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  • 1
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    Communications in Numerical Methods in Engineering 14 (1998), S. 229-240 
    ISSN: 1069-8299
    Keywords: filling of thin section ; finite element method ; surface tension ; interface element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interface element to model the pressure discontinuity due to surface tension when applied to the filling of a thin section cavity is presented. The equations used to form the element matrix for the interface element are the line integral form of the continuity and momentum equations. During the development of the finite element model, the pressure difference across the free surface due to surface tension is treated as an additional traction and is applied to all element sides which form the free surface. Simple numerical examples are then presented to illustrate the technique on the filling of a rectangular thin section cavity. © 1998 John Wiley & Sons, Ltd.
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  • 2
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    Communications in Numerical Methods in Engineering 14 (1998), S. 253-269 
    ISSN: 1069-8299
    Keywords: potential flow ; optimization approach ; sensitivity analysis ; adjoint variable method ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Potential flow problems around immersed bodies have been treated by an optimization approach. When the stream function is used as the field variable, the boundary values may not be known a priori and may be taken as the decision parameters to minimize integral objective functionals. The circulation integrals around the immersed bodies or the Kutta condition at the trailing edges of the bodies may be used to construct the objective function of optimization. The sensitivity analysis needed for the minimization process is performed by the adjoint variable method, while the numerical solutions of the primary (flow) and adjoint equations have been obtained by the finite element method. Having checked the present method with exact solutions and the classical superposition method, several flow problems involving one or more immersed bodies with or without circulation are investigated numerically. © 1998 John Wiley & Sons, Ltd.
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  • 3
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    Communications in Numerical Methods in Engineering 14 (1998), S. 289-304 
    ISSN: 1069-8299
    Keywords: stress intensity factors (SIF) ; finite element method (FEM) ; reciprocal work contour integral (RWCI) ; path-independent integrals (PII) ; displacement correlation technique (DCT) ; quarter-point displacement technique (QPDT) ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for improving the approximations of stress intensity factors computed from path-independent integrals is developed. The method uses Richardson's extrapolation. Numerical results are given to show the efficiency and the stability of the present method. © 1998 John Wiley & Sons, Ltd.
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  • 4
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    Communications in Numerical Methods in Engineering 14 (1998), S. 321-333 
    ISSN: 1069-8299
    Keywords: eigenvalue analysis ; sensitivity evaluation ; large-scale systems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general rank-1 matrix formula which allows for proper rearrangement of individual terms in multiproduct forms involving vectors and matrices. A far-reaching application of the new matrix formula to eigenvalue sensitivity evaluation is presented in the paper. Such an application reduces the sensitivity expressions to elegant, very fast and recursive forms with substantial savings in computer resources. The formula is applicable to rank-1 matrices of special structures which may constitute derivatives of the system state matrix, which is widely used in control system applications, with respect to various parameters of interest. In such cases, the use of the rank-1 formula yields exact non-approximate solutions which are identical to those obtained by other conventional formulas. The applicability of the rank-1 formula is believed to cover a wide variety of practical engineering systems pertaining to control and stability. © 1998 John Wiley & Sons, Ltd.
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  • 5
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    Communications in Numerical Methods in Engineering 14 (1998), S. 719-730 
    ISSN: 1069-8299
    Keywords: phase-change problems ; conduction-advection equation ; upwind weight function ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for solving transient multidimensional phase-change problems considering advective effects is presented. This temperature-based formulation includes the definition of a phase-change function able to deal with classical isothermal and non-isothermal phase-change cases. Moreover, a new upwind weight function is defined in order to avoid numerical oscillations in problems with dominant advective effects. Further, some important aspects related to its numerical implementation are also addressed. The ability of this methodology is illustrated, firstly, in the solution of a one-dimensional test example. Finally, the numerical simulation of a direct-chill continuous casting process is performed. © 1998 John Wiley & Sons, Ltd.
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  • 6
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    Communications in Numerical Methods in Engineering 14 (1998), S. 763-772 
    ISSN: 1069-8299
    Keywords: coupled vibrations ; Timoshenko beam ; boundary integral equation method ; symbolic computation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Symbolic computer algebra systems relieve one from the tedious task of different mathematical operations which are essential to obtain solutions. Due to their highly advanced features they have come to be used widely in computational mechanics. This paper describes an application of the modern computer algebra system Mathematica to the derivation of fundamental solutions necessary for the application of the boundary integral equation method. The problem treated is an asymmetric cross-section Timoshenko beam in free vibration. For this problem, the derivation of fundamental solutions involves lengthy mathematical operations which are very tedious if performed explicitly by hand. Therefore, using Mathematica we derive the fundamental solutions and generate the influence matrices from which the natural frequencies can be found. © 1998 John Wiley & Sons, Ltd.
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  • 7
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    Communications in Numerical Methods in Engineering 14 (1998), S. 751-761 
    ISSN: 1069-8299
    Keywords: acoustic ; electromagnetic ; integral equations ; scattering ; time domain ; radar cross-section ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Analysis of high frequency scattering using pulsed illumination generates surface fields which are small over most of the scatterer most of the time. A reformulation of the usual integral equation time domain approach which exploits this is presented. It is shown that cost scaling can be reduced, with costs reduced by an order of magnitude for the examples presented, with negligible accuracy loss. © 1998 John Wiley & Sons, Ltd.
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  • 8
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    Communications in Numerical Methods in Engineering 14 (1998), S. 797-808 
    ISSN: 1069-8299
    Keywords: mesh equidistribution ; area preserving map ; singular BVP ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an adaptive mesh method is employed to solve a class of singular boundary value problems. The approach is based on an area-preserving map and some mesh shape control in two-dimensional space. Two benchmark problems, which both involve singularities in physical domains, are tested. © 1998 John Wiley & Sons, Ltd.
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  • 9
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    Communications in Numerical Methods in Engineering 14 (1998), S. 195-208 
    ISSN: 1069-8299
    Keywords: differential quadrature method ; elastic torsion ; numerical solution ; Poisson equation ; Laplace equation ; geometric mapping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equation of an elastic prismatic shaft is the two-dimensional Poisson equation defined on the cross-sectional area of the shaft. In this paper, the differential quadrature method (DQM) is employed to solve the Poisson equation on some non-rectangular domains. Singularities, which may appear in the expression of stress components or boundary conditions at a degenerated point of the grid, are removed by means of the Taylor expansion. The results of three examples are compared with the exact solutions. It is shown that accurate results can be achieved by the DQM. In addition, three geometric transformations are conducted in the third example so that the effect of mapping on the convergence and accuracy of results is investigated. It is found that rapid convergence can be fulfilled if the degenerated point of the mesh falls on a Dirichlet boundary. The approach addressed in the paper can be extended to other potential problems governed by either the Poisson equation or the Laplace equation. © 1998 John Wiley & Sons, Ltd.
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  • 10
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    Communications in Numerical Methods in Engineering 14 (1998), S. 209-218 
    ISSN: 1069-8299
    Keywords: three-dimensional convection-diffusion equation ; fourth-order compact scheme ; iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present an explicit fourth-order compact finite difference scheme for approximating the three-dimensional convection-diffusion equation with variable coefficients. This 19-point formula is defined on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standard 7-point scheme in the context of basic iterative methods. Numerical examples are used to verify the fourth-order convergence rate of the scheme and to show that the Gauss-Seidel iterative method converges for large values of the convection coefficients. Some algebraic properties of the coefficient matrices arising from different discretization schemes are compared. We also comment on the potential use of the fourth-order compact scheme with multilevel iterative methods. © 1998 John Wiley & Sons, Ltd.
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  • 11
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    Communications in Numerical Methods in Engineering 14 (1998), S. 241-251 
    ISSN: 1069-8299
    Keywords: finite elements ; pollutant ; saturated porous medium ; semi-implicit method ; velocity correction ; mass transfer ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A practical problem of pollutant migration has been studied for different concentration differences and mass diffusivities using the finite element method. The results indicate that the pollutant takes years to travel 10 m into the water-saturated soil when the mass diffusivity and concentration differences are less. © 1998 John Wiley & Sons, Ltd.
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  • 12
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    Communications in Numerical Methods in Engineering 14 (1998), S. 277-285 
    ISSN: 1069-8299
    Keywords: numerical simulation ; steel ; quenching ; finite volume method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the basis of the control volume method the algorithm and computer program for prediction of the hardness distribution in quenched steel specimens with complex geometries have been developed. The algorithm and computer program are designed to solve 2D situation problems such as the quenching of complex cylinders, cones, spheres, etc. The computer program consists of three parts: automatic computation of domain and grid generation, computation of cooling curve in grid-points, and computation of hardness in grid-points. The mathematical model has been tested experimentally. The test showed that the model describes the hardness distribution in a quenched steel specimen of a complex form, with quite satisfactory accuracy. © 1998 John Wiley & Sons, Ltd.
