bluuebunny/crossref_metadata_2025_split huggingface dataset:
Local refinement techniques for elliptic problems on cell‐centered grids; II. Optimal order two‐grid iterative methods
Authors: Ewing R. E. , Lazarov R. D. , Vassilevski P. S. 
Published: October 2005

AbstractTwo preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell‐centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher‐order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG‐LS in the nonsymmetric case) are presented.
GMRESR: a family of nested GMRES methods
Authors: Van der Vorst H. A. , Vuik C. 
Published: October 2005

AbstractRecently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU‐time and memory requirements in typical CFD applications.
Backward error, sensitivity, and refinement of computed solutions of algebraic Riccati equations
Authors: Ghavimi Ali R. , Laub Alan J. 
Published: October 2005

AbstractIn this paper, a new backward error criterion, together with a sensitivity measure, is presented for assessing solution accuracy of nonsymmetric and symmetric algebraic Riccati equations (AREs). The usual approach to assessing reliability of computed solutions is to employ standard perturbation and sensitivity results for linear systems and to extend them further to AREs. However, such methods are not altogether appropriate since they do not take account of the underlying structure of these matrix equations. The approach considered here is to first compute the backward error of a computed solution X̂ that measures the amount by which data must be perturbed so that X̂ is the exact solution of the perturbed original system. Conventional perturbation theory is used to define structured condition numbers that fully respect the special structure of these matrix equations. The new condition number, together with the backward error of computed solutions, provides accurate estimates for the sensitivity of solutions. Optimal perturbations are then used in an iterative refinement procedure to give further more accurate approximations of actual solutions. The results are derived in their most general setting for nonsymmetric and symmetric AREs. This in turn offers a unifying framework through which it is possible to establish similar results for Sylvester equations, Lyapunov equations, linear systems, and matrix inversions.
Eigenvalue translation based preconditioners for the GMRES(k) method
Authors: Kharchenko S. A. , Yu. Yeremin A. 
Published: October 2005

AbstractThe paper considers a possible approach to the construction of high‐quality preconditionings for solving large sparse unsymmetric offdiagonally dominant, possibly indefinite linear systems. We are interested in the construction of an efficient iterative method which does not require from the user a prescription of several problem‐dependent parameters to ensure the convergence, which can be used in the case when only a procedure for multiplying the coefficient matrix by a vector is available and which allows for an efficient parallel/vector implementation with only one additional assumption that the most of eigenvalues of the coefficient matrix are condensed in a vicinity of the point 1 of the complex plane. The suggested preconditioning strategy is based on consecutive translations of groups of spread eigenvalues into a vicinity of the point 1. Approximations to eigenvalues to be translated are computed by the Arnoldi procedure at several GMRES(k) iterations. We formulate the optimization problem to find optimal translations, present its suboptimal solution and prove the numerical stability of consecutive translations. The results of numerical experiments with the model CFD problem show the efficiency of the suggested preconditioning strategy.
Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion
Authors: Elsner Ludwig , He Chunyang , Mehrmann Volker 
Published: October 2005

AbstractWe study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.
Some inverse eigenproblems for Jacobi and arrow matrices
Authors: Borges Carlos F. , Frezza Ruggero , Gragg William B. 
Published: October 2005

AbstractWe consider the problem of reconstructing Jacobi matrices and real symmetric arrow matrices from two eigenpairs. Algorithms for solving these inverse problems are presented. We show that there are reasonable conditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation. The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition.
Regions of convergence of the Rayleigh quotient iteration method
Authors: Pantazis Ricardo D. , Szyld Daniel B. 
Published: October 2005

AbstractThe Rayleigh quotient iteration method finds an eigenvector and the corresponding eigenvalue of a symmetric matrix. This is a fundamental problem in science and engineering. Parlett and Kahan have shown, in 1968, that for almost any initial vector in the unit sphere, the Rayleigh quotient iteration method converges to some eigenvector. In this paper, the regions of the unit sphere which include all possible initial vectors converging to a specific eigenvector are studied. The generalized eigenvalue problem Ax = λBx is considered. It is shown that the regions do not change when the matrix is shifted or multiplied by a scalar. These regions are completely characterized in the three‐dimensional case. It is shown that, in this case, the area of the region of convergence corresponding to the interior eigenvalue is larger than the area of those corresponding to any extreme one. This can be interpreted, with the appropriate choice of probability distribution, as: the probability of converging to an eigenvector corresponding to the interior eigenvalue is larger than the probability of converging to an eigenvector corresponding to any extreme eigenvalue. It is conjectured that the same is true for matrices of any order. Experiments in higher dimensions are presented which conform with the conjecture.
Completely parallelizable preconditioning methods
Authors: Gustafsson Ivar , Lindskog Gunhild 
Published: October 2005

