bluuebunny/crossref_metadata_2025_split huggingface dataset:
A method for smoothing derivatives of multilinear finite element fields
Authors: Langtangen H. P. 
Published: August 2005

AbstractAn improved method for calculating smooth derivatives of multilinear finite element fields is presented. The method is also applicable to finite difference schemes. A simple one‐dimensional model problem is discussed analytically, and the new method shows superior behaviour compared to existing popular smoothing techniques. Two‐ and three‐dimensional problems involving isoparametric elements are tested, and the results show improvements over the widely used global least‐squares method, with lumped mass matrix, especially at the boundaries and for non‐uniform meshes.
A fast numerical algorithm for calculating electromagnetic waves in an inhomogeneous slab
Authors: Winter D. F. , Bosley D. L. 
Published: August 2005

AbstractConsider a plane monochromatic electromagnetic wave normally incident on an absorbing dielectric slab, bounded by z = 0 and z = L, and whose electrical parameters ε, μ and σ are arbitrary functions of z. The media on either side of the slab have constant but generally different electrical properties. This paper describes an efficient numerical algorithm for calculating the electromagnetic field within the slab, as well as its absolute reflection and transmission coefficients. The waveform within the slab is represented by a new complex dependent variable satisfying a modified (complex) Helmholtz equation to be solved subject to mixed inhomogeneous conditions at the boundaries of the slab. If derivatives are replaced by nth‐order centred differences, the difference equation set is linear, sparse and efficiently solved by direct recursion. In this paper, complex arithmetic is avoided by replacing the complex Helmholtz equation with two coupled, real, second‐order ordinary differential equations. An algorithm of second‐order accuracy is developed which leads to a bitridiagonal difference equation set. Calculations are carried out for a variable‐property slab problem which can also be solved analytically. Numerical comparisons indicate that the method is accurate and efficient enough that a desk‐top computer is a practical computational machine.
Anomalous convection at low Prandtl number
Authors: Winters K. H. , Jack R. O. 
Published: August 2005

AbstractThe steady‐state natural convection of a fluid of low Prandtl number contained within a two‐dimensional rectangular box is simulated for conditions of an imposed horizontal temperature gradient and conducting horizontal surfaces. By the application of numerical bifurcation and continuation techniques combined with the finite‐element method the solution structure of the steady state equations is determined and a stable anomalous bicellular flow is found. In contrast to the normal unicellular flow that develops smoothly for increasing Prandtl number, the anomalous flow is associated with a disconnected branch that arises at a limit point. The derived solution structure clarifies certain phenomena observed in recent time‐dependent simulations of this problem.
Isentropic flow with cylindrical or spherical symmetry
Authors: Glaister P. 
Published: August 2005

AbstractA numerical scheme is presented for the solution of the equations of isentropic flow in a single spatial co‐ordinate. This includes flow in a duct of variable cross‐section as well as flow with cylindrical or spherical symmetry, and can prove useful when testing codes for the two‐dimensional equations governing isentropic flow. The scheme is applied with success to a problem involving a converging cylindrical shock and to a problem involving the interaction of converging and diverging cylidrical shocks.
A higher‐order method for computing eigenvalues of two‐point boundary‐value problems
Authors: Chawla M. M. , Subramanian R. 
Published: August 2005

AbstractWe present a new finite‐difference method of order h5 for computing eigenvalues of two‐point boundary‐value problems. Our method leads to a generalized seven‐diagonal symmetric and positive‐definite matrix eigenvalue problem.
A unified formulation of two existing time‐domain boundary‐element approaches
Authors: Gallego R. , Dominguez J. 
Published: August 2005