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  • 13
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    Communications in Numerical Methods in Engineering 14 (1998), S. 271-275 
    ISSN: 1069-8299
    Keywords: basis transformation ; interpolations ; finite elements ; thin plates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The 9 df thin plate element of Mohr and Mohr uses cubic interpolation to obtain values of w at the third points of the element sides, in turn interpolating from these and the vertex values within the element. Recently this element has been modified and successfully applied to ‘potential’ problems. Subsequently it was found that the interpolations of the element of Bazeley et al. (1965, 1968) gave identical results for potential problems. In the present paper it is shown that this is because the interpolations of the two elements are exactly equivalent. © 1998 John Wiley & Sons, Ltd.
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  • 14
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    Communications in Numerical Methods in Engineering 14 (1998), S. 313-319 
    ISSN: 1069-8299
    Keywords: fluid mechanics ; vortex dynamics ; viscous flow ; Navier-Stokes equation ; vortex methods ; splitting procedure ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme has been obtained rigorously from the initial-boundary value problem for the Navier-Stokes (NS) equations in the context of the vortex method. The technique is based on a transformation of the NS equation into a parabolic equation which has an exact solution. The numerical scheme is derived by expanding the exact solution in Taylor series in powers of a small time interval. Numerical implementation is developed with use of vortex particles to represent the vortex flow domain. The method is used to solve practical engineering problems. The technique can also incorporate turbulence modelling. © 1998 John Wiley & Sons, Ltd.
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  • 15
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    Communications in Numerical Methods in Engineering 14 (1998), S. 347-354 
    ISSN: 1069-8299
    Keywords: thin wire loop antenna ; integro-differential equation ; frequency domain ; current distribution ; the weak formulation ; finite element technique ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The circular loop antenna is analysed by using the electric field integro-differential equation in the frequency domain. The weak form of the integro-differential is derived and then the current distribution along the circular loop antenna is calculated by solving the resulting equation via the finite element technique. Accurate results are obtained using the linear shape and test functions. © 1998 John Wiley & Sons, Ltd.
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  • 16
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    Communications in Numerical Methods in Engineering 14 (1998), S. 355-365 
    ISSN: 1069-8299
    Keywords: transient dynamics ; interaction of the crack sides ; crack propagation ; time domain formulation ; boundary element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For two-dimensional solids the multiregion concept and the time-domain approach in the boundary element method are employed to model cracks in transient dynamics. The propagation of cracks and the closing and opening of crack sides are simulated by disconnecting and connecting degrees of freedom of a stationary mesh, as was also demonstrated recently in statics by Beer. An iterative technique is developed to determine the changes of the extent of the area where there is connection, contact or no contact at the interface between dynamically loaded regions. © 1998 John Wiley & Sons, Ltd.
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  • 17
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    Communications in Numerical Methods in Engineering 14 (1998), S. 941-957 
    ISSN: 1069-8299
    Keywords: geometrical non-linear ; UL formulation ; drilling degrees of freedom ; generalized conforming ; arc-length method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An updated Lagrangian formulation of the generalized conforming flat shell element with drilling degrees of freedom is derived based on the incremental equation of virtual work of a three-dimensional (3D) continuum for a purely geometric non-linear analysis of the space structure. While solving the non-linear equations, the Euler-Newton method and modified Euler-Newton method are used in static analyses, and the modified arc-length method and Newton arc-length method for post-buckling problems. A number of numerical examples are given to demonstrate the effectiveness of the proposed approach and programs. © 1998 John Wiley & Sons, Ltd.
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  • 18
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    Communications in Numerical Methods in Engineering 14 (1998), S. 473-491 
    ISSN: 1069-8299
    Keywords: temporal acceleration ; viscoelastic ; recovery ; Taylor-Galerkin ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a finite element study based on a technique associated with time extrapolation to accelerate the convergence rate to the steady state for viscoelastic flows. The approach adopted is a local extrapolation method attributed to Neville. Temporal extrapolation is embedded within a time-marching Taylor-Galerkin/pressure-correction scheme as applied to the solution of model channel flow, 4:1 plane contraction flow and flow past a circular cylinder. In particular, consideration is given to obtaining steady-state solutions for an Oldroyd-B model. When extrapolation is performed for stress and velocity or pressure, then stress and velocity overshoot, which consequently leads to divergence. In contrast, a stable numerical scheme emerges when only the stress is extrapolated. © 1998 John Wiley & Sons, Ltd.
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  • 19
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    Communications in Numerical Methods in Engineering 14 (1998), S. 505-517 
    ISSN: 1069-8299
    Keywords: hypersingular integral equation ; continuous elements ; stress analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method for the evaluation of boundary stresses directly from the BEM solution of elastostatic problems using the static boundary integral equation is presented. The technique is valid for corners and edges as well as smooth points on the boundary, and involves defining a new interpolation function for continuous elements which incorporate certain continuity conditions arising from the hypersingular nature of the integrals involved. An integration technique based on the singularity subtraction method using series expansions is adopted for the hypersingular intergrals. Results are shown to be more accurate than those obtained with conventional techniques. © 1998 John Wiley & Sons, Ltd.
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  • 20
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    Communications in Numerical Methods in Engineering 14 (1998), S. 539-547 
    ISSN: 1069-8299
    Keywords: boundary-only element analysis ; thermal cracking ; crack trajectory ; singular elements ; traction formula ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary element procedure is developed concerning the prediction of the quasistatic crack growth in uniformly heated bimaterials. This procedure assumes the existence of an initial small crack in one of the two phases, and further cracking progress from this point due to thermal loading. The resulting mixed boundary value problem is solved by applying an incremental boundary-only method in conjunction with the multidomain technique. Fracture characterizing parameters are evaluated utilizing special crack tip singular elements and appropriate formulas. The crack path is predicted using the strain energy release rate criterion, and the mesh is updated at the end of each increment. The presented results are in good agreement with previously reported experimental results and those obtained by the finite element method. Various numerical studies were conducted and interpreted concerning crack-path dependence on individual material property mismatch. © 1998 John Wiley & Sons, Ltd.
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  • 21
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    Communications in Numerical Methods in Engineering 14 (1998), S. 559-567 
    ISSN: 1069-8299
    Keywords: gust ; buffet ; random ; vibration ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A convenient and effective finite-element-based method for buffeting analysis of complex structures is presented. This method is very efficient for structures with the natural frequencies closely spaced because their corresponding modes and the cross-correlation terms between them should be included in the mode-superposition analysis. The imperfect correlation between gust excitations can also be dealt with conveniently. A numerical example is given which shows that by using this method the buffeting analysis of complex structures with thousands of degrees of freedom, dozens of imperfectly related excitations and a number of participating modes can be executed quite easily on an ordinary IBM/486 (or 586) personal computer. © 1998 John Wiley & Sons, Ltd.
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  • 22
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    Communications in Numerical Methods in Engineering 14 (1998), S. 519-527 
    ISSN: 1069-8299
    Keywords: shell element ; large strain ; sheet metal stamping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general method of large strain determination over the deformed surface of a sheet metal stamping. It is demonstrated that the conventional degenerated shell element with two normal rotation degrees of freedom is not suitable for large deformation, especially when large element rotation is present. This inaccuracy is primarily caused by the fact that the displacement field description used in the degenerated shell element is only a first-order approximation with respect to the two rotation degrees of freedom, and is therefore suitable only for small rotation angles. The new method presented in this paper replaces the two rotation DOFs with three new degrees of freedom to describe the rotation of the surface normal so that the element deformation can be accurately described with no limitation on the amount of deformation and rotation involved. The advantages of this new method are: (i) a linear and accurate expression of the displacement field in terms of nodal DOFs is obtained; (ii) the formulation is easily incorporated into any existing degenerated shell elements; (iii) the strain calculation is accurate for any amount of element rigid body rotation; (iv) if the method is used in surface grid analysis, the algorithm will not only provide correct surface strains, but also their variation through the thickness direction, i.e. the bending deformation. © 1998 John Wiley & Sons, Ltd.
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  • 23
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    Communications in Numerical Methods in Engineering 14 (1998), S. 597-608 
    ISSN: 1069-8299
    Keywords: inverse problems ; dual systems ; vibrating rod ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discretization of the differential equation governing the axial vibration of a rod with varying cross-section leads to a specially structured matrix pencil. This paper deals with the reconstruction of this pencil from its spectrum. An iterative algorithm for this problem and an analytic characterization of complementary solutions are given. The method is demonstrated on some examples. © 1998 John Wiley & Sons, Ltd.
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  • 24
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    Communications in Numerical Methods in Engineering 14 (1998), S. 621-632 
    ISSN: 1069-8299
    Keywords: segmentation ; finite elements ; adaptive ; image ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The image segmentation problem in computer vision is considered. Given a two-dimensional domain D and a function defined on it (the original image), the problem is to obtain a ‘cartoon’ associated with this function, namely to find a set of inner boundaries which divide D into subdomains (objects) in an optimal way. The optimality criterion used here is given by the Mumford-Shah (MS) and Blake-Zisserman model, which leads to a strongly non-linear problem. Related problems appear in multiphase continuum mechanics. An iterative procedure based on an h-adaptive finite element method is proposed for the solution of this problem. The mesh adaptivity enables an efficient solution technique, with the use of basic coarse discretization and a few local regions of high resolution where needed. © 1998 John Wiley & Sons, Ltd.
