bluuebunny/crossref_metadata_2025_split huggingface dataset:
Exploiting the physical symmetry of regular mesh in substructuring analysis
Authors: Lam Y. C. , Xiao‐Lin Liu 
Published: August 2005

AbstractA new technique of multi‐level substructuring based on a regular mesh is presented. The technique takes advantage of the physical symmetry and repetitivity generated by the regular mesh. A special node‐numbering/addressing system is developed to exploit the symmetry which results in the stiffness matrices not only being symmetrical about the leading diagonal, but a regular pattern emerging with respect to the other diagonal. The same pattern exists for their inverses. A new condensation scheme is used to take full advantage of the regular patterns. As a result, only about a quarter of the stiffness matrices and their inverses need to be processed, as compared to half when using the conventional method.Based on the technique, a two‐dimensional finite‐element analysis program FEMSUB has been implemented in the University's VAX network. Through a number of numerical tests, it is discovered that the new technique can result in savings of both core storage and computing time. The savings become more significant when the scale of a problem increases. The investigation indicates that the core storage requirement decreases when using substructures of higher levels. However, for computational efficiency, both the level of substructuring and the number of repeated substructures have an effect. Thus, a dimensionless parameter R (number of substructures used/maximum number of substructures) has been introduced to correlate the effect of the technique on computational efficiency.
A mapping of multi‐level problems to multi‐dimensional crossbar networks
Authors: Kolp Otto 
Published: August 2005

AbstractMappings are discussed from m‐dimensional process spaces to n‐dimensional crossbar networks which preserve the nearest‐neighbour relation between processes, i.e. neighboured processes are mapped to processors connected by a common crossbar. Even in the case of multi‐level process structures, a neighbouring relation between processes can be derived such that the neighboured processes can communicate directly.
Fast adaptive composite grid methods on distributed parallel achitectures
Authors: Lemke Max , Quinlan Daniel 
Published: August 2005

AbstractThe fast adaptive composite grid method (FAC) is an algorithm that uses uniform grids, both global and local, to solve partial differential equations. This method is known to be highly efficient on scalar or singe‐processor vector computers, due to its effective use of uniform grids and multiple levels of resolution of the solution. On distributed memory multiprocesssors, such methods benefit from their tendency to create multiple isolated refinement regions, which may be effectively treated in parallel. However, they suffer from the way in which the levels of refinement are treated sequentially in each region. Specifically, the finer levels must wait to be processed until the coarse‐level approximations have been computed and passed to them; conversely, the coarser levels must wait until the finer level approximations have been computed and used to correct their equations.The asynchronous fast adaptive composite method (AFAC) eliminates this bottleneck of parallelism. Through a simple mechanism used to reduce interlevel dependence, individual refinements levels can be processed by AFAC in parallel. The result is that the convergence rate of AFAC is the square root of that for FAC. Therefore, since both AFAc and FAC have roughly the same number of floating‐point operations, AFAC requires twice the serial computational time as FAC, but AFAC, may be much more efficiently parallelized.This paper presents a comparison of FAC and AFAC under a variety of conditions, including vectorization and parallelization. Results are presented for distributed memory multiprocessor architectures (SUPRENUM, Intel iPSC/2 and iPSC/860). The most crucial factor for the evaluation of both algorithms is the different computation/communication cost ratios of these architectures. It is shown that, under many circumstances, AFAC is superior to FAC in a parallel environment.
An efficient multigrid scheme for elliptic equations with discontinuous coefficients
Authors: Liu C. , Liu Z. , McCormick S. 
Published: August 2005

AbstractAn efficient multigrid scheme for elliptic equations with jump discontinuous coefficients is presented. It is based on a cell‐centred grid and finite‐volume method, with the diffusion coefficients at the jump interface being determined by a flux conservation condition. The diffusion coefficients on coarse grids are calculated by a simple restriction of the coefficients from the fine grid. An efficient interpolation operator, which is constructed by the so‐called effective area law, is developed. Computational results for a two‐dimensional scalar elliptic equation and for two‐phase porous media flow show that the new scheme achieves multigrid efficiency typical of the constant‐coefficient case.
Resolution of moving fronts using the self‐adaptive time‐dependent fast adaptive composite grid method
Authors: McKay S. M. , Thomas J. W. 
Published: August 2005

