form of the governing equations is evaluated for all the elements of the computational domain and kept as element-matrices and element-vectors. This results in a set of simultaneous equations corresponding to the global nodes of each element. Those elements that contain the boundary nodes are modified to incorporate the Dirichlet boundary conditions. A conjugate gradient iterative scheme is employed to solve the simultaneous equations in element form to get the solution at the global nodes. The matrix–vector products used in the conjugate gradient iterative solver are performed in element level, assembling only the element-level vectors to form the global vectors. Since the element-level computation has eluded the formation of global matrices, the numerical solution of three-dimensional Stokes equations using a mesh of size as high as 513 could be achieved on a personal computer. The algorithm is validated by comparing the results for a three-dimensional transient diffusion problem and Stokes flow in a lid-driven cubical cavity. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a locally refined tetrahedral mesh generation algorithm based on advancing front technique using optimization scheme with a non-uniform trial height has been developed for three dimensional forming simulations to improve the quality of the local mesh system and computational efficiency. To generate locally refined surface elements, the refinement region was identified by checking the local effective strain rate and minimum interior angle of a surface element, respectively. In addition, a limiting value for the edge length of the tetrahedron was introduced to avoid generation of extremely small triangular surface elements. The developed scheme was applied for numerical simulations of indentation and spur gear and connecting rod forging. The computational results indicate that the currently developed algorithm was successful in generating better mesh system to finish numerical simulations with relatively shorter computation time compared to the previous scheme with a uniform trial height available in the literature. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The redistribution and embedding are two main adaptive-grid methods. With use of initial structured grid, it is possible to combine these adaptive-grid techniques. It means that before the grid becomes unstructured, we employ redistribution technique and then use embedding method. It is used to solve three model problems, transonic and supersonic inviscid flows in channels with circular arc bump and with convergent part. The Euler equations are integrated to steady state by an explicit, finite volume, Ni's Lax–Wendroff type. The combination of adaptive-grid redistribution and embedding is complex, but it is shown in this paper that it is very efficient and worth to use it in large CPU time consuming problems. The results also show that the combination requires less grid points and therefore less memory space for prescribed accuracy. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper numerical methods for solving first-order hyperbolic partial differential equations are developed. These methods are developed by approximating the first-order spatial derivative by third-order finite-difference approximations and a matrix exponential function by a third-order rational approximation having distinct real poles. Then parallel algorithms are developed and tested on a sequential computer for an advection equation with constant coefficient and a non-linear problem. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new computer algorithm for generating spatially-correlated random fields. Such fields are often encountered in hydrology and hydrogeology and in the earth sciences and used as inputs for Monte Carlo simulations. The algorithm is designed by using a multilevel grid strategy and combining the matrix decomposition (MD) method and the screening sequential simulation (SSS) method. The idea originates from the facts: (i) the MD method accounts for all possible nodal correlation values and hence the accuracy of the method is high, but it can be extremely computationally intensive for fine meshes with large number of nodes, and (ii) the SSS method is more efficient because a small search neighbourhood for conditioning can be used due to the screening effect of measurements, however, for large separation distances, correlation values from the SSS method is significantly inferior to the values obtained by the MD method. Numerical examples are presented to demonstrate the new method. It is shown that the presented method is much more efficient than the MD method and more accurate than the SSS method. The new algorithm is also versatile: it can directly simulate fields of irregular geometry without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A variationally consistent framework leading to the concise design of both the ‘integrator’ and the associated ‘updates’ as related to the single step representations encompassing the so-called LMS methods for structural dynamics is described. The present paper shows for the first time, a consistent treatment involving both the ‘integrator’ and ‘updates’ that are inherent in the general context of designing the time integration process. Furthermore, the framework encompasses not only all the existing time integration algorithms that are dissipative and non-dissipative within the scope of LMS methods but also contains new optimal algorithms useful for practical applications—in the sense of accuracy, stability, numerical dissipation and dispersion, and overshoot characteristics of computational algorithms for time dependent problems encountered in structural dynamics. