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  • 101
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1467-1477 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, the existence, both locally and globally in time, the uniqueness of solutions and the non-existence of global solutions to the initial boundary value problem of a generalized Modification of the Improved Boussinesq equation utt-uxx-uxxtt=σ(u)xx are studied and a few examples are discussed. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 102
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1593-1617 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the following problem:ut-Δu=-f(u) in Ω×(0, T)≡QT,∂u ∂n=g(u) on ∂Ω×(0, T)≡ST,u(x, 0)=u0(x) in Ω, where Ω⊂∝N is a smooth bounded domain, f and g are smooth functions which are positive when the argument is positive, and u0(x)〉0 satisfies some smooth and compatibility conditions to guarantee the classical solution u(x, t) exists. We first obtain some existence and non-existence results for the corresponding elliptic problems. Then, we establish certain conditions for a finite time blow-up and global boundedness of the solutions of the time-dependent problem. Further, we analyse systems with same kind of boundary conditions and find some blow-up results. In the last section, we study the corresponding elliptic problems in one-dimensional domain. Our main method is the comparison principle and the construction of special forms of upper-lower solutions using related equations. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 103
    Electronic Resource
    Electronic Resource
    Springer
    Journal of autism and developmental disorders 28 (1998), S. 427-437 
    ISSN: 1573-3432
    Keywords: Genetics ; autism ; genotyping
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract Genetic factors are likely to play a major role in the etiology of autism. The genetics of the disorder is however complex, probably involving the action of several genes. In an attempt to identify autism susceptibility loci we are currently undertaking a systematic screening of the whole human genome using multiplex families. We describe the resources and the methods needed to achieve such a task, including extensive collection of family data, semiautomated genotyping technology, and specialized statistical approaches for linkage analysis of complex traits.
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  • 104
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 6 Ill.
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  • 105
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 12 Ill.
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  • 106
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 11 Ill.
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  • 107
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 2 Ill.
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  • 108
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 5 Ill.
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  • 109
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 2 Ill.
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  • 110
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 5 Ill.
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  • 111
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 6 Ill.
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  • 112
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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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  • 113
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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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  • 114
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 6 Ill.
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  • 115
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 6 Ill.
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  • 116
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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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  • 117
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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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  • 118
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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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  • 119
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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.
    Additional Material: 8 Ill.
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  • 120
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    Electronic Resource
    Chichester : Wiley-Blackwell
    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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  • 121
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    Chichester : Wiley-Blackwell
    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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  • 122
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    Chichester : Wiley-Blackwell
    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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  • 123
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    Chichester : Wiley-Blackwell
    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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  • 124
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    Chichester : Wiley-Blackwell
    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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  • 125
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    Chichester : Wiley-Blackwell
    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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  • 126
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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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  • 127
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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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  • 128
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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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    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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  • 130
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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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    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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  • 132
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 133
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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  • 134
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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  • 135
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    Numerical Linear Algebra with Applications 5 (1998), S. 147-164 
    ISSN: 1070-5325
    Keywords: eigenvalue problem ; Lanczos method ; power method ; Krylov information ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study Lanczos and polynomial algorithms with random start for estimating an eigenvector corresponding to the largest eigenvalue of an n × n large symmetric positive definite matrix. We analyze the two error criteria: the randomized error and the randomized residual error. For the randomized error, we prove that it is not possible to get distribution-free bounds, i.e., the bounds must depend on the distribution of eigenvalues of the matrix. We supply such bounds and show that they depend on the ratio of the two largest eigenvalues. For the randomized residual error, distribution-free bounds exist and are provided in the paper. We also provide asymptotic bounds, as well as bounds depending on the ratio of the two largest eigenvalues. The bounds for the Lanczos algorithm may be helpful in a practical implementation and termination of this algorithm. © 1998 John Wiley & Sons, Ltd.