AbstractThe fast adaptive composite grid method (FAC) is a discretization and solution method design to achieve efficient local resolution by constructing the discretization based on various regular grids and using these grids as a basis for fast solution. FAC is designed so as to share all of the attributes of the composite grid and multigrid methods. As is the case for most mesh refinement schemes, it is advantageous to optimally choose the grids so as to save both storage and computational costs. The FAC method has previously been shown to be an effective tool in obtaining numerical solutions of many types of steady problems. In addition time‐dependent problems with stationary fronts or singularities have also been resolved efficiently with FAC. An adaptive scheme has been developed and implemented that, based on given error tolerances, calculates the optimal time discretization and locates the spatial regions where more resolution is needed. Patches are set up to be used by the various FAC algorithms. The spatial refinement scheme is able to track areas of resolution which move across the domain, allowing for small composite grids at each time step.
Numerical investigation of convection/diffusion phase change of a metal with temperature‐dependent viscosity
Authors: Esikova N. B. , Iliev O. P. , Vabishchevich P. N. 
Published: August 2005

AbstractHeat and mass transfer during crystallization in a square cavity, involving natural laminary convection of liquid metal with temperature‐dependent viscosity, are investigated numerically on a grid with 51 × 51 nodes. A brief survey of existing techniques for convection/diffusion phase change problems is given. A fixed grid numerical methodology, based on the fictitious regions method, is used for solving the 2‐D Stefan problem coupled with the Navier–Stokes equations in the Boussinesq approximation. The viscosity variation is modelled by an exponential form, ν/ν0 = exp ( – α(T – 1)). The influence of the Grashof number and of the parameter α on heat and mass transfer are investigated.
A higher‐order accurate Petrov–Galerkin finite‐element method for elliptic boundary‐value problems
Authors: MacKinnon R. J. , Johnson R. W. , Langerman M. A. 
Published: August 2005

AbstractWe formulate a higher‐order (superconvergent) Petrov–Galerkin method by determining, using a finite‐difference approximation, the optimal selection of quadratic and cubic modifications to the standard linear test function for bilinear elements. Application of this method to linear elliptic problems results in improved accuracy and higher rates of convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are given.
Generalized conforming triangular elements for plate bending
Authors: Zhifei Long 
Published: August 2005

AbstractBased on the modified principle of potential energy, three triangular thin‐plate elements with nine degrees of freedom (LZ1, LZ2 and LZ3) are derived by using compatibility conditions for nodal deflection at each node and generalized compatibility conditions for average deflection and average normal slope along each side of the element. These generalized conforming elements are low‐order and high‐precision elements which pass the patch test. When overall considerations of accuracy, simplicity and reliability are taken into account, these new elements are the best 9‐DOF triangular thin‐plate elements currently available.
Modified Lanczos method for solving large sparse linear systems
Authors: Mai Tsun‐Zee 
Published: August 2005

AbstractGeneralized conjugate gradient methods are often used to solve large sparse non‐symmetric linear systems. Such systems often arise in the numerical solution of convection–diffusion problems. The Lanczos/Orthodir method proposed by Jea and Young suffers the roundoff error problem. In this paper a modified Lanczos/Orthodir method is considered. The modifications are based on Paige's computational procedure and on the adaptive restarting procedure. Numerical results showed that the modified Lanczos/Orthodir method is more stable than the original version. Furthermore, with the adaptive restarting scheme the method performed much better than the Lanczos/Orthomin method.
Crack propagation in tooth root with variable loading
Authors: Flašker Jože , Pehan Stanislav 
Published: August 2005

AbstractThe paper describes the numerical method for calculating the crack propagation in the tooth root of a case‐hardened and hardened gear. The method is based on the linear elastic fracture mechanics taking into account the total values of loadings and properties of the individual layers of the gear material. The main points are the determination of the stress intensity factor and the numerical calculations of the crack propagation, crack speed and path1.
A comparison of TVD Lax–Wendroff methods
Authors: Rider William J. 
Published: August 2005

AbstractThis paper compares two formulations of Lax–Wendroff TVD methods. The basis of comparison is to the results of several test problems providing both qualitative and quantitative results. Results show that using an upwind biased limiter provides higher resolution of both smooth and discontinuous solutions from a lower amount of induced numerical viscosity. The conclusion is that a limiter should have as small a support as possible in order to limit its effects if high resolution is the object.
On a numerical solution of a class of partial differential equations of mixed type, not adding artificial terms
Authors: Pogu M. , De Cursi J. E. Souza 
Published: August 2005

AbstractA relaxation‐like method for the numerical solution of a class of partial differential equations of mixed type is presented. The equations of this class have not yet been solved by functional outlines. The numerical method does not add artificial terms to the original equation.
How to deal with hypersingular integrals in the symmetric BEM
Authors: Holzer S. 
Published: August 2005