AbstractTwo apparently different time‐domain boundary‐element formulations for plane‐stress/plane‐strain elastodynamic problems exist in the literature. The present paper shows why one of the formulations, which is valid for a particular type of interpolation function, forms part of the other, which can be used with any interpolation function. The main differences presented in the past between the two existing time‐domain boundary‐element methods were based on an incorrect expression of the tractions in the complete plane due to the rectangular impulse load. Results obtained in the past which were presented to evaluate the differences between the two formulations are shown to be incorrect. A compact expression for the fundamental solution integrated along a time step when the time interpolation functions of all the boundary variables are assumed to be piecewise constant is presented. This integral gives the same tractions as those corresponding to a rectangular impulse load.
A variational inequality principle in solid mechanics and application in physically non‐linear problems
Authors: Desong Sha , Huanchun Sun , Zhongding Zhang , Fuxin Yin 
Published: August 2005

AbstractA variational inequality principle which is suitable for various constitutive laws of elasto‐plasticity is given in this paper. Then the variational inequality is reduced to a linear complementary problem by using incremental theory and the finite‐element methods.
The integrity of geometrical boundaries in the two‐dimensional delaunay triangulation
Authors: Weatherill N. P. 
Published: August 2005

AbstractThe Delaunay triangulation has recently received attention as a viable method for construction computational meshes. However, an arbitrary boundary definition which must be preserved in the triangulation process will not, in general, satisfy the geometrical definition on which the Delaunay construction is founded. The effect of this is that the integrity of the given boundary edges will be violated and the computational mesh will not conform to the applied geometrical shape. A method is proposed whereby boundary data are supplemented with points to ensure that imposed boundary edges are preserved during the Delaunay triangulation. The method is illustrated on a geometry of an estuary which exhibits highly complex geometrical features.
Comments on a simple algorithm for the plotting of contours
Authors: Singh Chandan 
Published: August 2005

AbstractWe consider a paper by Stelzer and Welzel (1987) about a new contour lines algorithm. Because of its exactness and its convincing straightforwardness we have tested it and incorporated it into our post‐processing software. This paper describes some aspects we experienced during the numerical experimentation which may be helpful for people considering using the method. Although the cited paper deals with both linearly interpolated isoparametric elements and quadratic ones we have restricted ourselves to the linear type to keep the relationships as simple as possible.
Numerical modelling of crack propagation using multi‐variable and breakable finite elements
Authors: Zhang J. Y. , Hsu T. R. , Wang I. Q. 
Published: August 2005

AbstractIn this study, the advantage of the multi‐variable finite‐element model based on the generalized virtual work principle is described. The model has been applied to the elasto‐plastic fracture analysis with finite deformations. Using the multi‐variable finite‐element model with a‘breakable finite‐element’ concept, the authors proposed an algorithm which can more accurately simulate the crack growth. Numerical examples illustrate that the algorithm presented can be successfully used to predict whether the crack growth is stable or unstable. The rupture effective strain is considered as a fracture criterion, and some comparisons between various criteria are also provided.
Using preconditioned conjugate gradient for solving consecutive linear systems
Authors: Blanc J. Y. , Comon P. , Trystram D. 
Published: August 2005

AbstractOne can point out several applications to the solution of consecutive linear systems with symmetric positive‐definite matrices. Such problems arise, for instance, in signal processing, modellization of grid systems, stress analysis and automatic control. We describe in this paper an efficient and robust method based on an original preconditioned conjugate gradient algorithm, and compare it with the usual methods (Cholesky, modified Cholesky when successive systems are modified by an update of given rank, and incomplete Cholesky factorization) in terms of computational complexity.
A fundamental solution for a plate on an elastic half‐space
Authors: Stolle Dieter F. E. 
Published: August 2005

AbstractThis contribution deals with the development of a fundamental solution for an elastic plate supported by an elastic half‐space. The author briefly discusses problems associated with using an existing fundamental solution, and then develops an alternative solution using an approximate foundation reaction function which is obtained from the concept of equivalent thickness and Boussinesq's solution for an elastic half‐space. The singular solution can be easily incorporated into existing boundary‐element codes, and makes use of material parameters which are directly related to the material properties of each layer. An approximation to the fundamental solution is also suggested. Comparisons between approximate and exact solutions are presented, and limitations are discussed.
An isoparametric finite‐element stokes flow test problem
Authors: Maslanik Miriam K. , Sani Robert L. , Gresho Philip M. 
Published: August 2005