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The δ-type discrete singular convolution (DSC) algorithm has recently been proposed and applied to solve kinds of partial differential equations (PDEs). With appropriate parameters, particularly the key parameter r in its regularized Shannon's kernel, the DSC algorithm can be more accurate than the pseudospectral method. However, it was previously selected empirically or under constrained inequalities without optimization. In this paper, we present a new energy-minimization method to optimize r for higher-order DSC algorithms. Objective functions are proposed for the DSC algorithm for numerical differentiators of any differential order with any discrete convolution width. Typical optimal parameters are also shown. The validity of the proposed method as well as the resulted optimal parameters have been verified by extensive examples. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses the necessity and handling of non-linear constraint equations to describe the behaviour of properties of the loading system such as, e.g. smooth free-rotating loading platens. An exact, non-linear formulation for a smooth loading platen is derived and its incorporation into the equilibrium equations is presented. For this purpose, the Lagrange multiplier method is used. The solution of the equilibrium equations by means of a Newton–Raphson algorithm is also outlined. The proposed approach is validated on a patch of two finite elements and applied to a compression-bending test on a pre-notched specimen. It is observed that use of a linearized approximation of the boundary constraint can lead to errors in the description of the motion of the constrained nodes. Thus, the non-linear formulation is preferable. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces an elastic predictor/return mapping integration algorithm for a simplified version of the Lemaitre ductile damage model, whose return mapping stage requires the solution of only one scalar non-linear equation. The simplified damage model differs from its original counterpart only in that it excludes kinematic hardening. It can be used to predict ductile damage growth whenever load reversal is absent or negligible—a condition met in a vast number of practical engineering applications. The one-equation integration scheme proves highly efficient in the finite element solution of typical boundary value problems, requiring computation times comparable to those observed in classical von Mises implementations. This is in sharp contrast to the previously proposed implementations of the original model whose return mapping may require, in the most general case, the solution of a system of 14 coupled algebraic equations. For completeness, a closed formula for the corresponding consistent tangent operator is presented. The performance of the algorithm is illustrated by means of a numerical example. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes an optimization algorithm based on a special convex approximation technique and a robust numerical solution procedure. The employed approximation technique involves automatic adjustability in order to ensure good convergence properties. Additionally, it guaranties convexity and a special form of the approximate problems. Consequently, these problems can be transformed into very simple and quasi-unconstrained dual problems which are solved by a robust and reliable numerical solution procedure. A few examples illustrate the use of the algorithm. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An adaptive iteration algorithm is presented in this paper for structural modal reanalysis of topological modifications. The rules of adaptation are given. The method is based on matrix perturbation and can be implemented easily on the computer. A little computation effort is involved, which is very important for topological modification with the increase of the joints and the number of degrees of freedom. In order to illustrate the method, three examples are given. The results show that the proposed method is effective for structural modal reanalysis of topological modifications. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recently, a new type of time step integration algorithms using complex time steps has been proposed. For linear problems, the algorithms are higher order accurate, unconditionally stable and have directly controllable numerical dissipation. Solutions with high accuracy can be generated using large time steps. In this paper, the algorithms are extended to solve non-linear problems. The pseudo-force approach is adopted in treating the non-linear terms. To maintain the solutions accuracy, the pseudo-force is reconstructed by interpolation. Special treatments are required to compute the excitation at the complex time steps. Several numerical examples are analysed. It is observed that the complex time step method can be computationally more efficient than the Newmark method when very accurate numerical solutions are required. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents an implementation of the Newton–Krylov–Schwarz methodology for stabilized, adaptive finite element approximations of compressible Navier–Stokes equations. Special emphasis is laid on preconditioning of the GMRES method within Newton iterations. Several Schwarz preconditioners are compared on a benchmark problem, including a new implementation of multiplicative preconditioner for matrix-free GMRES, that can be interpreted as accelerated block Gauss–Seidel iterations. Numerical examples show a good performance of the new algorithm, for single step problems and overall simulations. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an objective formulation for the anisotropic elastic–plastic problems at large strain plasticity. The constitutive equations are written in a rotating frame. The multiplicative decomposition of the deformation gradient is adopted and the formulation is hyperelastic based. Since no stress rates are present and the incremental constitutive law was formulated in a rotating frame, the formulation is numerically objective in the time integration. Explicit algorithm was proposed and has been optimized with regard to stability and accuracy. The incremental law was integrated in fast Lagrangian analysis of continua (FLAC) method to model anisotropic elastic–plastic problems at finite strain. Structural tests are carried out for isotropic and orthotropic materials. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a class of adaptive refinement algorithms for generating unstructured meshes in two and three dimensions. We focus on skeleton-based refinement (SBR) algorithms as proposed by Plaza and Carey (Appl. Numer. Math. 2000; 32:195) and provide an extension that involves the introduction of the graph of the skeleton for meshes consisting of simplex cells. By the use of data structures derived from the graph of the skeleton, we reformulate the SBR scheme and devise a more natural and consistent approach for this class of adaptive refinement algorithms. As an illustrative case, we discuss in detail the graphs for 2D refinement of triangulations and for 3D we propose a corresponding new face-based data structure for tetrahedra. Experiments using the 2D algorithm and exploring the properties of the associated graph are provided. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the accurate modal perturbation analysis in the non-self-adjoint eigenvalue problem. Complete perturbation items are obtained from the given straightforward process, satisfying two conditions in a modal analysis: the eigenvalue equations and normality condition. The zeroth-order perturbation, solved from equations in a form of Rayleigh quotient, is employed in the later perturbations, which helps to improve the accuracy of analysis. Two examples are given to show the modal perturbation with distinct eigenvalues and with close eigenvalues. It is confirmed that the algorithm is applicable to any mode with a distinct eigenvalue, repeated eigenvalues, or close eigenvalues, and can give an improved accuracy. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new scheme of time stepping for solving non-linear dynamic problems. By expanding variables in a discretized time interval, FEM-based recurrent formulae are derived leading to a self-adaptive algorithm for different sizes of time steps. There will be no requirement of iteration for the non-linear solutions. Numerical validation shows satisfactory results. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to give analysis of the covolume method for solving general self-adjoint elliptic problems. We first present some useful superconvergence results for the deviation between the solution of the covolume method and the solution of the induced finite element method, in the energy norm and maximum norm, respectively. With these results, we then reproduce the maximum norm estimates obtained by Chou and Li for the covolume method easily. Furthermore, based on the covolume method, we propose a high-accuracy algorithm for solving general self-adjoint elliptic problems. Compared with the original covolume method, the computation work of the new algorithm is increased slightly, but the approximate error is improved remarkably. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents an extension of a stress resultant based axisymmetric shell element by Reissner to the elasto-plastic computations. In the elastic range, the element exhibits exact kinematics for large displacements and rotations thus enabling the use of large increments in the global equilibrium path continuation. In order to preserve this desired property also in the elasto-plastic range, the general closest point projection algorithm is utilized for the elasto-plastic stress increment computation. In the case of the used element, consistent linearization of the stress updating algorithm results in a very simple form so that the element offers an efficient and computationally cheap approach to the large deflection elasto-plastic axisymmetric shell problems. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the newly generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results in a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm for the generation of general shape functions is presented here. The algorithm is coded using the Macsyma program which has symbolic/algebraic manipulation capabilities. The current technique is based on the direct approach of calculating shape functions which is seldom used due to manual algebraic tediousness. Listing of the code is included in this paper as well as examples showing how it correctly generates some of the common shape functions with ease. Two examples of new shape functions were created for C2 elements. Hence, the more useful purpose of this algorithm is that it can be used to investigate the existence of new types of shape functions by making use of the power of symbolic computational software. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, Lanczos and Arnoldi reduction methods as the special cases of the generalized Hessenberg method are briefly reviewed. Attention is paid to the effect of symmetry of matrices on the behaviour of the reduction schemes, such as serious numerical breakdown. Based on the summation decomposition of matrices, two structures of the upper Hessenberg form of a general unsymmetric matrix and their relationship are revealed, in terms of which, Arnoldi reduction schemes for unsymmetric matrices can be reformulated in two respective forms. The relationship between the reformulated reduction scheme and the current Lanczos schemes for skew and symmetric matrices are also discussed. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]