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  • 25
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    Communications in Numerical Methods in Engineering 14 (1998), S. 633-645 
    ISSN: 1069-8299
    Keywords: error estimation ; boundary elements ; adaptive mesh ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation for the boundary element method is developed. The nodal error is estimated from the difference of two solutions - one from the original BEM solution, and the other from interpolation of the original solution. Based on nodal errors, a matrix analysis is carried out to calculate the corresponding errors at source points. Two formulae for estimating global percentage errors are proposed in the paper. The first formula uses nodal errors directly to estimate element error, and the second uses an integral form to calculate element error to eliminate extremely high mesh concentration near areas with singular solutions. An h-version adaptive mesh refinement is implemented to study the accuracy of the proposed error estimation. Numerical examples show that the error estimator can correctly guide mesh refinement, and a final mesh can be obtained in a few iterations. © 1998 John Wiley & Sons, Ltd.
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  • 26
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    Communications in Numerical Methods in Engineering 14 (1998), S. 647-655 
    ISSN: 1069-8299
    Keywords: finite difference methods ; stability and convergence of numerical methods ; advection schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses implementation strategies for second-order finite difference discretizations of advection. Purely explicit and implicit methods both have disadvantages, and we consider semi-implicit schemes in which the flux is split into a primary implicit part and a secondary explicit correction. One-dimensional scalar advection is used as a model problem to analyse the leading order error terms and the stability of the schemes. Some of the splittings turn out to be unconditionally stable, but accuracy or monotonicity may deteriorate for large time steps. © 1998 John Wiley & Sons, Ltd.
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  • 27
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    Communications in Numerical Methods in Engineering 14 (1998), S. 697-708 
    ISSN: 1069-8299
    Keywords: incompressible flow ; generalized streamline operator ; upwinding tensor ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present work the backward-facing step problem is analysed in the framework of the finite element method. It is a very well-known benchmark problem for the numerical resolution of the incompressible Navier-Stokes equations. In particular, a generalized streamline operator technique (GSO) is used in the numerical approach to these equations. The results show very good agreement with those reported by other authors using different methodologies. © 1998 John Wiley & Sons, Ltd.
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  • 28
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    Communications in Numerical Methods in Engineering 14 (1998), S. 773-781 
    ISSN: 1069-8299
    Keywords: indirect address lists ; unstructured grids ; shared-memory parallel machines ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A way has been found to form indirect addressing lists in parallel on shared-memory parallel machines. The maximum possible speed-up for typical tetrahedral grids is approximately 1:23. The algorithm requires an additional scratch array to shift from the serial ‘elements surrounding points’ to the parallel ‘elements surrounding processors surrounding points’ paradigm. The algorithm developed is general in nature, i.e. applicable to all indirect addressing lists. All numerical methods requiring the construction of indirect data structures, such as sparse matrix linear algebra procedures, field and particle solvers operating on unstructured grids, and network flow applications should see a benefit from this algorithm when running on shared-memory parallel machines. © 1998 John Wiley & Sons, Ltd.
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  • 29
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    Communications in Numerical Methods in Engineering 14 (1998), S. 783-792 
    ISSN: 1069-8299
    Keywords: substructure ; frontal technique ; heat transfer ; moisture transfer ; displacement ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: This paper presents a substructuring-frontal combined algorithm for the analysis of fully coupled heat, moisture and displacement problems in unsaturated soil. The method adopted for solving the assembled matrix equations has a significant bearing on the computer storage requirement and execution time. Numerical examples are given to validate the proposed model. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 809-819 
    ISSN: 1069-8299
    Keywords: finite element analysis ; diffusion problems ; minimum time step size ; Engineering ; Numerical Methods and Modeling
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    Notes: The solution of the equation system of the finite element method for diffusion problems is presented in the format of a sequence. The characteristics of the numerical results can thus be known through an analysis of this ‘theoretical expression’ of the solution. The characteristics of the sequence are analysed to yield expressions for the minimum time step size. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 849-861 
    ISSN: 1069-8299
    Keywords: outgoing boundary condition ; Berkhoff ; discrete ; non-local ; surface waves ; scattering ; Engineering ; Numerical Methods and Modeling
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    Notes: A discrete non-local (DNL) boundary condition is used to solve the water waves propagation problem over variable depth. This condition is obtained by means of full solution of the discrete Helmholtz operator in a structured network. We consider a simulation of wave propagation around a circular island located on either a paraboloidal shoal or constant depth bathymetry. Such examples confirm the important improvement in accuracy for the DNL method over standard conditions in the near field. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 59-63 
    ISSN: 1069-8299
    Keywords: Delaunay triangulation ; mesh colouring ; mesh coarsening ; Engineering ; Numerical Methods and Modeling
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    Notes: A new algorithm is described for automatic coarsening of Delaunay triangulations. The method automatically identifies the nodes of the mesh which are candidates for deletion in each region to be coarsened. The mesh coarsening procedure is to regenerate a Delaunay triangulation for all the remaining nodes in the solution domain. The adapted mesh retains a high quality for two reasons: (i) because a set of nodes have been used to obtain the coarse mesh, which are equidistant apart in some sense defined by the original mesh; (ii) because the triangulation is Delaunay. A two-dimensional example demonstrates the quality of the mesh after coarsening. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 35-42 
    ISSN: 1069-8299
    Keywords: potential problems ; rectangular finite element ; consistency criteria ; rigid body modes ; constant straining modes ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: This short paper demonstrates how the matrix for a 4-node potential finite element can be derived from the conditions of ‘rigid body movement’, symmetry and consistency, and the requirement that the element solve exactly the case of φ=xy. This derivation is intended to be a simple illustration of the ideas of Bergan and others. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 135-149 
    ISSN: 1069-8299
    Keywords: multiphase immiscible flow ; deforming porous media ; fully coupled ; soil displacements ; fluid pressures ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fully coupled numerical model has been developed which describes multiphase fluid flow through soil: namely gas, water and a non-aqueous phase liquid (NAPL) in a deforming porous media for subsurface systems. A multiphase flow model, based on the two-phase flow model of Brooks and Corey, is presented to express the dependence of saturation and relative permeability on the capillary pressure. Non-linear saturation and relative permeability functions are incorporated into a Galerkin finite element model which is subsequently used to simulate multiphase immiscible fluid flow under saturated and unsaturated conditions in porous media. The governing partial differential equations, in terms of soil displacements and fluid pressures, which are coupled and non-linear, are solved by the finite element method. Numerical implementation of the formulation is discussed, and example problems demonstrate the model and solution procedure. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 151-160 
    ISSN: 1069-8299
    Keywords: genetic algorithms ; evolutionary-genetic analogy ; heat transfer ; finite elements ; numerical analysis ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: A new approach was developed for the analysis of problems of physics governed by laws of conservation. The methodology establishes an analogy between various aspects of evolution and genetics of life processes and inanimate physical systems. This analogy is then used to generate solutions to physical problems in a similar way to which organisms in nature solve problems imposed by environmental constraints. Finite difference and finite elements approximations are used in the numerical implementation of the method and a simple two-dimensional problem is solved to illustrate the method. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 181-194 
    ISSN: 1069-8299
    Keywords: oscillating flow ; Keulegan-Carpenter number ; finite element method ; in-line force ; transverse force ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: The results of a numerical study of the viscous oscillating flow around a circular cylinder at Reynolds number=200 and Keulegan-Carpenter number=20 are presented. The finite element method was used for the solution of the Navier-Stokes equations, in the formulation where the streamfunction and the vorticity are the field variables. The computation revealed a complicated flow pattern at which the flow is not periodic but switches between different modes at various oscillation cycles. The vortex shedding patterns occurring at different cycles were identified by means of numerical flow visualization. The traces of the hydrodynamic forces were derived from the solution, and the hydrodynamic coefficients of the in-line force were evaluated. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 219-228 
    ISSN: 1069-8299
    Keywords: boundary integral ; spectral strip ; curvature geometries ; Engineering ; Numerical Methods and Modeling
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    Notes: The non-element boundary spectral strip method is developed for solution of problems in curvature domains. The method, which uses a spectral Fourier approximation for expansion of the variables along the boundaries, shows an exponential convergence behaviour. A remarkable reduction in problem size and improved accuracy of results is achieved by the method as compared to the boundary element method. The method is illustrated by some physical problems from elastostatics. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 305-312 
    ISSN: 1069-8299
    Keywords: error bound ; non-linear eigenvalue ; linearization ; dynamic stiffness matrix ; matrix pencil ; Engineering ; Numerical Methods and Modeling