AbstractA class of parallelizable preconditioned iterative methods for the solution of certain finite difference or finite element linear systems of equations is presented. The methods are based on calculation of approximate inverses of the SSOR factorization. The speed of the methods may be increased by making the approximation of the inverse more accurate. The construction of the preconditioning as well as the solution of the preconditioning systems (realized by matrix–vector multiplication) can be made in parallel over the total amount of meshpoints. The methods are suitable for implementation on massively parallel computers such as connection machines. Problems with constant as well as strongly varying orthotropy are examined and the methods are compared to other parallel techniques with respect to rate of convergence, computational complexity and consumed CM200 computing time. We report a small but significant decrease in computing time compared to the (until now) most frequently used completely parallel preconditioning, the Jacobi method.
Note on a modified Conjugate Gradient Method
Authors: Wood Winifred L. 
Published: October 2005

AbstractMr. Bruce Irons recently1 proposed a modification of the Conjugate Gradient Method. This note shows that if the matrix of the original set of equations is symmetric this method will have the same terminal property as the usual Conjugate Gradient Method except for a particular case when it will not converge at all. If the matrix is not symmetric we cannot deduce the usual terminal property.
Exact Mises limit loads for cylindrical shells
Authors: Haydl H. M. , Sherbourne A. N. 
Published: October 2005

AbstractNumerical solutions for limit loads of pressurized cylindrical cantilever shells are given for the exact Il'yushin yield surface.It is suggested that the numerical approach can be used for more complex problems for which the exact solution based on equation (2) has not been obtained to date.
Multiple constraints in structural optimization
Authors: Gellatly R. A. , Helenbrook R. G. , Kocher L. H. 
Published: October 2005

AbstractThis paper considers the problem of solving the optimality criteria equations for a truss structure. A unique Newton‐Raphson method for optimizing redundant structures subject to multiple constrainsts on displacement and member sizes is presented. Both equality and inequality constraints are considered. The characteristics of this approach along with least squares and recursive techniques for the solution of the non‐linear optimality criteria equations are examined numerically for several sample problems. This new formulation offers the advantages of a reduction in the number of dependent variables, ease of incorporation of various types of constraints, and very rapid convergence.
Optimal design of bending elements
Authors: Armand Jean‐Louis , Lodier Bernard 
Published: October 2005

AbstractDerivation of an optimality criterion for finite element structural representations using constant‐moment plate‐bending triangular elements ispresented. Numerical examples of minimum‐mass design of both simply‐supported and clamped elastic plates for concentrated and distributed loading conditions under a single displacement constraint serve to illustrate the suggested procedure. Interpretation of the solution obtained and difficulties involved are discussed in the light of recent application of optimal control theory to structural optimization.
A comparison of stability and accuracy of some numerical models of two‐dimensional circulation
Authors: Sasaki Y. K. , Reddy J. N. 
Published: October 2005

AbstractThe purpose of the paper is two‐fold: Firstly, we develop stream function‐‐vorticity and primitive variable finite element models of two‐dimensional barotropic equations that satisfy the conservation of mean vorticity, mean squared vorticity (or enstrophy) and mean kinetic energy, and scondly, we present a comparative study of a number of numerical schemes for their accuracy in phase speed as well as in amplitude calculations for a two‐dimensional, time‐dependent, stream function‐‐vorticity equation for periodic fluid motion in a channel. A circular vortex is placed in a uniform channel flow of a constant velocity (U) as an initial condition. An analytic solution exists for the problem such that the vortex moves with a constant speed U conserving the shape of the vortex:

where U, ψ0 a are constants. This example makes it easier to identify the cause of phase speed error, either due to linear or non‐linear processes, and furthermore, to find a satisfactory scheme for time integration. The numerical schemes compared include: Arakawa Jacobian,1 Arakawa–Matsuno scheme, Galerkin finite element, Lax–Wendroff, leap‐frog, and Crank–Nicholson. The effect of a variational adjustment (see Sasaki16) is also studied. Computational time, RMS errors in stream function and vorticity, and the conservation of the mean kinetic energy and enstrophy are compared at the end of 120 (one period) and 240 (two periods) time steps. The study indicates that the numerical scheme that employs finite elements in space (same as Arakawa Jacobian) and Crank–Nicholson in time is the most accurate among the schemes studied.
A conforming solution to curved plate bending problems
Authors: Caramanlian C. 
Published: October 2005