AbstractTwo‐dimensional Stokes flow of an incompressible Newtonian fluid about a horizontal cylinder situated next to a moving wall is presented and suggested as a non‐trivial benchmark problem. Both the primitive variable Galerkin finite‐element and the exact solutions are generated on a sequence of refined meshes; error norms and convergence rates are presented for the C0 bilinear‐velocity/C−1 piece‐wise constant‐pressure and the C0 biquadratic‐velocity/C−1 linear‐pressure quadrilateral elements.
The Jacobian derivative method for three‐dimensional fracture mechanics
Authors: Barbero E. J. , Reddy J. N. 
Published: August 2005

AbstractThis paper presents a new algorithm to compute the distribution of the strain energy release rate along the crack front for three‐dimensional cracks (e.g. surface cracks). The algorithm is economical and accurate. The algorithm is illustrated via two‐dimensional and three‐dimensional examples including a surface crack in a cylinder under internal pressure and side‐grooved compact‐test specimens. It is shown, via specific examples, that only a single, self‐similar virtual crack extension is necesary to accurately compute the strain‐energy release‐rate distribution along the crackfront.
A selective reduced integration triangular plate element
Authors: Ferahi M. , Tabarrok B. , Cleghorn W. L. 
Published: August 2005

AbstractA triangular plate element, allowing transverse shear deformations, is developed in this paper. The element is compatible and employs rotations and slopes as well as lateral deflection as degrees of freedom. Through static condensation it is possible to remove the slopes and form a less complex, incompatible element, involving only the lateral deflection and rotations. Illustrative examples are presented to demonstrate the performance of the element before and after condensation.
Unsteady thermal stress analysis in three‐dimensional problems by means of boundary‐element method
Authors: Ochiai Y. , Ishida R. 
Published: August 2005

AbstractThe boundary integral formulation for unsteady thermal stresses in three‐dimensional quasi‐static problems is proposed. It is shown that three‐dimensional unsteady thermal stress problems can be solved easily without the volume integral by means of the thermoelastic displacement potential and the boundary‐element method. It is also shown that the time integral can be easily carried out analytically. In order to investigate the accuracy of this method, unsteady thermal stress distributions for a cube are obtained.
Location and structure of the nearest singularity of a perturbation series
Authors: Kwok Yue‐Kuen 
Published: August 2005

AbstractThe incompressible potential flow over a perturbed body is used as a model to shed light into the nature of the nearest singularity of a perturbation series. The solutions for various physical quantities are developed as a formal perturbation expansion in powers of a parameter up to 30 terms. The tedious computation is relegated to a computer. The calculations reveal that the location and structure of the nearest singularity of a pertubation series do change with the field point at the which the series is evaluated. Also the radius of convergence and behaviour of the perturbation series do depend significantly on the choice of the physical quantities. These results may provide salutary information for the analysis of computer extended pertubation series.
Space–time partial hybrid stress element for linear elastodynamic analysis of anisotropic materials
Authors: Jing Hung‐Sying 
Published: August 2005

AbstractThe variational basis and finite‐element implementation for the space‐time partial hybrid stress element is presented in this paper. Through convolution integration and dividing the six stress components into flexural (σx,σy,σz,τxy) and transverse shear (τxz, τyz) parts, the Hellinger‐Reissner functional or the total potential energy functional can be modified as the basis for constructing the space‐time partial hybrid stress element. By assuming Hermitian interpolation functions in time, displacement field for flexural stresses, and hybrid stress for transverse shear, the space‐time partial hybrid stress element can be established for linear elastodynamic analysis consistently without any contradiction.
Low‐order mixed method finite elements in non‐linear elasticity
Authors: Goleniewski G. 
Published: August 2005

