bluuebunny/crossref_metadata_2025_split huggingface dataset:
New techniques for fast hybrid solutions of systems of equations
Authors: Mandel J. , Miranker W. L. 
Published: August 2005

AbstractA fast analogue solver with limited precision is used as a preconditioner in an iterative process which develops full digital precision. This hybrid process is highly parallel, and, in principle, it can be faster than digital computations alone. A problematic feature of this process is that the low analogue precision can adversely affect convergence speed. New techniques are introduced to address this limitation. A partial separation of analogue imprecision and poor problem condition is made. Fully parallel digital (smoothing) iterations are introduced to eliminate the effect of random errors which accompany analogue–digital conversion. Application is made to the problem of repeated summation.
A unified treatment of superconvergent recovered gradient functions for piecewise linear finite element approximations
Authors: Goodsell G. , Whiteman J. R. 
Published: August 2005

AbstractPiecewise linear finite element approximations to two‐dimensional Poisson problems are treated. For simplicity, consideration is restricted to problems having Dirichlet boundary conditions and defined on rectangular domains Ω which are partitioned by a uniform triangular mesh. It is also required that the solutions u ∈ H3 (Ω). A method is proposed for recovering the gradients of the finite element approximations to a root mean square accuracy of O(h2), both at element edge mid‐points and element vertices, using simple averaging schemes over adjacent elements. Piecewise linear interpolants (respectively discontinuous and continuous) are then fitted to these recovered gradients, and are shown to be O(h2) estimates for ∇u in the L2‐norm, and thus superconvergent. A discussion is given of the extension of the results to problems with more general region and mesh geometries, boundary conditions and with solutions of lower regularity, and also to other second‐order elliptic boundary value problems, e.g. the problem of planar linear elasticity.
Fully vectorizable block preconditionings with approximate inverses for non‐symmetric systems of equations
Authors: Diaz J. C. , Macedo C. G. 
Published: August 2005

AbstractWe used a conjugate gradient type method, with preconditioning, to solve the sparse linear systems arising from the discretization of PDEs. With such methods, the main obstacles for complete vectorization have been the preconditioning calculation and its application step within the iteration: for the matrices obtained using 5‐ or 9‐point discretization operators, some well known existing preconditionings (like ILU) require a block‐recursive procedure which prevents vectorization. Preconditioners based on nested incomplete factorization, which require the calculation of approximate inverses of tridiagonal matrices, allow complete vectorization of the application step. We present a formulation of such a preconditioning, using a Frobenius norm minimization to calculate the inverses, which also allows complete vectorization of the inverses' calculation, thus making the iterative solver completely vectorizable. Numerical experiments show that the method is robust over a range of symmetric and non‐symmetric problems, and up to 4 times faster than other existing methods, such as ILU, depending on the computer and compiler being used. We also show the importance of diagonal scaling used in conjunction with other preconditionings and present some theoretical results concerning the approximate inverses of tridiagonal matrices, calculated using the Frobenius norm minimization.
The vectorization of ITPACK 2C
Authors: Oppe Thomas C. 
Published: August 2005

AbstractITPACK 2C14 is a package of seven iterative algorithms for solving sparse linear systems represented by Au = b, where A is symmetric and positive definite or mildly non‐symmetric. This paper describes the techniques used to vectorize the iterative algorithms in the ITPACK 2C package for the Cyber 205 and Cray X‐MP vector computers. The resulting package was named ITPACKV 2C.15 The basic iterative methods in ITPACK 2C are described in terms of matrix–vector multiplications and forward and backward solutions, and the techniques used in the vectorization of these and other computational kernels are given. Results of experiments using ITPACK 2C and ITPACKV 2C are given, including a comparison of megaflop rates and timings for two model problems.
Multigrid solution and grid redistribution for convection–diffusion
Authors: Carey G. F. , Pardhanani A. 
Published: August 2005

AbstractWe examine multigrid solution for convection–diffusion problems in which convective effects are significant. In particular, we consider the case where the fine grid satisfies the associated cell or diagonal dominance condition but coarse grid levels violate this condition. Related numerical experiments are conducted. We also introduce an alternative local elliptic projection technique and compare this with interpolating the error corrections from coarse to fine grids. In addition, we demonstrate the use of grid redistribution and optimization techniques in the multilevel context.
A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods
Authors: Cerrolaza M. , Alarcon E. 
Published: August 2005