AbstractA curved triangular element for plate bending is developed, using the displacement method of formulation. The element has one outwardly curved side and conforms on an arbitrary quadratic boundary.To the user, the element appears as a single curved triangle. Internally, however, the element is subdivided into a straight‐sided triangle and a ‘curved segment’. The straight‐sided triangle is extensively documented in the literature2‐5 and is referred to in the paper as the Cowper triangle. The curved segment is a two‐noded element with 12 degrees‐of‐freedom. It has one straight side and one curved side.Independent expansions are assumed in each domain and explicit shape functions derived. The theoretical solution to a few practical problems is contained in each of the two expansions. In such cases, the curved triangle produces perfect results. Otherwise, the accuracy is of the same order as that obtained in similar problems with straight boundaries.The method is easily extended to elements of higher order.
Elastoplastic BIE analysis of cracked plates and related problems. Part 1: Formulation
Authors: Cruse T. A. , Polch E. Z. 
Published: October 2005

AbstractThe boundary‐integral equation formulation for two‐dimensional, planar fracture mechanics based on the use of a special Green's function forms the basis of this analytical paper. The Green's function method is extended to problems of anelastic strain distributions (e.g. elastoplasticity, thermal gradients, residual strains) through a volume (area) integral. The role of the elastic Green's function for the crack problem on the distribution of elastoplastic strains is reviewed. Further, new analytical results for elastic stress intensity factor models for the residual strain and thermal gradient problems are presented. Part 2 of this paper outlines the numerical solution strategy and results for several test problems.
A new triangular discrete Kirchhoff plate/shell element
Authors: Dhatt G. , Marcotte L. , Matte Y. 
Published: October 2005

AbstractWe present a new 6‐node triangular bending element (called DKTP) based on a discrete Kirchhoff model. A corresponding new flat‐shell element, DLTP, having quadratic variation of in‐plane displacement is also presented. This element has 6 degrees‐of‐freedom (u, v, w, θx, θy, θz) at each corner node and 3 degrees‐of‐freedom (u, v, w) at each mid‐side node. Detailed numerical experimentation is presented to demonstrate the efficiency and reliability of these elements.
Computation of hybrid element matrices by elimination techniques
Authors: Chieslar J. D. , Ghali A. 
Published: October 2005

AbstractThree functionals, the modified forms of the Hu–Washizu, Hellinger‐Reissner, and complementary energy principles, as developed by Pian, Chen, and Kang1.2 are stated. Finite element discretization of each is presented and the ensuing computations developed, resulting in the element stiffness matrix, with displacement degrees‐of‐freedom only, and the stress recovery matrices. Subroutines are presented for this purpose where the close relationship of the three principles is exploited to result in a compact hybrid element technique. The techniques herein reviewed are assumed applicable at the individual element level. The usual summation over all elements in the model is implied.
Three‐dimensional elastic finite element study of the skid resistance of grooved pavement
Authors: Moore I. D. , Purushothaman N. , Heaton B. S. 
Published: October 2005

AbstractA three‐dimensional finite element model has been developed to simulate the sliding of a rubber block over a grooved road surface. The model makes use of the symmetries of the problem to simplify the analysis, so that two‐dimensional isoparametric elements of both rectangular and triangular configuration have been extended into the third dimension. A procedure for analysing the behaviour of any one groove to groove unit of the pavement is also developed, and this is extended so that the contact between the sliding rubber block and the leading edge of each raised pavement section is analysed. Preliminary comparisons between theoretical calculations and experimental measurements indicate that the finite element procedure provides an accurate and economical estimate of the behaviour of the rubber slider as it is pressed into a grooved pavement. Elastic predictions of sliding resistance seem reasonable at low sliding speeds, but viscoelastic rubber analysis appears necessary if higher speed skid resistance is to be predicted.
Accuracies of numerical solution methods for the pressure‐modified von Mises model
Authors: Lee J. H. 
Published: October 2005

AbstractThe accuracy of three numerical algorithms—the tangent‐stiffness radial‐return, secant‐stiffness radial‐return and simple radial‐return methods—is analysed against exact solutions for the pressure‐modified von Mises yield criterion with the associated flow rule. The governing equations of the exact solutions are derived using a simple and innovative geometrical approach, in terms of a pair of non‐linear, first order differential equations, in rate change of the deviatoric radius and in rate change of angular locations on the deviatoric plane. For both accuracy and efficiency, and for small and large time steps, the secant‐stiffness radial‐return method is the best of all.
Finite element analysis of plane couple‐stress problems using first order stress functions
Authors: Wood R. D. 
Published: October 2005