AbstractThe symmetric boundary‐element method for mixed boundary‐value problems is currently gaining increasing interest as it permits the derivation of symmetric matrices. It is even possible to obtain positive‐definite finite‐element stiffness matrices for BEM subregions, and therefore the method provides a very straightforward coupling to the finite‐element method (FEM). The BEM subregions can be handled like FEM substructures in a domain decomposition context. The symmetric BEM uses the full set of integral representations for the 2n types of boundary data for self‐adjoint problems of order 2n and solves them in a weighted residual (Galerkin) sense. The main difficulty of the method is caused by the need to compute hypersingular integrals arising from the integral representations of the Neumann boundary data. It is the object of the paper to show that, for 2‐D problems on polygonal domains, these hypersingular integrands pose no problem at all, even for higher‐order approximations. The present approach makes use of analytical integrations as far as possible. The integrals of the hypersingular expressions are derived completely within the framework of simple engineering mathematics. The problem is reduced to the computation of weakly singular integrals even for C0 continuous approximations.
Self‐adaptive finite‐element simulation of bipolar, strongly reverse‐biased pn‐junctions
Authors: Kornhuber Ralf , Roitzsch Rainer 
Published: August 2005

AbstractThe potential distribution of bipolar, strongly reverse‐biased pn‐junctions can be described by a double obstacle problem for the Laplacian. The problem is solved by a self‐adaptive finite‐element method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse‐biased pn‐junction with multistep field plate and stop electrode to illustrate its efficiency and reliability.
A simple local error estimator and an adaptive time‐stepping procedure for direct integration method in dynamic analysis
Authors: Li X. D. , Zeng L. F. , Wiberg N.‐E. 
Published: August 2005

AbstractA simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher‐order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post‐processing technique. Accordingly, an adaptive time‐stepping procedure, which automatically adjusts the time‐step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single‐DOF problems, a two‐DOF problem and a multi‐DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
Numerical solution of Burger's equation
Authors: Mittal R. C. , Singhal Poonam 
Published: August 2005

AbstractIn the present paper numerical solutions of the one‐dimensional Burger equation are obtained. The technique of finitely reproducing non‐linearities introduced by Bazley is used. This technique when applied to Burger's equation gives a method where a system of non‐linear ordinary differential equations is to be solved. The present method produces very accurate results in comparison to finite‐difference of finite‐element methods.
Standard eigenvalue analysis by boundary‐element method
Authors: Kamiya N. , Andoh E. 
Published: August 2005

AbstractA method for analysing eigenvalues of the Helmholtz equation using a standard existing subroutine for eigenvalue determination is developed in this paper. It is based on the boundary integral equation formulation known as the multiple reciprocity method (MRM). The above‐mentioned formulation, having polynomial matrices in terms of the eigenvalue as the coefficient matrices, is transformed into the standard‐type eigenvalue problem. The resulting formulation makes it possible to determine the required eigenvalues only by boundary discretisation without any initial rough estimation.
Trefftz‐like numerical method for linear boundary‐value problems
Authors: Khokhlov A. V. 
Published: August 2005

AbstractA generalized Trefftz method for solution of linear boundary‐value problems for partial differential equation sets is presented. An approximate solution is constructed as a linear combination of basis functions satisfying the differential equations involved and forming a complete sequence. Unknown factors are determined through minimizing some norm of the approximate solution boundary‐value deviation from the current boundary data. A unified formulation constitutes the foundation for various modifications and particular applications.The approach enables one to: reduce the problem geometrical dimensionality by one; construct a smooth approximate solution satisfying the governing differential equation; use a universal set of approximating functions for problems with identical equations and varying in boundary conditions; develop a closed, semi‐analytical computational algorithm requiring small input and producing extremely high output accuracy; obtain approximate solution error bounds in inner points via its deviation from prescribed values on the boundary and easily control the degree of accuracy of the numerical results by the residual values at boundary points; treat solution singularities caused by singular boundary conditions precisely.The technique developed has proved to be effective in fluid mechanics, elastostatics, Saint‐Venant's theory for torsion and bending prisms, potential and elastic plate bending problems.
Efficient three‐dimensional model of rolling using an explicit finite‐element formulation
Authors: Edberg Jonas , Lindgren Lars‐Erik 
Published: August 2005

AbstractRolling is simulated by a three‐dimensional finite‐element model with elastoplastic constitutive equations. The use of an explicit finite‐element formulation, instead of the more commonly used implicit formulation, has reduced the required computing time. The larger of the models used is one step towards a general and complete computational model of rolling. Results from experiments and from two‐ and three‐dimensional calculations are compared.
Simple curved shear beam elements
Authors: Choi Jong Keun , Lim Jang Keun 
Published: August 2005

