bluuebunny/crossref_metadata_2025_split huggingface dataset:
Improving the efficiency of incomplete Choleski preconditionings
Authors: Papadrakakis Manolis , Dracopoulos Michael C. 
Published: August 2005

AbstractTechniques based on the idea of preconditioning have significantly improved the efficiency of classical iterative methods. In this work two preconditioning approaches based on incomplete Choleski factorization have been further refined, with the result that both storage requirements and solution times have been greatly improved. The first is based on the rejection of certain terms of the factorization process according to their magnitude. An efficient computational handling of the incomplete factorization is proposed which improves substantially the complicated addressings and the overall efficiency of the iterative method. The second preconditioning matrix is based on a rejection criterion relative to the position of the non‐zero terms of the coefficient matrix. Such preconditioners have been proposed in the past but experience with the application of the finite‐element method is not favourable since the factorization very often becomes unstable or the rate of convergence is not satisfactory. The modifications proposed here give this type of incomplete factorization both robustness and efficiency.
Beam cantilevered from elastic support: Finite‐element modelling
Authors: Cook Robert D. 
Published: August 2005

AbstractA beam, modelled by standard beam elements, is to be connected to a plane, which is modelled by quadrilateral elements. Beam elements include rotational d.o.f. but quadrilateral elements do not. The connection is made by extending the beam into the plane by an additional beam element. Herein we present a formula for the stiffness of the additional beam element so that the elasticity of the support is properly represented.
A simple quadrilateral shear panel element
Authors: Chen Harn C. 
Published: August 2005

AbstractA shear panel element of general quadrilateral shape is so formulated that it assumes a state of constant shear flow. This is achieved by using isoparametric shape functions to approximate the displacement field and then using the mean of the strain‐displacement matrix to evaluate shear strain and the resulting stiffness matrix. Numerical examples show that the element reproduces analytical solutions when its shape is rectangular and behaves satisfactorily when its shape is not rectangular.
On the relation of the cell discretization algorithm to the primal hybrid finite element method
Authors: Coffey Mark W. 
Published: August 2005

AbstractWe point out the connection between the cell discretization algorithm and the primal hybrid finite‐element method. There is a very close relationship between these two non‐conforming methods. In particular, an important result between Lagrange multipliers and normal derivatives obtains in both cases. Sample numerical evidence verifying this connection is presented for a simple two‐dimensional elliptic problem.
On shock capturing for pure water with general equation of state
Authors: Cooke Charlie H. , Chen Tze‐Jang 
Published: August 2005

AbstractThe numerical investigation of shock phenomena in gas or liquid media where enthalpy is the preferred thermodynamic variable poses special problems. When an expression for internal energy is available, the usual procedure is to employ a splitting scheme to remove source terms for the Euler equations, then upwind‐biased shock capturing algorithms are built around the Riemann problem for the conservative system which remains. However, when the governing equations are formulated in terms of total enthalpy, treatment of a pressure–time derivative as a source term leads to a Riemann problem for a system where one equation is not a conservative law. The present research establishes that successful upwind‐biased shock capturing schemes can be based upon the pseudoconservative system. The method is applied to numerical simulations of shock wave propagation in pure water.
Indefinite elliptic problem preconditioning
Authors: Vassilevski P. S. 
Published: August 2005

AbstractBased on investigating the eigenvalue distribution of the preconditioned matrices that arise in the finite‐element discretization of indefinite elliptic problems with preconditioning matrices, constructed on the basis of the principal coercive part of the considered elliptic problems, it is proved that the Krylov subspace CG‐type methods like MINRES converge with a rate of convergence determined only by the stability properties of the discrete problem in terms of a priori estimates and the accuracy of the preconditioning matrix with respect to the principal coercive part of the considered finite‐element stiffness matrix. This is also demonstrated by numerical experiments. The method is of practical interest if there are only a few negative eigenvalues.
On the damping ratio of multi‐degree‐of‐freedom systems
Authors: Man Liu , Wilson J. M. 
Published: August 2005