AbstractThe numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM).Thus, a new procedure, based upon a bi‐cubic co‐ordinate transformation and oriented towards the numerical evaluation of both the CPV integrals and some others which contain different types of singularity is developed.Both the ideas and some details involved in the proposed formulae are presented, obtaining rather simple and‐attractive expressions for the numerical quadrature which are also easily embodied into existing BEM codes.Some illustrative examples which assess the stability and accuracy of the new formulae are included.
A move coordination method for alternative loads in structural optimization
Authors: Chibani Lahbib , Burns Scott A. , Khachaturian Narbey 
Published: August 2005

AbstractA decomposition technique for alternative loading conditions in the integrated optimal structural design is developed. The method, called the move coordination, consists of partitioning the large structural optimization problem into a set of smaller coupled subproblems. In each subproblem only one loading condition is considered and the subproblems are solved in a parallel cyclic way. The coupling among the subproblems is accomplished through the introduction of coordinating constraints between each subproblem. These constraints ensure that the final design is the same and feasible for all subproblems. The method developed is illustrated by two examples of member sizing of truss structures using the integrated optimal design formulation and geometric programming. The method presents the advantage of reducing the size of the optimization problem as well as the computer processing time. The method is also suitable for implementation on computers using parallel processing.
Consistent higher degree Petrov–Galerkin methods for the solution of the transient convection–diffusion equation
Authors: Westerink J. J. , Shea D. 
Published: August 2005

AbstractThe solution of the convection–diffusion equation for convection dominated problems is examined using both N + 1 and N + 2 degree Petrov–Galerkin finite element methods in space and a Crank–Nicolson finite difference scheme in time. While traditional N + 1 degree Petrov–Galerkin methods, which use test functions one polynomial degree higher than the trial functions, work well for steady‐state problems, they fail to adequately improve the solution for the transient problem. However, using novel N + 2 degree Petrov–Galerkin methods, which use test functions two polynomial degrees higher than the trial functions, yields dramatically improved solutions which in fact get better as the Courani number increases to 1·0. Specifically, cubic test functions with linear trial functions and quartic test functions in conjunction with quadratic trial functions are examined.Analysis and examples indicate that N + 2 degree Petrov–Galerkin methods very effectively eliminate space and especially time truncation errors. This results in substantially improved phase behaviour while not adversely affecting the ratio of numerical to analytical damping.
A numerical model for the thermo‐elasto‐plastic behaviour of a material
Authors: Ray Sujit K. , Utku Senol 
Published: August 2005

AbstractThis paper presents a numerical model for the thermo‐elasto‐plastic behaviour of an isotropic material. The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening. This unique model can be used both for isothermal and non‐isothermal cases. The original formulation for the non‐isothermal three‐dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided. The finite element implementation of this model is also outlined.
An effective quadrilateral plate bending element
Authors: He‐Xiang Lü , Shu‐Ning Xu 
Published: August 2005

AbstractAn effective arbitrary quadrilateral thin plate bending element with a quasi‐conforming, QCQ element, is presented in this paper. The elements pass the patch test with constant strain and the patch test with linear strains approximately. When the element degenerates to a rectangle the patch test with linear strains is passed. The calculation of the element stiffness matrix is simple without numerical integration. The numerical examples show that the QCQ element has a higher accuracy and a faster convergence rate.
A dynamic programming method for analysis of bridges under multiple moving loads
Authors: Adeli Hojjat , Ge Yaojun 
Published: August 2005

AbstractA dynamic programming (DP) method is presented for analysis of statically determinate and indeterminate bridges subjected to moving loads such as those specified by the American Association of State Highway and Transportation Officials (AASHTO) specifications. These loads consist of uniform lane loading, two‐axle truck loading and two‐axle truck plus one‐axle semitrailer loading. The solution of the DP problem is based on the use of influence line diagrams and extremum functions. Recurrence formulae have been developed for various types of AASHTO live loads. The procedure presented in this article is quite general and can be applied to any type of structures with linear behaviour and any type of moving loads. Six examples are presented: a simply‐supported beam, a simply‐supported Pratt truss, an arch bridge, a continuous Pratt truss, a continuous frame and a cable‐stayed bridge.
Coupled bending–torsional dynamic stiffness matrix for beam elements
Authors: Banerjee J. R. 
Published: August 2005