AbstractA mixed method finite‐element formulation for non‐linear plane‐strain elastic deformations is described. Incompressibility is built in explicitly. All fields have piecewise linear approximants over triangles except pressure, which is taken to be constant over matched pairs of triangles. The code is used in an investigation of the tilting mode of deformation of bonded rubber blocks. In particular the variation of tilting moment with aspect ratio is focused on for a range of tilting angles.
Numerical comparison of momentum interpolation methods and pressure—velocity algorithms using non‐staggered grids
Authors: Kobayashi M. H. , Pereira J. C. F. 
Published: August 2005

AbstractFinite‐volume calculations of laminar separated flow around a fence are presented using a non‐staggered grid system. Using the pressure‐weighted interpolation method (PWIM), the role of the under‐relaxation factor in this method has been studied. The performance of two pressure‐velocity coupling algorithms, viz. SIMPLE and PISO, have been compared as well as the solution fields obtained using non‐staggered and staggered grids. A detailed study has been conducted to investigate the occurrence of physically unrealistic convective velocities in the solution fields.The numerical results show that solutions obtained using non‐staggered grids are as accurate as those obtained using staggered grids. The presence of very small under/overshoots in the estimated convective fluxes is related to the simultaneous presence of high Péclét numbers and rapidly varying pressure gradients. However, for the complex separated flow investigated, no induced errors were detected in the solution field.
A comparison of gradient recovery methods in finite‐element calculations
Authors: Hawken D. M. , Townsend P. , Webster M. F. 
Published: August 2005

AbstractIn this paper we consider methods of gradient recovery in the context of primitive‐variable finite‐element solutions of viscous flow problems. Two methods are considered: a global method based on a Galerkin weighted residual procedure, and a direct method where gradients are recovered directly at individual nodes. The direct method has the benefit of utilizing the property of superconvergence as a natural consequence of its formulation, and furthermore requires no smoothing matrix to obtain the gradients at the nodal points. The two recovery schemes are considered with respect to two benchmark viscous flow problems of differing complexity. Both schemes are shown to produce comparable results, although the direct recovery method is found to be significantly more cost‐effective than the global method.
A numerical approach to find parameters using experimental data
Authors: Qamar Ihtzaz , Husain S. Wilayat 
Published: August 2005

AbstractA numerical technique is presented to determine the unknown parameters in a given relationship using the experimental data. In this technique we formulate the required number of independent relationships by integration applied to various parts of the data along with the criterion of the least‐squares error with respect to one parameter. The results for two sample systems, one with two parameters and the other with three parameters, are presented. Comparison with the published work shows that the proposed method is less sensitive to the inaccuracies in the experimental data and generates a better fit than the existing methods such as the ordinary least‐squares technique. The method can easily be extended to systems with any number of parameters.
Finite‐element analysis of wrinkling membranes
Authors: Roddeman Dennis G. 
Published: August 2005

AbstractA theoretical model for wrinkling membranes is used to develop a membrane element. Instead of deriving explicit expressions for the nodal forces and the stiffness matrix, the equivalent nodal forces are obtained by numerically simulating the virtual change of the element internal energy; the stiffness matrix follows from numerical differentiation of the nodal forces. Two examples illustrate the capabilities of the element.
An inverse finite‐element technique to determine the change of phase interface location in two‐dimensional melting problems
Authors: Ruan Yimin , Zabaras Nicholas 
Published: August 2005

AbstractThis paper is concerned with a two‐dimensional inverse phase change problem of particular importance to the analysis and design of welding processes. Specifically, a deforming finite‐element technique is proposed to calculate the change of phase interface location in two‐dimensional melting problems from temperature measurements at points inside the solid phase. The method is based on a minimization of the error between the measured and modelled temperatures at the sensor locations. It contains smoothing in time by utilizing future temperature data to calculate current values of the interface location as well as spatial smoothing. Several two‐dimensional examples are presented to illustrate the effectiveness of the proposed numerical model.
Exact discretization of an Euler beam element at specific frequencies corresponding to selected element boundary conditions
Authors: Downs B. 
Published: August 2005