AbstractThe damping parameter is commonly used when assessing a vibration system or analysing dynamical response, as well as reducing vibration levels. A basic step towards analysing a damped system is to solve its complex eigenvalues. However, the solution is computer‐time‐consuming. An alternative way is to get the damping ratio matrix so that the behaviour of the system in each mode can be determined. This paper presents a simple means of identifying the corresponding relation between the mode number and its damping ratio by a matrix perturbation method which leads to the transformation perturbation or TP method. The equivalence of the complex eigenproblem of damped systems and transformed damping matrix in calculating the damping ratios is also discussed.
On stress intensity factor computation from the quarter‐point element displacements
Authors: Lim I. L. , Johnston I. W. , Choi S. K. 
Published: August 2005

AbstractIn conjunction with the quarter‐point element, a wide range of stress intensity factor computation techniques may be employed. Of these, the displacement correlation technique (DCT) and the quarter‐point displacement technique (QPDT) have been in common use. It has been suggested by various investigators that the DCT is more rational in formulation and should therefore be more accurate than the QPDT. However, published numerical studies provide conflicting results on the relative performance of either technique. To resolve this anomaly, this study provides a detailed investigation on the DCT and QPDT performance. On the basis of considering the second term in Westergaard's expression and supported by numerical experiments, it is concluded that the QPDT would generally perform better than the DCT.
Note on sensitivity analysis to improve eigenvalue analysis
Authors: Chen Lien‐Wen , Ku Der‐Ming 
Published: August 2005

AbstractThe stability behaviour of a cantilever beam, carrying a concentrated mass at the free end and subjected to a uniformly distributed follower force, is studied by the finite‐element method. In the present finite‐element formulation, the Timoshenko beam theory is utilized to derive the governing equations of motion. In order to more quickly and efficiently obtain the critical load for such a non‐conservative system, a numerical technique which utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial‐and‐error technique. The high accuracy and rapid rate of convergence through the combination of the present finite‐element model and the numerical algorithm are demonstrated with the numerical example given.
Application of PLTMG to a stream function problem
Authors: Mooney J. R. 
Published: August 2005

AbstractThe finite‐element package PLTMG was designed to solve a wide variety of non‐linear, scalar elliptic PDEs. In this paper we examine the application of PLTMG to the solution of a potential flow problem using the stream function formulation. The flow problem is that of irrotational steady flow through a shallow lake with prescribed inflows and outflows. A two‐dimensional (vertically integrated) model is used. One or more islands may be present. The paper focuses on the advantages of the stream function formulation for obtaining accurate streamlines and partial residence times as opposed to using a potential function formulation. If islands are present the stream values at the island boundaries are unknowns which must be determined to fulfil a condition of zero circulation round each island. Thus, if N islands are present, an N‐fold linear continuation must be performed to determine the solution.
Hierarchical modelling of discontinuous fields
Authors: Fish J. 
Published: August 2005

AbstractA methodology has been developed to hierarchically model discontinuous fields by means of the s‐version of the finite‐element method. This is achieved by overlaying portions of the finite‐element mesh where discontinuities need to be embedded with a finite‐element mesh which is discontinuous across the crack faces (containing unconstrained double nodes along the discontinuity). By this technique crack propagation can be simulated by advancing the crack front in the superimposed mesh only, keeping the base mesh fixed and unaware of the crack existence. The hierarchical structure of the method ensures computational efficiency, especially in linear systems. Numerical experiments for mode I and mixed‐mode problems are presented to validate the present formulation.
Contaminant infiltration into a pressurized tube with a fabric end cap with turbulent external flow
Authors: Robertson S. R. 
Published: August 2005