AbstractA complementary energy based variational principle, using first order stress functions, is developed for plane linear elastic couple‐stress problems. The principle is analogous to that used in a total potential energy based Mindlin/Reissner thick plate bending analysis and as such is a generalization of the classical analogy between plate stretching and plate bending. Traction boundary conditions are enforced using a Lagrange multiplier technique. The resulting C0 finite element ‘equilibrium stress model’ is validated by investigating the reduction of the stress concentration factor associated with a small hole in a field of uniform tension.
A mixed explicit‐implicit (EI) algorithm for creep stress analysis
Authors: Chen G. G. , Hsu T. R. 
Published: October 2005

AbstractA mixed explicit‐implicit numerical integration algorithm for creep stress analysis is presented in this paper. This method allows simultaneously use of, and thus benefit from, both these integration schemes. The continuum damage constitutive model is also implemented in this algorithm. The present method is suitable for the prediction of creep crack growth in solids using the continuum damage approach.Numerical examples using different constitutive equations have been included to demonstrate the high efficiency of the proposed algorithm.
Assumed strain stabilization procedure for the 9‐node Lagrange shell element
Authors: Belytschko Ted , Wong Bak Leong , Stolarski Henryk 
Published: October 2005

AbstractAn assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9‐node shell element. The stabilization procedure can be justified based on the Hellinger–Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co‐ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9‐node element. Example problems show good accuracy and an almost optimal rate of convergence.
Eigenvalue analysis of compatible and incompatible rectangular four‐node quadrilateral elements
Authors: Hacker W. L. , Schreyer H. L. 
Published: October 2005

AbstractExact analytical expressions for the eigenvalues of the elastic stiffness matrix are obtained for the four‐node, rectangular, quadrilateral element. A procedure is given for identifying alternative hourglass modes and eigenvalues which render the element incompatible but with non‐monotonic convergence assured. A convergence study confirms that for the special case of when the hourglass modes coincide with beam bending the element can serve as a beam element. Analytical expressions are given for the resulting element stiffness matrix.
Analysis of locking and stress oscillations in a general curved beam element
Authors: Prathap G. , Naganarayana B. P. 
Published: October 2005

AbstractIn this paper, we have attempted to provide new insights into the phenomenon of shear and membrane locking in a general quadratic curved beam element. Locking is seen to be accompanied by significant quadratic oscillations in the axial force and cubic oscillations in the shear force. The functional reconstitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations. The orthogonally correct field‐consistent interpolations are determined for the optimal form of the element using an elegant concept of expanding strain interpolations in terms of Legendre polynomials. The popular two‐point Gaussian integrated version of the element is shown to be non‐orthogonal, resulting in a cubic oscillation in the shear force that curiously vanishes at the Barlow points.
Finite element modelling of crack tip behaviour in viscoelastic materials. Part I: Linear behaviour
Authors: Krishnaswamy P. , Tuttle M. E. , Emery A. F. , Ahmad J. 
Published: October 2005

AbstractA finite element algorithm which can be used to model either linear or non‐linear viscoelastic material behaviour is described. The algorithm is verified for the linear case by comparing numerical and analytical solutions for (a) a uniaxial tensile specimen, and (b) an infinite plate with a hole subjected to a remote uniaxial stress. The algorithm is then used to determine the stress and strain fields near the tip of a moving crack in a linear viscoelastic medium. Numerical solutions for both growing and healing cracks are compared with results expected based upon the extended correspondence principle. Excellent agreement between theoretical and numerical solutions is obtained in all cases. Sources of numerical error in the FE solution procedure are identified and documented. The algorithm has not been verified for the non‐linear case, since (except for very simple geometries and loading configurations) no closed‐form solutions involving non‐linear viscoelastic material behaviour are available. A comparison between the measured and predicted response of a non‐linear viscoelastic material behaviour will be presented in a following paper.
A unified numerical integration formula for the perfectly plastic von Mises model
Authors: Wu W. 
Published: October 2005

AbstractThe accuracy of numerical integration of the perfectly plastic constitutive equation of von Mises is examined. Based on the analysis of the three existing numerical integration schemes a unified numerical integration formula (UNIF) is derived, which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately. According to the UNIF there are, in fact, many integration schemes depending on the direction of the trial stress. The validity of the UNIF is verified by presenting ten contours of constant angular error calculated with the UNIF. We then come to the conclusion that the three widely used schemes are by no means the most accurate ones. Some other schemes with better accuracy are thereby suggested. The determination of the number of substeps is also discussed in conjunction with the UNIF, when a multi‐step method is used.