AbstractExplicit expressions for the coupled bending–torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam. Implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made. The application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted. The correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks.
PCG methods in transient FE analysis. Part I: First order problems
Authors: Smith I. M. , Wong S. W. , Gladwell I. , Gilvary B. 
Published: August 2005

AbstractThe performances of some PCG (preconditioned conjugate gradient) algorithms are evaluated in the solution of first order time dependent parabolic partial differential equations, such as the heat conduction equation, which have been spatially discretized using finite elements. ‘Consistent mass’ discretizations are preferred by the authors to ‘lumped mass’ ones and various preconditioners are then compared—diagonal, incomplete Choleski and EBE (‘element‐by‐element’). Recommendations are made and implications for parallel computation outlined.
An assumed strain finite element model for large deflection composite shells
Authors: Yeom C. H. , Lee S. W. 
Published: August 2005

AbstractA nine node finite element model has been developed for analysis of geometrically non‐linear laminated composite shells. The formulation is based on the degenerate solid shell concept and utilizes a set of assumed strain fields as well as assumed displacement Two different local orthogonal co‐ordinate systems were used to maintain invariance of the element stiffness matrix. The formulation assumes strain and the determinant of the Jacobian matrix to be linear in the thickness direction. This allows analytical integration in the thickness direction regardless of ply layups. The formulation also allows the reference plane to be different from the shell midsurface. The results of numerical tests demonstrate the validity and the effectiveness of the present approach.
Symmetry‐preserving return mapping algorithms and incrementally extremal paths: A unification of concepts
Authors: Ortiz Michael , Martin John B. 
Published: August 2005

AbstractIn this work we seek to characterize the conditions under which an elastic–plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo‐internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.
Free vibration of symmetrically laminated plates using a higher‐order theory with finite element technique
Authors: Mallikarjuna  , Kant T. 
Published: August 2005

AbstractA C0 finite element formulation of the higher‐order theory is used to determine the natural frequencies of isotropic, orthotropic and layered anisotropic composite and sandwich plates. The material properties that are typical of high modulus fibre reinforced composites are used to show the parametric effects of plate aspect ratio, length‐to‐thickness ratio, degree of orthotropy, number of layers and lamination angle/scheme. The present theory is based on a higher‐order displacement model and the three‐dimensional Hooke's laws for plate material. The theory represents a more realistic quadratic variation of the transverse shearing strains and linear variation of the transverse normal strains through the plate thickness. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. The results presented should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results.
Free and forced vibrations of plates by boundary and interior elements
Authors: Providakis C. P. , Beskos D. E. 
Published: August 2005

AbstractA direct boundary element method is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions. The formulation employs the static fundamental solution of the problem and this creates not only boundary integrals but surface integrals as well owing to the presence of the inertia force. Thus the discretization consists of boundary as well as interior elements. Quadratic isoparametric elements and quadratic isoparametric or constant elements are employed for the boundary and interior discretization, respectively. Both free and forced vibrations are considered. The free vibration problem is reduced to a matrix eigenvalue problem with matrix coefficients independent of frequency. The forced vibration problem is solved with the aid of the Laplace transform with respect to time and this requires a numerical inversion of the transformed solution to obtain the plate dynamic response to arbitrary transient loading. The effect of external viscous or internal viscoelastic damping on the response is also studied. The proposed method is compared against the direct boundary element method in conjunction with the dynamic fundamental solution as well as the finite element method primarily by means of a number of numerical examples. These examples also serve to illustrate the use of the proposed method.
An upwind method for solving transport–diffusion–reaction systems
Authors: Bermudez A. , Durany J. , Posse M. , Vázquez C. 
Published: August 2005

AbstractA combination of the characteristics method and finite elements techniques is applied to solve a coupled heat transfer–chemical reaction system in the stationary case. The solution of the non‐linear discretized system is obtained by using Newton's algorithm. Finally, numerical results for several problems are presented to test the accuracy and stability of the method.
Efficient approximation concepts using second order information
Authors: Fleury Claude 
Published: August 2005