AbstractA short pressurized tube with a fabric end cap is placed concentrically within a longer, larger tube with a contaminated, turbulent flow. The effects of external velocity and internal pressure on the infiltration of contaminant into the pressurized tube are studied. The SIMPLER finite‐difference method, together with the two equation model of turbulence, is used to model the flow.
A new plate shell element of 16 nodes and 40 degrees of freedom by relative displacement method
Authors: Xu Xing , Cai Ruifeng 
Published: August 2005

AbstractAn isoparametric plate shell element of 16 nodes and 40 degrees of freedom is developed in this paper directly from 3‐D elastic theories. In order to overcome the difficulties caused by straightforward use of a 3‐D formulation, the relative displacement method is introduced. For curved shell elements, the use of the orthogonal curvilinear co‐ordinate system greatly reduces the computer effort. The new element can conveniently solve shell problems with variable thicknesses and also easily link with other finite elements using displacement d.o.f. such as 8‐node to 21‐node 3‐D elements. Numerical examples demonstrate the efficiency of the element.
Performance of a Hermitian element for a beam with rotational constraints
Authors: Wisniewski K. , Turska E. , Schrefler B. A. 
Published: August 2005

AbstractThe behaviour of a Hermitian two‐node element based on the Bernoulli beam equation is examined. The assumed constraints generate rotation‐dependent distributed moments. It is shown that for these moments a potential exists, and that a rigid translation is the only rigid body mode of the element. The analysis of the Bernoulli equation demonstrates that very large values of α= e/EI enforce the condition w,x = 0, resulting in displacements equal to zero. The element is examined for two types of constraints. The first type of constraint, diminishing rotations of a beam (α < 0), yields regular solutions which, however, seem to have a non‐differentiality near the end of the beam. A special procedure is developed to evaluate analytical solutions for long beams or stiff constraints, for which computer accuracy is exceeded. For the second type of constraint, enlarging rotations of a beam (α > 0), a highly oscillatory nature of the solution is proven.
Perturbation based on boundary‐element technique in structural vibration analysis
Authors: Liu Han‐Bing , Chen Su‐Huan , Liu Zhong‐Sheng 
Published: August 2005

AbstractThis paper, based on the boundary‐element technique, presents a perturbation method which can be applied to reanalysis of the eigenvalues and eigenvectors in an elastic structure. Regarding the shape changes of a structure as the perturbation of its surface nodes within the neighbourhood of the given values, this method uses the perturbation formula to obtain the eigensolutions of the modified system without solving the generalized eigenvalue problem. Finally, the authors give some sample examples to demonstrate the validity of the method.
The application of a numerical model of heat and mass transfer in unsaturated soil to the simulation of laboratory‐based experiments
Authors: Thomas H. R. , King S. D. 
Published: August 2005

AbstractA numerical model of coupled heat and mass transfer in unsaturated soil, recently proposed by the authors, is used to simulate a laboratory‐based experimental test. The modelling approach adopted is based on the use of the capillary potential and the temperature as independent variables. The experimental results have recently been presented in the literature by other workers. Very good correlations are obtained of both steady‐state values of variables and the times required to reach steady‐state conditions. The results achieved lend confidence to the numerical modelling approach proposed and extend the range of applications of the model hitherto achieved to that of a further generic soil type, namely a silt.
Incompressible viscoplastic flow analysis using a quadrilateral 2‐D element based on mixed interpolation of tensorial components
Authors: Dvorkin Eduardo N. , Canga Marcelo E. 
Published: August 2005

AbstractIn the Eulerian description of metal forming operations usually rigid/incompressible viscoplastic material models are used. In this paper a quadrilateral 2‐D finite‐element formulation for incompressible viscoplastic flow analysis is developed. The element (QMITC) is based on mixed interpolation of tensorial components, and the incompressibility constraint is imposed via the penalty method. It is shown that the resulting element does not lock either in plane strain rate flows or in axisymmetric flows, that the oscillations in the pressure predictions (checkerboard) tend to zero when the mesh is refined and that the solutions for some typical benchmark problems are very accurate.
Solution of the advection–diffusion equation using the spline function and finite elements
Authors: Szymkiewicz R. 
Published: August 2005