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    Notes: In connection with previously published work, this paper presents further results about the bounding properties of eigenvalues provided by a linear eigenmatrix formulation A-λB. The linear eigenmatrix is formed by expressing the elements of a non-linear dynamic stiffness matrix, K(λ), as linear functions of the eigenparameter λ. This is achieved by choosing two fixed values of the eigenparameter and calculating K(λ) at these two values. The eigenvalues of A-λB provide error bounds on the exact eigenvalues of the non-linear eigenmatrix if the two fixed values chosen are below the lowest pole of K(λ). Choosing two identical fixed values, the error bounds on the exact eigenvalues provided by traditional linearization techniques are found as special cases. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 335-346 
    ISSN: 1069-8299
    Keywords: pressure-correction scheme ; incompressible flow ; spurious boundary layer ; Engineering ; Numerical Methods and Modeling
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    Notes: The paper presents a discussion of some phenomena related to the pressure-correction scheme implemented in a spectral element or finite element context. Of particular interest are the spurious boundary layers created around prescribed boundaries in which the pressure exhibits spurious behaviour. The flow is very prone to singular behaviour, especially around geometrical singularities. That is why this phenomenon is studied using as an example the flow in a diverging channel with sharp changes in the angle. The reasons for, and a possible remedy to, the singular (and aphysical) behaviour of the numerical solution are discussed. The results of the numerical experiments clearly support the conclusions of this discussion. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 419-427 
    ISSN: 1069-8299
    Keywords: random structure ; stochastic method of weighted residual ; dynamic response ; spline function ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: The paper develops a new stochastic weighted-residual method for predicting the dynamic response of a random structure under random excitation. This is achieved by employing a discretization technique in the time domain based on the method of weighted residuals. A trial function involving a third-order B-spline basis function is applied to a replacement of time integration of stochastic finite element dynamic equations of the structure. Efficient analysis techniques for the mean values and the variances of the dynamic response are described in detail. Numerical solution results of examples indicate that the approach presented herein effects an economical and efficient solution for such an analysis when compared with Monte Carlo simulation. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 437-449 
    ISSN: 1069-8299
    Keywords: finite elements ; explicit dynamics ; near incompressible deformation ; large strains ; tetrahedron ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper presents a simple linear tetrahedron element that can be used in explicit dynamics applications involving nearly incompressible materials or incompressible materials modelled using a penalty formulation. The element prevents volumetric locking by defining nodal volumes and evaluating average nodal pressures in terms of these volumes. Two well-known examples relating to the impact of elasto-plastic bars are used to demonstrate the ability of the element to model large isochoric strains without locking. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 451-461 
    ISSN: 1069-8299
    Keywords: hypersingular integral equation ; plane elasticity crack problem ; stress intensity factors ; Engineering ; Numerical Methods and Modeling
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    Notes: The hypersingular integral equation approach is suggested to solve the plane elasticity crack problem with circular boundary. The complex variable function method is used in the formulation. In the equation the crack opening displacement function is used as the unknown function, and the traction on the crack face as the right-hand term. A numerical integration rule is used to evaluate the hypersingular integral. Numerical examples are given to demonstrate the use of the approach. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 497-504 
    ISSN: 1069-8299
    Keywords: identification ; viscoelasticity ; correspondence principle ; boundary elements ; Engineering ; Numerical Methods and Modeling
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    Notes: A parameter identification procedure for viscoelastic materials is presented, which is formulated based on the elastic-viscoelastic correspondence principle. The proposed method is developed by using Newton's iteration scheme, the method of least squares and the one-dimensional minimization method. The boundary element discretization and the numerical inversion of the Laplace transform are used for linear viscoelastic analysis. Two numerical examples are included to demonstrate the validity of the method. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1-8 
    ISSN: 1069-8299
    Keywords: frequency condensation method ; large matrix systems ; Guyan method ; Engineering ; Numerical Methods and Modeling
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    Notes: A frequency condensation method is presented for solving the eigenvalue problem of a large matrix system. The eigenproblem is reduced to a smaller problem by condensing the stiffness and mass matrices. As distinct from the Guyan method, the frequency condensation method is based on approximation preserving eigenvalues in a preset frequency range and effective procedure of master and slave selection. A numerical example and comparison with subspace iteration and Lanczos methods demonstrate good accuracy and the high performance of this method. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 23-34 
    ISSN: 1069-8299
    Keywords: Gauss-Poisson equation ; exact discrete conservation ; discrete divergence ; Engineering ; Numerical Methods and Modeling
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    Notes: We consider numerical methods which exactly preserve the Gauss-Poisson equation when solving the charge conservation and Maxwell-Ampère's equations. Apart from the well-known leap-frog method, we present two situations where this property is verified, one with rectangular mesh and functions defined at the center of the cells, and one with a finite volume type of formulation on triangles. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 51-58 
    ISSN: 1069-8299
    Keywords: arc-length method ; user control ; accumulated arc-length control ; non-linear analysis ; predefined deformation states ; convergence ; Engineering ; Numerical Methods and Modeling
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    Notes: The arc-length method has been widely used in non-linear analysis of structures. While it can handle complex load-deflection paths effectively, the analyst has no control over the load incrementation scheme to achieve convergence to specific locations along the load-deflection path. There are a number of situations in which such control is necessary, for example when convergence to predefined load levels, displacement levels or stress levels is required. This paper describes an improved arc-length method in which this deficiency is overcome. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 43-49 
    ISSN: 1069-8299
    Keywords: lumped mass matrix ; Hermitian finite difference operators ; flexural wave propagation ; numeric velocity dispersion ; Engineering ; Numerical Methods and Modeling
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    Notes: Hermitian finite difference operators are employed to formulate a new diagonal mass matrix for solving flexural wave propagation problems. The dynamic equilibrium for moments is considered. The consistency of the formulation is evident because these operators explicitly present second-order convergence. Numerical results indicate that the velocity dispersion is very close to the consistent mass matrix. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 103-134 
    ISSN: 1069-8299
    Keywords: computational quantifier elimination ; edge crack ; feasibility (consistency) conditions ; fracture mechanics ; numerical methods in engineering ; parametric inequality constraints ; Engineering ; Numerical Methods and Modeling
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    Notes: In this paper, an attempt is made to show the usefulness of computational quantifier elimination (CQE) techniques in computer algebra inside classical numerical methods in engineering for the derivation of feasibility (consistency) conditions in problems with weakly parametric linear inequality constraints (with the parameters appearing only in their right-hand sides). A simple, but non-trivial, straight edge-crack problem in fracture mechanics under linear inequality constraints both on the applied loading along the crack faces and on the value of the stress intensity factor at the crack tip (associated with the Green/weight function method, numerical approximations and classical numerical integration) is used for an elementary illustration of the proposed approach. In this application, the method used tries to imitate the theoretical principle of the linear programming methods. The manually obtained related result is expressed as a disjunction of conjunctions of inequalities (as is frequently the case in similar CQE problems), and concrete numerical results are also displayed. The related influence of various approximations and the application of the trapezoidal quadrature rule are also considered in some detail. Further possibilities could concern the application of the approach to other numerical methods in engineering (such as to the finite and the boundary element methods, to singular and hypersingular integral equation methods, etc.) combined with efficient algorithms for linear inequality constraints such as the old Fourier and the recent Weispfenning elimination methods. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 161-178 
    ISSN: 1069-8299
    Keywords: finite elements ; unsteady incompressible flows ; fractional-step ; equal-order-interpolation ; pQ2Q1 element ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: Implementation of an equal-order-interpolation velocity-pressure element pair is presented for the finite element solution of incompressible viscous flows. A fractional-step method is employed for temporal discretization. The element pair, also called a pseudo-biquadratic velocity/bilinear pressure element (pQ2Q1), consists of a bilinear pressure element and bilinear velocity elements defined on subdivisions of the pressure element. This pair satisfies the so-called ‘Ladyzhenskaya-Babuska-Brezzi’ condition. Considerable savings in computational cost are achieved due to the reduced number of elements for pressure. A modification of the element is realized for a better representation of curved surfaces. Two test cases, namely the lid-driven cavity flow and impulsively started circular cylinder in cross-flow, are used to assess the accuracy and efficiency of the element compared to a regular bilinear velocity-pressure (Q1Q1) element pair. Computational results presented show that the pQ2Q1 element solutions require less memory and CPU time compared to Q1Q1 element solutions, for at least the same accuracy. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 839-847 
    ISSN: 1069-8299
    Keywords: coupled models of dynamic electroelasticity ; generalized solutions ; metrics weaker than L2 ; spectrum of a priori estimates ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: In this paper we deal with a model of coupled non-stationary electroelasticity with displacements and potential given on the boundary of a body. We construct a numerical scheme for modelling electromechanical interactions in the body, and present a spectrum of a priori estimates for the solution of this scheme. Such estimates allow us to prove the convergence of the scheme to a generalized solution of the differential problem from W22(QT) with the second order of accuracy in a weaker than L2 metric. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 821-837 
    ISSN: 1069-8299
    Keywords: diagonally implicit Runge-Kutta methods ; parallelism ; stiffness ; stability ; Engineering ; Numerical Methods and Modeling