AbstractThe primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems. The basic idea is to generate such an information at the expense of only one more ‘virtual load case’ in the sensitivity analysis part of the finite element code. To achieve this goal a primal–dual approach is employed, that can also be interpreted as a sequential quadratic programming method.Another objective is to relate the proposed method to the well known family of approximation concepts techniques, where the primary optimization problem is transformed into a sequence of non‐linear explicit subproblems. When restricted to diagonal second derivatives, the new approach can be viewed as a recursive convex programming method, similar to the ‘Convex Linearization’ method (CONLIN), and to its recent generalization, the ‘Method of Moving Asymptotes’ (MMA).This new method has been successfully tested on simple problems that can be solved in closed form, as well as on sizing optimization of trusses. In all cases the method converges faster than CONLIN, MMA or other approximation techniques based on reciprocal variables.
A study of stabilization and projection in the 4‐node Mindlin plate element
Authors: Wang Xiao‐Jun , Belytschko Ted 
Published: August 2005

AbstractIn this paper, a Mindlin plate element is formulated based on the Hellinger–Reissner principle and the γ‐technique. The stiffness consists of a constant stress (one‐point quadrature) matrix and a stabilization matrix. The stabilization matrix is compared with those previously proposed. In addition, the element uses a projection to modify the nodal displacements so that the patch test is satisfied. The projection matrix is based on a mode decomposition. Several numerical cases are presented, and it is shown that the mode decomposition projection is necessary both for satisfaction of the patch test and convergence.
An improved procedure for solving transient heat conduction problems using the boundary element method
Authors: Davey K. , Hinduja S. 
Published: August 2005

AbstractIn employing the boundary element method to solve transient heat conduction problems, domain integrals need to be calculated. These integrals can be calculated either by directly discretizing the domain, or indirectly by utilizing a time‐marching scheme which requires the time integrations to be evaluated from the initial time. Although the second approach overcomes the need for domain discretization, it has the disadvantage of requiring large storage and CPU time for increasing number of time steps.This paper is concerned with a procedure which approximates the domain integrals without the need for domain discretization. The time‐marching scheme is employed so that the domain integrals can be calculated at a particular time with a known weighting and temperature distribution. These integrals can then be utilized to approximate similar domain integrals with a different weighting. It is shown that the method proposed dramatically reduces the storage requirements and CPU time, even for a small number of time divisions.
Modal parameter identification using Z‐transforms
Authors: Mickleborough N. C. , Pi Y. L. 
Published: August 2005

AbstractA method for the time domain identification of modal parameters of a vibrating structure using Z‐transformation sequences is presented in this paper.This identification proceeds using the Z‐transfer function of a vibrating structure from which an auto‐regressive and moving‐average (ARMA) model of the vibrating structure is derived. From this ARMA model and time domain data, the modal parameters can be identified. The time domain data can be obtained from single point or multiple shaker excitation modal testing. To demonstrate the application and efficiency of the method, a test on a simulated cantilever beam is presented.
Numerical analysis of crack‐tip fields using the hodograph transformation
Authors: Silling S. A. 
Published: August 2005

AbstractA numerical method is discussed for analysis of anti‐plane shear crack‐tip fields in linear and non‐linear materials, including possible anisotropy. The method is based on the hodograph transformation. It allows efficient computation of singular stress fields because the transformed partial differential equation to be solved numerically is linear. The inversion of the transformation is also done numerically. The method is promising for the study of localizations, since regions with the largest stress gradients are automatically discretized with the finest mesh owing to the nature of the transformation.
The use of profile reduction algorithms with a frontal code
Authors: Duff I. S. , Reid J. K. , Scott J. A. 
Published: August 2005

AbstractWe study profile reduction algorithms when used to order the elements for the frontal solution of a system of linear equations with a symmetric sparsity pattern. We consider two distinct procedures for producing an efficient element ordering; one based on assembling the pattern of the finite‐element matrix, reordering the variables and using the new variable order to resequence the elements, and the other based on generating adjacency lists for the elements themselves and reordering the elements directly.We compare the results of using several variants of these algorithms in conjunction with the Harwell frontal code, MA32, on the CRAY‐2 for a range of practical problems. We find that, given suitable enhancements, both approaches are practical and neither is consistently superior to the other.