AbstractThis paper deals with the solution of the one‐dimensional advection–diffusion equation. The method of solution is based on the process‐splitting technique. The transport equation is split up into the advection part and the diffusion part at every time step. The advection transport equation is solved by a method of characteristics using a spline function for interpolation. This solution approach proves to be very effective because it reduces numerical dispersion and wiggles. The diffusion equation is solved by the standard Galerkin finite‐element method. A comparison of calculations with the results of Holly and Preissmann and with analytical solutions demonstrates the great accuracy of the proposed method.
An element error indicator and a related stress‐improvement procedure
Authors: Cook Robert D. 
Published: August 2005

AbstractA posteriori error indicators for strain energy error in finite‐element solutions have recently been shown to be effective. A popular error indicator, usually denoted by η, makes use of ‘error energy’, i.e. strain energy associated with the difference between the conventional element stresses σ and a smoothed stress field constructed from σ. It is intended that η be constructed by summing element contributions and that it be applied at the global level. The present study suggests that an error indicator applicable at the element level can be obtained by combining an element value of η with information about stress gradient and strain energy density. It is also shown how the stress gradient information can be used to obtain more accurate stresses at mesh boundaries.
Bandwidth reduction of rectangular matrices
Authors: Kaveh A. 
Published: August 2005

AbstractTwo graph‐theoretical algorithms are developed for bandwidth reduction of rectangular matrices. A K‐total graph is defined for a selected cycle basis, generalized cycle basis and cut set basis of a graph. This transforms a simultaneous ordering of the elements of a basis and members of a graph into that of a nodal numbering of its K‐total graph.The first algorithm uses the K‐total graph and results in banded equilibrium and self‐stress matrices. The second employs a nodal ordering algorithm followed by a member ordering process. This algorithm can be used for optimizing the bandwidth of member‐cocycle incidence matrices, resulting in banded equilibrium matrices.
An efficient wave input procedure for infinite media
Authors: Zhao Chongbin , Valliappan S. 
Published: August 2005

AbstractAn efficient wave input procedure in the finite and infinite element coupled model is presented in this paper. Compared to the previous wave input method, the main advantage of the present wave input procedure lies in its computational efficiency because only a small region of the medium needs to be modelled by finite elements. The equivalence between the present wave input procedure and the previous one has been theoretically proven when a harmonic wave propagates vertically in an isotropic homogeneous elastic half‐space. In addition, the accuracy of the present wave input method has been evaluated based on the solutions obtained for SH‐wave, SV‐wave and P‐wave scattering problems in a semicircular canyon for which analytical solutions are already available.
Generalized conforming quadrilateral plate element by using semi‐loof constraints
Authors: Zhifei Long 
Published: August 2005

AbstractA 12‐DOF quadrilateral element for plate bending is formulated based on the concept of generalized compatibility and semi‐Loof constraints. The element DOFs are defined with the conventional displacements at corner nodes and the semi‐Loof constraints are used in the formulation. This element is a generalized conforming one which passes Irons' patch test and can be used to solve problems with complicated boundaries. When overall considerations of simplicity, accuracy and reliability are taken into account, this new element is one of the best 12‐DOF quadrilateral plate‐bending elements currently available.
The Gauss–Laguerre quadrature rule for finite‐part integrals
Authors: Ioakimidis N. I. 
Published: August 2005

AbstractThe classical Gauss–Laguerre quadrature rule for the semi‐infinite integration interval [0,∞] is modified and applied to the case of the weight function exp(‐x)/x corresponding to finite‐part (or, equivalently, hypersingular) integrals. The new set of orthogonal polynomials is constructed and it is seen to consist of linear combinations of the classical Laguerre polynomials with appropriately determined coefficients. The zeros of these modified Laguerre polynomials are seen to be distinct, but one of these lies outside the integration interval. Formulae for the corresponding weights are also given and numerical values and results are presented. The present results generalize the corresponding results for the finite interval [0,1] to semi‐infinite intervals and they are applicable to a variety of applied mechanics and related problems, where finite‐part integrals appear in a natural way.
Iterative method of integral relations scheme for wake flows
Authors: Yang R.‐J. , Yeung W.‐S. 
Published: August 2005