AbstractWe have developed two curved beam elements with two nodes, CSCC and CSLC, based on Timoshenko's beam theory and the curvilinear co‐ordinate system. These curved beam elements have been modified from the conventional strain element, which has been applied only to Euler beam analysis. Therefore they do not have any spurious constraints and locking characteristics. They also show rapid and stable convergence on the wide ranges of beam length to height ratio for linear and non‐linear analyses.
Some remarks on post‐processing and negative norm estimates for approximations to non‐smooth solutions of hyperbolic equations
Authors: Bales Laurence A. 
Published: August 2005

AbstractSome formulae and an error estimate for post‐processing approximations to solutions of hyperbolic partial differential equations are derived. The post‐processing is applied to a fully discrete approximation of the discontinuous solution of an initial boundary‐value problem for the wave equation in one space dimension to reduce oscillations and construct a much more accurate approximation to the solution.
Application of iterative global/local finite‐element analysis. Part 1: Linear analysis
Authors: Whitcomb John D. , Woo Kyeongsik 
Published: August 2005

AbstractIterative global/local finite‐element stress analysis was used to perform linear analysis of two configurations with local damage. One was a tubular joint with local debonding; the other was a fibre matrix unit cell with debonding along part of the interface. The global/local procedure was shown to be both accurate and efficient for both configurations.
BEM analysis of reduced dynamic stress concentration by multiple holes
Authors: Providakis C. P. , Sotiropoulos D. A. , Beskos D. E. 
Published: August 2005

AbstractThe reduction of stress concentration around a circular hole in a dynamically loaded plate by introducing auxiliary holes around the original hole is studied numerically. The solution of this plane stress problem is carried out in the Laplace transformed domain with the aid of the boundary‐element method, and subsequently the time domain response is obtained by numerically inverting the transformed solution. Numerical examples are presented which demonstrate a stress reduction as high as 18 per pent by the introduction of two auxiliary holes in the loading direction for the uniaxial case.
Numerical procedure for calculation of temperature evolution in composite elements with internal cavities
Authors: Luyckx P. , Stienon P. , Franssen J‐M. , Dotreppe J‐C. , Hogge M. 
Published: August 2005

AbstractIn the paper a computation code based on the finite‐element method for temperature evolutions in composite elements with internal cavities is presented. It is suitable for the analysis of various thermal problems encountered in mechanical and civil engineering such as fire risk assessment. It is based on a plane isoparametric triangular element with six nodes allowing the modelling of curved boundaries. In order to analyse composite steel‐concrete elements and to take into account the non‐linearities coming from the temperature‐dependent material properties and from the boundary conditions, an implicit integration scheme is used. Another advantage of the program is the possibility of describing internal cavities with convection and radiation exchanges. In order to show the capacity of the program two examples are presented. Comparisons have been made with experimental and other numerical results, exhibiting very good agreement.
Criteria for eliminating oscillation in analysis of heat‐conduction equation by finite‐element method
Authors: Ouyang Huajiang , Xiao Ding 
Published: August 2005

AbstractIn finite‐element analysis of transient heat conduction, oscillatory results are quite common. Several criteria for eliminating oscillation which permit choice of time step length and/or element mesh and type are sensibly derived and proved with a different methodology from those of previous work. Numerical examples are presented to show their validity and usefulness.
Direct simulation of turbulent flow and heat transfer in a channel. Part II: A Green's function technique for wavy walls
Authors: Rutledge J. , Sleicher C. A. 
Published: August 2005

AbstractThe possibility of improving heat transfer rates by the imposition of a wavy boundary led to this extension of direct simulation of heat transfer in turbulent flow in a channel. This part of the paper shows how a pattern of micro‐riblets on the surface and parallel to the flow is incorporated into the solution of the Navier‐Stokes and temperature equations. The channel is two‐dimensional with walls at different but uniform temperatures, and the fluid properties are constant. The presence of the patterns presents a considerable computational problem that can be largely overcome by the use of a discrete Green function technique. The method is illustrated by making short‐time calculations of the velocity and temperature fields for a Prandtl number of 0.72, a Reynolds number based on channel half‐width and bulk velocity of 2800, and a sinusoidal pattern with a height of 5 wall units.
Numerical procedure for thermal creep stress in mass concrete structures
Authors: Du Chongjiang , Liu Guangting 
Published: August 2005

AbstractIn the paper the experimental results considering the effects of temperature on the elastic modulus and creep of concrete are introduced into the mathematical models of the three‐dimensional finite‐element method to improve the calculation of creep stresses in mass concrete structures. The finite‐element implementation of the exponential algorithm for concrete creep at variable temperatures is studied. The numerical solution procedure for thermal creep stresses in mass concrete structures with temperature effects is presented and a three‐dimensional finite‐element program is developed.