AbstractThe exact discretization of simply supported rectangular thin plate elements for transverse vibration analysis, using the product of simply supported Euler beam properties, justifies this further study of Euler beams having a variety of end conditions. Five sets of boundary conditions, including the simply supported case, are examined and the theory for exact discretization is developed. Satisfactory verification of the discretization is obtained by eigenvalue analysis in all five cases. Applying the discretized properties to multi‐element beam analysis reveals an ill‐conditioning problem, present also in the conventional static matrices, for most combinations of end conditions. This problem does not occur for the simply supported element, whose discretized properties are then used to develop a highly accurate, frequency‐dependent mass matrix for use with the static stiffness matrix. Several comparisons are made of the results of eigenvalue error analysis.
On fitting stability regions of second derivative multi‐step methods
Authors: De Oliveira Paula , Patrício Fernanda 
Published: August 2005

AbstractA class of second‐derivative two‐step methods, S(2), with order 5 and depending on two parameters – which are used to adapt the stability region while minimizing the truncation error coefficient – is constructed. An analysis of two subclasses of S(2)–A(0) stable methods and methods with finite stability interval ‐ with their stability and accuracy properties is presented. Numerical examples are also included.
A generalized finite‐difference solution of parabolic 3‐D problems on multi‐connected regions
Authors: Pennati V. , De Biase L. , Feraudi F. 
Published: August 2005

AbstractA method for the solution of 3‐D parabolic problems on multi‐connected regions is presented. The domain discretization is automatic: at first the boundary is approximated by means of polyhedra; subsequently a Cartesian orthogonal non‐uniform grid is generated. The differential operator is discretized by a Crank‐Nicolson scheme, coupled with general finite‐difference formulae (GFDF).Some test problems are presented to show the efficiency of the method.
Observations on numerical method dependent solutions of a modified Duffing oscillator
Authors: Addison P. S. , Chan A. H. C. , Ervine D. A. , Williams K. J. 
Published: August 2005

AbstractNumerical solutions of a non‐linear oscillator have been produced by various methods. Some unexpected discrepancies have been found in the solutions obtained. This behaviour is reported herein, and the implications to the application of numerical methods to non‐linear dynamical systems are discussed.
A set of three drivers for BOXMG: A black‐box multigrid solver
Authors: Bandy Victor , Sweet Roland 
Published: August 2005

AbstractIn this paper we present three drivers for the Fortran software packages BOXMG and BOXMGP. They both act as black‐box matrix solvers for symmetric positive‐definite matrices using a multigrid method. There are two drivers, BBMG and BBMGP, that simplify the interface to BOXMG and BOXMGP, respectively. The other driver, DIVMG, provides a user‐friendly driver to both BOXMG and BOXMGP for a special class of problems. The DIVMG driver solves a two‐dimensional second‐order partial differential equation in divergence form on a rectangular domain with any combination of the following boundary conditions: Dirichlet, Neumann, Robin and periodic. The BBMG and BBMGP drivers, like the BOXMG solvers, still require the user to define the system of equations, while on the other hand the DIVMG driver also performs the discretization and only requires the user to define the problem.
The time‐parallel multigrid method
Authors: Horton Graham 
Published: August 2005

AbstractWe consider the problem of solving time‐dependent partial differential equations on an MIMD computer. Conventional methods for the solution of this type of equation when discretized by an implicit method such as backward Euler proceed by solving a sequence of problems iteratively. It is shown that, despite the sequential nature of this process, several processors may be employed to solve at several time steps simultaneously, a technique which we shall refer to as time‐parallelism. Details of a time‐parallel multigrid method based on the parabolic multigrid method due to Hackbusch and of a smoothing technique applicable to the two‐dimensional unsteady incompressible Navier‐Stokes equations are given. The parallel complexity of the method is shown to be qualitatively superior to that of previous parallel algorithms. Efficiencies obtained by an implementation of the method on a parallel Transputer system are presented.