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    Notes: In this paper we propose a parallel diagonal iteration process for solving a low-order implicit Runge-Kutta method of Lagrange type. The resulting scheme can be regarded as a parallel singly diagonally implicit Runge-Kutta (PSDIRK) method and it is strongly A-stable when the classical linear test model is used. On a two-processor computer, this method requires the solution of two implicit relations (sequential time units) per step and per processor. We compare our method with some sequential and parallel methods from the literature for solving linear as well as non-linear stiff problems and semidiscretized convection-diffusion equations. The numerical experiments show the behaviour of our method with regard to the other methods. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 871-877 
    ISSN: 1069-8299
    Keywords: nearest neighbours ; Voronoi diagram ; Delaunay triangulation ; computational geometry ; algorithms ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper deals with the largest interior angle property of the Voronoi nearest neighbours and the Delaunay triangulation in two dimensions. It is indicated that each interior angle opposite to an edge of a Delaunay triangle is the largest of the interior angles opposite the same edge of all possible triangles on the same side. Based on this property, the algorithms for finding the Voronoi neighbours of a point (site) and for constructing the Delaunay triangulation are presented. The algorithms are especially useful for the meshless methods developed in recent years. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 907-920 
    ISSN: 1069-8299
    Keywords: Stokes problem ; meshless ; MLS interpolant ; Engineering ; Numerical Methods and Modeling
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    Notes: In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D problems and deformable domains. First, taking into consideration that Dirichlet boundary conditions are not applicable a posteriori as in finite elements, a variational weak formulation that includes all kinematic restrictions (Dirichlet and incompressibility) is derived. Then the discretized resultant equations using a moving least-squares (MLS) interpolant for velocity and pressure fields are presented. Finally, the performance of the MLS interpolation is analysed by comparing numerical and analytical solutions, paying attention to the selection of the polynomial degree for the basis function and its orthogonalization. Different aspects of numerical implementation are discussed. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 921-930 
    ISSN: 1069-8299
    Keywords: non-linear Richards equation ; mixed-hybrid finite elements ; quasi-Newton methods ; fast-secant methods ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: Groundwater flow in partially saturated porous media is modelled by using the non-linear Richards equation, which is discretized in the present work by using linear mixed-hybrid finite elements.The discretization produces an algebraic non-linear system, which can be solved by an iterative fixed-point algorithm, the Picard method. The convergence rate is linear, and may be too poor for practical applications. A superlinear convergence rate is obtained by considering a Broyden-type approach, based on the Shermann-Morrison formula.The local character of the Broyden method can be overcome by an accurate estimate of the initial solution, that is by appropriately initializing the computation via some (relaxed) Picard iterations. This strategy needs a convergence criterion to decide when switching from the Picard to the quasi-Newton method, which is crucial for the effectiveness of the scheme, as illustrated by some numerical experiments.We also consider the non-linear algebraic problem from a different viewpoint. Instead of applying the quasi-Newton method directly to such a non-linear system, we applied it to the non-linear function tied to the Picard scheme. Each function evaluation requested by such an algorithm corresponds to a local step of the Picard method, which is then used to compute a Broyden displacement. The present technique can be seen as an accelerated Picard algorithm.We compare the performances of these algorithms when applied to a stationary and a time-dependent benchmark problem. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 897-906 
    ISSN: 1069-8299
    Keywords: preconditioning ; conjugate gradient ; finite elements ; shells ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Preconditioned Krylov subspace methods have proved to be efficient in solving large, sparse linear systems in many areas of scientific computing. The success of these methods in many cases is due to the existence of good preconditioning techniques. In problems of structural mechanics, like the analysis of heat transfer and deformation of solid bodies, iterative solution of the linear equation system can result in a significant reduction of computing time. Also many preconditioning techniques can be applied to these problems, thus facilitating the choice of an optimal preconditioning on the particular computer architecture available.However, in the analysis of thin shells the situation is not so transparent. It is well known that the stiffness matrices generated by the FE discretization of thin shells are very ill-conditioned. Thus, many preconditioning techniques fail to converge or they converge too slowly to be competitive with direct solvers. In this study, the performance of some general preconditioning techniques on shell problems is examined. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 959-961 
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    Keywords: Stokes problem ; finite element ; eigensystems ; Engineering ; Numerical Methods and Modeling
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    Notes: The use of mixed finite element methods in discretizing the Stokes equations leads to systems involving the so-called pressure matrix. Some new spectral properties of this important matrix are here presented for the Q1-P0 element. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 381-392 
    ISSN: 1069-8299
    Keywords: porous medium ; fluid flow ; electromechanical coupling ; FEM ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: We consider a coupled problem of the deformation of a porous solid, flow of a compressible fluid and the electrical field in the mixture. The governing equations consist of balance of the linear momentum of solid and of fluid, continuity equations of the fluid and current density, and a generalized form of Darcy's law which includes electrokinetic coupling. The compressibility of the solid and the fluid are taken into account. We transform these equations to the corresponding finite element relations by employing the principle of virtual work and the Galerkin procedure. The nodal point variables in our general formulation are displacements of solid, fluid pore pressure, relative velocity of the fluid and electrical potential. Derivation of the FE equations is presented for small displacements and elastic solid, which can further be generalized to large displacements and inelastic behaviour of the solid skeleton.According to this formulation we can include general boundary conditions for the solid, relative velocity of the fluid, fluid pressure, current density and electrical potential. The dynamic-type non-symmetric system of equations is solved through the Newmark procedure, while in the case of neglect of inertial terms we use the Euler method.Numerical examples, solved by our general-purpose FE package PAK, are taken from biomechanics. The results are compared with those available in the literature, demonstrating the correctness and generality of the procedure presented. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 397-407 
    ISSN: 1069-8299
    Keywords: 3D mesh generation ; adaptive refinement ; Engineering ; Numerical Methods and Modeling
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    Notes: An adaptive finite element (FE) method for the solution of three-dimensional elasto-static problems is described. The computational domain is represented by an assembly of tetrahedral elements and the mesh adaptation is achieved by a 3D bisection method using an error estimator procedure coupled with an automatic 3D mesh generator. The performance of the method is demonstrated using a number of examples. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 429-436 
    ISSN: 1069-8299
    Keywords: stress intensity factor (SIF) ; singular finite element ; double cracks ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: Using the quasi-compatible finite element method advanced by Zhichao and Lisu (1990), the influence of the size of a plate with double cracks on the stress intensity factor is studied. Many numerical computations are carried out and various data, curves and formulae are given. It is shown clearly how the stress intensity factors of double cracks are affected by the size of the cracked body. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 463-472 
    ISSN: 1069-8299
    Keywords: multibody systems ; non-linear analysis ; static equilibrium ; constrained optimization ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper presents four different approaches to the solution of the non-linear static-equilibrium problem in complex linkages, including rigid and elastic elements. The error function is based on the potential of the system, and includes rigid elements by means of non-linear constraints. To this end use is made of Lagrange multipliers, along with the primal-dual method, penalty functions and weighted stiffness, comparisons being made between them. A Newton-Raphson method is used in seeking function minima for equilibrium positions. This procedure is also directly applicable to the other linkage and multibody position problems. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1109-1117 
    ISSN: 1069-8299
    Keywords: Engineering ; Numerical Methods and Modeling
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    Notes: The symmetry present in Green's functions is exploited to significantly reduce the matrix assembly time for a Galerkin boundary integral analysis. A relatively simple modification of the standard Galerkin implementation for computing the non-singular integrals yields a 20-30 per cent decrease in computation time. This faster Galerkin method is developed for both singular and hypersingular equations, and applied to symmetric-Galerkin implementations in two dimensions for the Laplace equation and for orthotropic elasticity. In three dimensions, the modified algorithm has been implemented for the singular equation for the Laplace and elastodynamics equations. Comparison timing results for standard and modified algorithms are presented. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1097-1108 
    ISSN: 1069-8299
    Keywords: grid generation ; finite point method ; mesh free techniques ; Engineering ; Numerical Methods and Modeling
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    Notes: An algorithm to construct boundary-conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point distance and an initial triangulation of the surface. Borrowing a key concept from advancing front grid generators, one point at a time is removed and, if possible, surrounded by admissible new points. This operation is repeated until no active points are left. Timings show that the scheme is about an order of magnitude faster than volume grid generators based on the advancing front technique, making it possible to generate large (〉106) yet optimal clouds of points in a matter of minutes on a workstation. Several examples are included that demonstrate the capabilities of the technique. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 671-679 
    ISSN: 1069-8299