AbstractThe orthonormal method of integral relations (MIR) is extended to calculate wake flow problems. Two previous difficulties are overcome: (1) the non‐constant integral domain is eliminated by introducing a linear transformation in the formulation; (2) the difficulty associated with determining unique orthonormal weighting functions is overcome by an iterative scheme. The new formulation is applied to calculate a wake flow. A high‐order solution for N up to 4 is obtained with relative ease.
The construction of nearly orthogonal multiblock grids for compressible flow simulation
Authors: Marchant M. J. , Weatherill N. P. 
Published: August 2005

AbstractA method is described whereby structured multiblock meshes can be constructed from the solution of elliptic partial differential equations and which possess the property of orthogonality close to boundaries and near orthogonality within the domain. To construct grids for viscous flow simulations which have appropriate point distributions close to solid boundaries these grids are used with point redistribution formulations. The result is high‐quality grids for use with both inviscid and viscous flow simulation algorithms. Examples using the approach are given, and these include grids for single and multicomponent aerofoils and bluff bodies.
Numerical solution of regularized long‐wave equation
Authors: Jain P. C. , Shankar Rama , Singh T. V. 
Published: August 2005

AbstractA combination of the splitting method and the cubic spline technique has been used to solve a non‐linear regularized long wave (RLW) equation. The accuracy and the stability of the proposed method are discussed. Then, two numerical examples are solved to illustrate the robustness of the algorithm. The results are in good agreement with the available results.
Iterative solution of the stream function–vorticity equations using a multigrid solver with finite elements
Authors: Davis M. B. , Carey G. F. 
Published: August 2005

AbstractThe solution of the stream function–vorticity equations is developed using a multigrid method to improve efficiency in a finite‐element p‐method. The equations are discretized using 2‐D Lagrange finite elements (linear, quadratic and cubic) and solved in iteratively decoupled form using successive approximation and continuation methods. The comparative performance of several multigrid and direct matrix solvers is investigated with respect to convergence characteristics and time performance on the Cray Y‐MP.
Stability of the multiple reciprocity method for transient heat conduction
Authors: Ramesh Palghat S. , Lean Meng H. 
Published: August 2005

AbstractThe multiple reciprocity method is based on using higher‐order fundamental solutions to eliminate domain integrals encountered in transient boundary integral formulations. The paper considers the numerical stability of this approach through an eigenvalue decomposition of the system matrix. We demonstrate that the multiple reciprocity method for transient heat conduction is stable only for appropriately chosen time steps.
Computation of outflow flux for convection‐dominated transport equations
Authors: Semper Bill 
Published: August 2005

AbstractAn a posteriori point‐wise outflow flux recovery scheme which capitalizes on the hyperbolic nature of convection‐dominated transport models is proposed. The scheme is seen to be robust in that it can be applied to any upwind finite‐difference or finite‐element approximation, and gives a superconvergent approximation to the outflow flux.
Multi‐level iterative technique and aggregation concept with semi‐analytical preconditioning for solving boundary‐value problems
Authors: Bulgakov V. E. 
Published: August 2005

AbstractSome iterative multi‐level approaches for solving large‐scale finite‐element elliptic problems are proposed. It is suggested that these approaches be used in combination with an aggregation technique. On the basis of the aggregation concept a new efficient preconditioning procedure in the inner iterative scheme of the algorithm is developed. This procedure is derived from the fundamental solution of a corresponding elliptic problem. The efficiency of the approaches is demonstrated by numerical examples.