    Keywords: advection-diffusion ; semi-Lagrangian ; stability ; accuracy ; QUICKEST ; DISCUS ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper describes the incorporation of diffusive transport into the original semi-Lagrangian DISCUS algorithm for pure advection. An explicit treatment of diffusion is adopted following the approach used in the QUICKEST algorithm for advection-diffusion. The semi-Lagrangian treatment of the advection term relaxes the small time step restriction normally associated with Eulerian treatments of advection, but the Eulerian treatment of the diffusion term imposes conventional limitations on the scheme. Numerical experiments of advection-diffusion, however, indicate that DISCUS has advantages over the QUICKEST scheme for advection-diffusion in three key areas: stability, accuracy and computational efficiency. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 709-717 
    ISSN: 1069-8299
    Keywords: fluid dynamics ; multiphase-flow ; lattice gases ; Engineering ; Numerical Methods and Modeling
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    Notes: Nearly all CFD methods can be considered as discretization methods for partial differential equations, such as finite difference, finite volume, finite element, spectral or boundary integral element methods. Virtually unrecognized by the scientific mainstream in computational fluid dynamics (CFD) during the last decade, a completely different approach to flow simulation has been developed in computational physics.The basic idea of lattice-gas solvers (LGS) goes back to the cellular automation concept of John von Neumann. LGS use objects (‘cells’), being extremely simple compared to finite boxes or finite elements. The state of a cell is usually described by only a few bits therefore often two orders of magnitude more cells are used for a simulation with LGS than ‘elements’ in a finite element computation. LGS are explicit time-stepping procedures; no equation systems have to be solved. Thus every time-step is extremely cheap in terms of CPU power compared to standard procedures, yet again much shorter time-steps have to be used. LGS are inherently parallel and are suitable to coarse-grain as well as to fine-grain parallelization.The paper will discuss some advantages and disadvantages of lattice-gas solvers and present LG simulation results of two-phase flow with moving boundaries on a microscope scale for a two-dimensional test geometry of randomly distributed equally sized disks where the effect of surface tension on the steady-state saturation will be demonstrated. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1155-1170 
    ISSN: 1069-8299
    Keywords: shell problem ; Naghdi model ; finite elements ; mixed elements ; Engineering ; Numerical Methods and Modeling
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    Notes: The subject of this work is the construction of some special finite elements for the numerical solution of Naghdi cylindrical shell problems. The standard numerical approximation of the shell problem is subjected to the shear and membrane locking phenomenon, i.e. the numerical solution degenerates for low thickness. The most common way to avoid locking is the use of modified bilinear forms to describe the shear and membrane energy of the shell. In this paper we build a family of special finite elements that still follow the above strategy by introducing a linear operator that reduces the influence both of the shear and membrane energy terms. The main idea comes from the non-standard mixed interpolated tensorial components (MITC) formulation for Reissner-Mindlin plates. The performance of the new elements is then tested for solving benchmark problems involving very thin shells. The results show both the properties of convergence and robustness. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 367-380 
    ISSN: 1069-8299
    Keywords: bevel gears ; instantaneous mesh stiffness ; load distribution ; FEM ; Engineering ; Numerical Methods and Modeling
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    Notes: A new method, namely the normal stiffness matrix along contact line (NSMACL) method, for analysing gears, is proposed. The new method uses the static coagulation technique to coagulate the global stiffness matrix of all contact teeth into a lower-order NSMACL. By adding the concert deformation condition and equilibrate condition, the relation between the torque acting on the driving gear and the load along the contact lines can be established, and the contact stress and gear tooth deformation can also be obtained. Three-dimensional (3D) highly accurate solid models of gear teeth have been established, in which the contact range and the whole finite element model can be automatically adjusted with the change of meshing process. Spur and helical bevel gears can be analysed using these models. Example models and results are presented. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 409-418 
    ISSN: 1069-8299
    Keywords: adaptive refinement procedure ; nearly incompressible problems ; error estimation ; Engineering ; Numerical Methods and Modeling
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    Notes: A numerical study is carried out employing some selected 2D elements and an automatic adaptive refinement procedure for the solution of a problem involving a nearly incompressible material. For a material with Poisson's ratio close to 0·5, it is found that both hybrid elements and high-order Lagrangian triangles can be used to provide a reliable solution. Furthermore, the rate of convergence of the elements is not affected by the high value of Poisson's ratio, and a near-optimal convergence rate is achieved in all the numerical tests run. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 529-537 
    ISSN: 1069-8299
    Keywords: finite element ; plate bending ; triangular element ; displacement method ; polynomial function ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper investigates the importance and accuracy of a family of high-order triangular elements. After a brief review of characteristics of high-order triangular elements, six new incompatible 13-node triangular elements are presented. The accuracy of the proposed elements is illustrated by comparing their numerical results with the other investigators' solutions, and the best element is introduced. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 549-558 
    ISSN: 1069-8299
    Keywords: finite elements ; adaptive analysis ; error estimate ; rh-method ; r-method ; h-method ; Engineering ; Numerical Methods and Modeling
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    Notes: An rh-method, which combines r- and h-methods, is proposed for cost-effective adaptive FE analysis in two-dimensional linear elastic problems. Through various numerical test examples, the rh-method is compared with the h-method. From these examples it is concluded that the rh-method has the advantages of both the r- and h-methods, so that the rh-method can minimize the computational time required for the adaptive analysis. The algorithm of the rh-method can be implemented easily in existing h-adaptive FE codes, since the r-method is independently combined with the h-method. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 569-580 
    ISSN: 1069-8299
    Keywords: structural optimization ; approximation concepts ; envelope function ; Engineering ; Numerical Methods and Modeling
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    Notes: In the present paper, a quasi-analytic method for solving structural optimization problems has been developed by co-ordinated use of mathematical transformations, high-quality approximation and a two-level approximation strategy. The method which has the advantages of both generality in applications and high efficiency in computations is especially of benefit to large practical design problems. Several typical examples of different sorts have been optimized to test its power. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 581-593 
    ISSN: 1069-8299
    Keywords: finite elements ; electromagnetics ; numerical simulation ; electric furnaces ; electrodes ; Engineering ; Numerical Methods and Modeling
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    Notes: In this paper we give a numerical method based on finite element discretizations to simulate the thermoelectrical behaviour of electrodes for electric reduction furnaces. After introducing the mathematical model we take advantage of the cylindrical symmetry of the problem to compute boundary conditions for the Maxwell equations. Thermal and electrical problems are coupled and non-linear because of the Joule effect and the fact that thermal conductivity and electrical resistivity depend on temperature. A classical piecewise linear finite element method on a triangular mesh is used to discretize weak formulations in cylindrical co-ordinates for the two problems. Then an iterative algorithm is proposed to solve the coupled discrete system. Numerical results are shown both for an analytical test and for a real industrial electrode. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 609-620 
    ISSN: 1069-8299
    Keywords: quadrilateral finite-element generation ; three-dimensional surfaces ; CAD/CAM interface ; topological information generation ; node sampling on edges ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: In this paper, a general approach to automatic generation of quadrilaterals on three-dimensional surfaces is presented. The approach is based on the mapping method for surface meshing and the looping method for generation of quadrilaterals on the mapped plane. Several schemes including a coedge treatment scheme, an allowable tolerance and distance scheme, a multipatch treatment scheme with new mapping functions and a remapping scheme are proposed. Several realistic application examples are given, which show the generality of the presented approach. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 657-670 
    ISSN: 1069-8299
    Keywords: flux intensity factors ; singularities ; multiple singular points ; eliptic PDEs ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: A simple method for computing the flux intensity factors associated with the asymptotic solution of elliptic equations having a large convergence radius in the vicinity of singular points is presented. The Poisson and Laplace equations over domains containing boundary singularities due to abrupt change of the boundary geometry or boundary conditions are considered. The method is based on approximating the solution by the leading terms of the local symptotic expansion, weakly enforcing boundary conditions by minimization of a norm on the domain boundary in a least-squares sense. The method is applied to the Motz problem, resulting in extremely accurate estimates for the flux intensity factors. It is shown that the method converges exponentially with the number of singular functions and requires a low computational cost. Numerical results to a number of problems concerned with the Poisson equation over an L-shaped domain, and over domains containing multiple singular points, demonstrate accurate estimates for the flux intensity factors. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 681-692 
    ISSN: 1069-8299
    Keywords: finite elements ; contact/friction problem ; Lobatto integration ; Engineering ; Numerical Methods and Modeling
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    Notes: Because the 20-node solid element of the serendipity family does not fulfil the physical contact requirements properly (the equivalent nodal forces include negative values) a 21-node three-dimensional transient element for the non-linear contact/friction problem is investigated. Construction of the shape functions is described. The proposed transition element is established by adding one node to the top or bottom face of the basic 20-node solid serendipity element for an effective connection between the contact region (21-node elements) and the rest of the structure (20-node elements) with minimum degrees of freedom possible. Comparisons with results calculated for the 3D-contact problem using the combinations of the 8-node element connected to 20-node finite elements prove the high accuracy and overall superiority of the present method. The numerical examples are shown to illustrate the validity and efficiency of the developed technique. The approach may be employed easily in existing computer codes. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 9-22 
    ISSN: 1069-8299
    Keywords: finite element method ; optimal control theory ; Navier-Stokes equations ; Lagrange multipliers ; adjacent equations ; Sakawa-Shindo method ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: This work presents control of vorticity for buoyancy-driven flows. The governing set of equations includes Navier-Stokes and heat transfer equations. The basic formulation for the control problem is derived using Lagrange multipliers and the Pontryagin minimum principle. Control values are found using the Sakawa-Shindo method. Control was accomplished using velocity components. Numerical examples present control of vorticity for Rayleigh-Bernard convection in an enclosed cavity for a wide range of Ra numbers. The current formulation proved reliable and fast. Optimal control was obtained and turned out to be adequate. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 65-75 
    ISSN: 1069-8299
    Keywords: Convection-diffusion equation ; difference method ; AGE (alternating group explicit) method ; Engineering ; Numerical Methods and Modeling
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    Notes: Some modified AGE methods for the convection-diffusion equation are developed in this paper. Firstly, there is a treatment on the convection term in the equation which is different from that in the AGE method by Evans and Abdullah (1985). Secondly, upwind-type schemes are used for the convection dominated diffusion problems. All the modified AGE methods in the paper are unconditionally stable. The numerical example is given to show the effectiveness of the methods. The methods have the obvious property of parallelism. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 81-86 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Notes: An efficient method for calculating the transient response of Timoshenko and Mindlin type structures is to use explicit time integration combined with increased rotatory inertia. Numerical stability analysis shows that time step variations are important in determining how much to increase the inertia. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 87-101 
    ISSN: 1069-8299
    Keywords: isoparametric general quadrilateral finite elements ; normal (geodesic) co-ordinates ; distortion measures ; inverse maps ; Engineering ; Numerical Methods and Modeling
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    Notes: Utilizing systematically differential geometry the paper describes a method which substantially improves results obtained by Yuan et al. (1994), though the same technique is used in both articles. An 8-node isoparametric element with curved boundaries is analysed as an object of differential geometry. Inverse transformations between normal (geodesic) co-ordinates and natural (isoparametric) co-ordinates are derived in terms of a Taylor series which is convergent and does not need many terms to give an excellent approximation of the element shape with four curved sides. The concept of local normal co-ordinates results in the definition of distortion measures of a plane element. It is shown, by exploring the theory of geodesic curves, that the distortion parameters of a chord quadrilateral, spanned on the corner nodes of the 8-node element with curved boundaries, are the basic distortion measures for this 8-node element. Thus, significant reduction of the number of these parameters, from 12 to 4, from previous works is obtained. For the purpose of the finite element method, which is very sensitive to a shape of quadrilateral elements, only basic deviation measures from a regular form of a plane element are of interest. The distortion measures due to curvatures of sides seem to be of secondary significance in the analysis if straight sides of the chord quadrilateral and curved boundaries are isomorphic. The mathematical analysis used is quite general and relies strongly on differential geometry. The results are independent of co-ordinate systems. The meaning of element distortion measures is suggested. This analysis can be extended to curved surfaces in R3. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 963-975 
    ISSN: 1069-8299
    Keywords: cylindrical gears ; load distribution ; stress ; deformation ; stiffness ; FEM ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: A method, namely the normal stiffness matrix along contact line (NSMACL) method, for analysing gears is proposed. Three-dimensional (3D) finite element (FE) solid models have been established. Cylindrical gears - spur and helical, external and internal, hobbling and slotting, different parameters and materials - can be analysed using these models. Results such as load distribution along the contact lines, deformations and stiffness at any contact position, and contact stresses are presented. Calculation results show that the trend of gear tooth deformation coincides with the tested ones using the dynamic speckle photography method. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1013-1025 
    ISSN: 1069-8299
    Keywords: assumed natural strain ; plate bending ; triangular ; finite element ; six-node ; Engineering ; Numerical Methods and Modeling
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    Notes: In this paper, a six-node triangular C0 plate bending element is developed by the assumed natural strain method. In the element, all the sampled natural transverse shear strains are chosen such that the latter has a favourable constraint index and the strains are optimized with respect to a linear pure moment field. The element passes the patch tests, yields satisfactory accuracy and shows no sign of shear locking in all the problems considered. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1027-1037 
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    Keywords: least-squares ; mixed finite element ; superconvergence ; Engineering ; Numerical Methods and Modeling
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    Notes: A least-squares mixed finite element method for the second-order non-self-adjoint two-point boundary value problems is formulated and analysed. Superconvergence estimates are developed in the maximum norm at Gaussian points and at Lobatto points. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 997-1012 
    ISSN: 1069-8299
    Keywords: potential flow ; finite element method ; wave resistance ; absorbing boundary condition ; free surface flow ; partial discretization ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the computational domain through the outlet plane. It can be shown that this method ensures a non-negative wave-resistance, in contrast with straightforward integration of the normal pressure forces. However, this calculation should be performed on a transverse plane located far behind the ship. Traditional Dawson-like methods add a numerical viscosity that dampens the wave pattern so that some amount of momentum flux is lost, and resulting in an error in the momentum balance. The flow field is computed, then, with a centred scheme with absorbing boundary conditions. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 977-993 
    ISSN: 1069-8299
    Keywords: third-order KdV equation ; fifth-order KdV equation ; pseudo-spectral ; implicit method ; unconditional stability ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the third- and fifth-order Korteweg-de Vries equations and their generalizations. The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time.An important advantage to be gained from the use of this method over the pseudo-spectral scheme proposed by Fornberg and Whitham (a Fourier transform treatment of the space variable together with a leap-frog scheme in time) which is conditionally stable, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable.The method presented here is for the Korteweg-de Vries equations and their generalized forms, but it can be implemented to a broad class of non-linear wave equations (equation (1)), with obvious changes in the various formulae.To illustrate the application of this method, numerical results portraying a single soliton solution and the collision of two solitons are reported for the third- and fifth-order Korteweg-de Vries equations. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1039-1046 
    ISSN: 1069-8299
    Keywords: eigenvalue analysis ; plane notch problem ; numerical solution ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel numerical solution technique for evaluating eigenvalues in a plane notch problem is suggested. In both real value and complex value cases, the problem for evaluating the eigenvalue is reduced to finding the roots of a function F(x)=0, and the roots can be evaluated by the well known half-division method in numerical analysis. Finally, two examples with the calculated results are presented. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1047-1053 
    ISSN: 1069-8299
    Keywords: design analysis ; boundary elements ; re-analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A combination of an automated boundary element elasticity analysis with an interactive sketching tool allows rapid stress calculations early in the design process. The inclusion in the system of a provision for automated re-analysis following a design modification overcomes the limitations of earlier re-analysis approaches, providing a rapid update of stress contours following sequential changes of different design features. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1055-1065 
    ISSN: 1069-8299
    Keywords: boundary element method ; domain integrals ; dual reciprocity method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper a new technique is presented for transferring the domain integrals in the boundary integral equation method into equivalent boundary integrals. The technique has certain similarities to the dual reciprocity method (DRM) in the way radial basis functions are used to approximate the body force term. However, the resulting integrals are evaluated in a much simpler way. Several examples are presented to demonstrate the validity and accuracy of the proposed paper. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1089-1094 
    ISSN: 1069-8299
    Keywords: total-Lagrangian finite-element analysis ; experiment ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A total-Lagrangian displacement-based finite-element model of initially curved beams undergoing large displacements and rotations is derived using a beam theory that fully accounts for large rotations and extensionality by using Jaumann stress and strain measures. To verify the accuracy of the finite-element model, a test fixture has been built and used to test the large twisting of a circular band. The finite-element results agree closely with the experimental results. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1067-1088 
    ISSN: 1069-8299
    Keywords: submarine pipelines ; non-linear static analysis ; finite element model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A non-linear finite element numerical procedure is adopted for predicting the bending stresses developed along highly curved submarine pipelines during the installation process from a laybarge towards an irregular sea floor. The problem of partial seabed-pipeline and stinger-pipeline contact is tackled by means of a point iterative calculation approach. The geometric non-linearity embedded in the beam flexural theory enables major deformations of the submarine line structures to be accurately modelled. Numerical calculations tend to be demanding, especially when large differences occur between the pipeline and seabed configurations. Three structural problems of practical significance provide a suitable application platform for testing the efficiency of the mathematical model. A Fortran subroutine implementing the fundamental procedures of the proposed numerical theory is included. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 89
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1119-1131 
    ISSN: 1069-8299
    Keywords: Reissner-Mindlin plate ; finite element method ; p version ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the finite element (FE) approximation of the Reissner-Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p/hp version of the standard FE method is used. These guidelines allow quantities of engineering interest to be predicted numerically with great confidence near the boundary. We illustrate this through numerical computations in the case when both boundary layers and corner singularities are present. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 90
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1133-1141 
    ISSN: 1069-8299
    Keywords: differential quadrature element method ; rectangular plate ; static analysis ; free vibration analysis ; numerical method ; stepped plate ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The differential quadrature (DQ) element method proposed by Wang and Gu in 1997 has been extended to analyse rectangular plate problems. The methodology is worked out in detail and some numerical examples are given. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1143-1154 
    ISSN: 1069-8299
    Keywords: super-element ; cracked plate ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the formulation of a super-element for the dynamic problem of a cracked plate, a geometric series of similar elements is designed. This group of elements is generated layer by layer, approaching infinitely small size around the point of singularity. The relations between similar elements for the stiffness matrix and the mass matrix are established. The concept of matrix condensation is applied to formulate the super-element by using these relationships. This method presents a feasible approach to the solution of the cracked problem with an arbitrary order of stress singularity. The method is computationally economical. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1171-1179 
    ISSN: 1069-8299
    Keywords: linear θ method ; time-domain BEM ; stability ; scalar wave ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A linear θ method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson θ method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and flux (for scalar waves) is assumed in the time interval θΔt. A comparison between numerical results obtained from the standard formulation and from the linear θ method studied here shows the latter to be more stable than the former. The effect of varying θ for different values of time steps is also studied in this paper. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 731-749 
    ISSN: 1069-8299
    Keywords: superconvergence ; corrected conjoint polynomial ; weight functions ; element patch ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A superconvergent element patch based stress extraction strategy is proposed for general FE postprocessing and/or error estimation procedures in adaptive finite element analysis. Generalized weight functions are proposed for discrete least-square functionals, and a corrected conjoint polynomial fitting procedure is presented to ensure accurate stress extraction from the element domain once the primary level stress parameters have been evaluated. A numerical example is presented to fix the parameters of the weight functions. Several plane stress examples are solved using QUAD4 elements, and results are compared to those of the node patch based extraction method using the conventional conjoint polynomial method. It is shown that the proposed technique yields more accurate results with enhanced local convergence. Although the method may be applied to higher-order elements too, only QUAD4 elements are chosen for the present examples since the present secondary refitting strategy assumes superconvergent points only to be at element centroids. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 863-869 
    ISSN: 1069-8299
    Keywords: advection-diffusion ; two-dimensional ; streamtube ; DISCUS ; accuracy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes a substantial improvement to an existing modelling approach for two-dimensional solute transport. The flow field is represented by a series of streamtubes in which advection is simulated using a highly accurate semi-Lagrangian numerical scheme. Transverse mixing between the streamtubes is treated with a standard numerical method for diffusion. Numerical experiments demonstrate that accurate simulations of the longitudinal dispersion caused by the interaction of a simple transverse velocity profile and transverse diffusion can be obtained over a wide range of time-steps provided that the diffusion occurring during the time-step is properly accounted for. The model is ultimately limited by the relatively poor numerical treatment of transverse diffusion, but this could be remedied by employing an enhanced numerical method for this term. The paper concludes that this is an area in which future modelling efforts need to be directed. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 879-893 
    ISSN: 1069-8299
    Keywords: derogatory eigenproblems ; Jordan blocks ; Jordan chains ; Segre characteristic ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The major obstacle to determination of the Jordan chains for a highly degenerated eigenproblem is that the triangular combinations of the principal vectors in a Jordan chain are also principal vectors and the linear combinations of the eigenvectors of all Jordan blocks associated with the same eigenvalue are also eigenvectors. These indeterminate constants will hide the Jordan block structure and make the analysis very difficult. We propose an extended matrix method to find the Jordan chains and eliminate the indeterminate constants so that the Jordan block structure can be computed sequentially. An example with the Segre characteristic [(321)11] is given. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 931-940 
    ISSN: 1069-8299
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids. © 1998 John Wiley & Sons, Ltd.
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    Journal of Biomedical Materials Research 39 (1998), S. 469-477 
    ISSN: 0021-9304
    Keywords: poly(urethane)s ; monocyte-derived macrophages ; cholesterol esterase ; biodegradation ; biostability ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine , Technology
    Notes: Monocytes adherent to implanted biomaterials differentiate into macrophages while synthesizing large amounts of degradative enzymes, including cholesterol esterase (CE), which previously has been shown to degrade poly(urethane)s. Human peripheral blood monocytes were cultured on tissue culture grade polystyrene (PS), and two model poly(urethane)s were synthesized from (1) polycaprolactone (PCL) and (2) polytetramethylene oxide (PTMO), both with 2,4-toluene diisocyanate (TDI) and ethylene diamine (ED). The increase in CE and total protein per cell were measured on days 8 and 28 in culture and normalized to the DNA content per cell. At day 8 there consistently were fewer cells remaining on the PTMO-based polymer than on the PCL-based polymer or the PS (p 〈 0.05). When comparing day 28 to day 8, there was more CE activity and protein per cell on all materials. However, there was a disproportionate synthesis of CE per mg of total protein on PS and TDI/PCL/ED whereas on PTMO there was not. Significantly, there was more protein and CE per cell on PTMO than on PS or TDI/PCL/ED (p 〈 0.05). This in vitro model system of the chronic phase of inflammation has shown that it is possible to culture monocytes for a month and assess the material surface itself as a potent activator of the differentiation into macrophages without secondary stimulation. Since CE has been shown to degrade poly(ether and ester)-based poly(urethane)s, the differential production of this enzyme relative to the total protein on different surfaces may impact on the potential long-term biostability of an implanted material. © 1998 John Wiley & Sons, Inc. J Biomed Mater Res, 39, 469-477, 1998.
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    Journal of Biomedical Materials Research 39 (1998), S. 491-497 
    ISSN: 0021-9304
    Keywords: biomaterial ; mechanism of calcification ; diffusion chamber ; calcium-containing deposits ; protein sorption ; SEM-XRMA ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine , Technology
    Notes: In experiments in vivo using diffusion chambers, the morphology and composition of calcium-containing deposits on natural and artificial biomaterials that had no direct contact with cells were studied using scanning electron microscopy with energy dispersion X-ray microanalysis. It was revealed that the formation of a protein layer containing protein-calcium complexes is the key event in biomaterial calcification. A mechanism of formation of a calcium-containing protein matrix that creates the conditions for supersaturation of the crystal-forming medium over critical value has been proposed. The formation of nuclei of insoluble calcium phosphate starts predominantly deep in an adsorbed protein layer enriched by calcium ions. © 1998 John Wiley & Sons, Inc. J Biomed Mater Res, 39, 491-497, 1998.
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    Journal of Biomedical Materials Research 39 (1998), S. 511-515 
    ISSN: 0021-9304
    Keywords: dental resin ; antibacterial activity ; Streptococcus mutans ; curing ; adhesion ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine , Technology
    Notes: In this study, the antibacterial monomer 12-methacryloyloxydodecylpyridinium bromide (MDPB) and an adhesion-promoting phosphoric monomer were incorporated into Bis-GMA-based dental resin and its antibacterial activity after curing was investigated. The experimental resin containing MDPB and 10-methacryloyloxydecyl dihydrogen phosphate (MDP) was polymerized and washed with methanol, and the bacteriostatic and bactericidal effects against Streptococcus mutans were determined. Growth of S. mutans was strongly inhibited by contact with the surface of cured MDPB/MDP-containing resin, although the bactericidal effect was small. Cured MDPB/MDP-containing resin also showed an inhibitory effect against in vitro plaque formation on its surface by S. mutans. The bactericide immobilized in Bis-GMA-based resin demonstrated bacteriostatic activity as a contact antimicrobial even when adhesion-promoting phosphoric monomer was incorporated into the materials. © 1998 John Wiley & Sons, Inc. J Biomed Mater Res, 39, 511-515, 1998.
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    Journal of Biomedical Materials Research 39 (1998), S. 531-535 
    ISSN: 0021-9304
    Keywords: artificial skin ; collagen-glycosaminoglycan matrix ; keratinocytes ; guinea pigs ; skin regeneration ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine , Technology
    Notes: Deep skin wounds in the adult mammal close spontaneously by epithelialization, wound contraction, and scar synthesis. In previous wound healing studies, it has been unsuccessfully attempted to separate from each other the natural processes that close wounds. In this study, we attempted to isolate skin regeneration from spontaneous processes of wound closure using “island” grafts. A porous analog of the extracellular matrix, composed of a graft copolymer of type I collagen and chondroitin 6-sulfate, was seeded with uncultured autologous keratinocytes and served to induce regeneration of the dermis and the epidermis. Grafts of the copolymer, measuring 1 × 2 cm, were placed in the center of 5 × 6-cm wounds in guinea pigs. By day 14, the edges of the island grafts were clearly separated from the host epidermis and dermis by a distinct bed of granulation tissue. Histologic study of island grafts on day 14 showed that the copolymer grafts had largely degraded and that a new epidermis and dermis had been synthesized in its place. The thickness of the new epidermis increased as the density of cells seeded into the graft increased. No synthesis of epidermis or dermis was observed in the granulation tissue outside the perimeter of the island grafts. We conclude that island grafting allows the study of early events in skin regeneration in isolation from epithelialization, contraction, and scar synthesis. © 1998 John Wiley & Sons, Inc. J Biomed Mater Res, 39, 531-535, 1998.
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