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  • 136
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    Numerical Linear Algebra with Applications 5 (1998), S. 203-217 
    ISSN: 1070-5325
    Keywords: boundary value problem ; boundary element method ; preconditioning ; fast Fourier transform ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The algebraic properties of the matrix arising for the three-dimensional Dirichlet problem for Lamé equations in a rotational domain by the boundary element method are considered. The use of the special basis leads to a matrix having a block structure with sparse blocks. The possible strategies for the efficient solution of the above problem are discussed. © 1998 John Wiley & Sons, Ltd.
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  • 137
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    Numerical Linear Algebra with Applications 5 (1998), S. 299-311 
    ISSN: 1070-5325
    Keywords: iterative methods ; singular linear systems ; index of a matrix ; M-splittings ; multi-splittings ; Q-matrices ; Markov chains ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Given a singular M-matrix of a linear system, convergent conditions under which iterative schemes based on M-multisplittings are studied. Two of those conditions, the index of the iteration matrix and its spectral radius are investigated and related to those of the M-matrix. Furthermore, a parallel multisplitting iteration scheme for solving singular linear systems is suggested which can be applied to practical problems such as Poisson and elasticity problems under certain boundary conditions, the Neumann problem, and in Markov chains. A discussion of that multisplitting scheme, based on Gauss-Seidel type splittings is given for computing the stationary distribution vector of Markov chains. In this case a computational viable algorithm can be constructed, since only the nonsingularity of one weighting matrix of the multisplitting is needed. © 1998 John Wiley & Sons, Ltd.
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  • 138
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    Numerical Linear Algebra with Applications 5 (1998), S. 275-297 
    ISSN: 1070-5325
    Keywords: GMRES method ; Krylov subspace methods ; non-symmetric linear systems ; homotopy curve tracking ; sparse matrix ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: GMRES(k) is widely used for solving non-symmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram-Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES(k) which tunes the restart value k based on criteria estimating the GMRES convergence rate for the given problem is proposed here. This adaptive GMRES(k) procedure outperforms standard GMRES(k), several other GMRES-like methods, and QMR on actual large scale sparse structural mechanics postbuckling and analog circuit simulation problems. There are some applications, such as homotopy methods for high Reynolds number viscous flows, solid mechanics postbuckling analysis, and analog circuit simulation, where very high accuracy in the linear system solutions is essential. In this context, the modified Gram-Schmidt process in GMRES, can fail causing the entire GMRES iteration to fail. It is shown that the adaptive GMRES(k) with the orthogonalization performed by Householder transformations succeeds whenever GMRES(k) with the orthogonalization performed by the modified Gram-Schmidt process fails, and the extra cost of computing Householder transformations is justified for these applications. © 1998 John Wiley & Sons, Ltd.
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  • 139
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    Numerical Linear Algebra with Applications 5 (1998), S. 347-362 
    ISSN: 1070-5325
    Keywords: almost incompressible elasticity ; finite elements ; semi-coarsening refinement ; algebraic multilevel ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The constant γ in the strengthened Cauchy-Buniakowski-Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two-dimensional elasticity problem by bilinear rectangle finite elements. Two semi-coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio.As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi-coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 93-116 
    ISSN: 0170-4214
    Keywords: continuum mechanics ; elasticity ; viscoelasticity ; viscoplasticity ; semilinear evolution equations ; Galerkin approximation ; energy estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Uniaxial semilinear Miller's equations describing the shearing motion of a steel layer with small deformation and stress are solved uniquely using energy and hardening estimates up to the first derivatives. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 463-477 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the time-harmonic Maxwell equations in the high-frequency case for a heterogeneous medium, i.e., a medium which is composed by a conductor and a perfect insulator, or, in other words, a loaded cavity. As a consequence of a suitable compactness result, we prove that Fredholm alternative holds for such a problem. Since the kernels of the considered operator and of its adjoint are proven to be trivial, a unique solution exists for each given datum. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 142
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 733-755 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In space-based robotics, one of the most important problems is the disturbance to the satellite attitude and to the satellite microgravity environment caused by satellite mounted robot operation. This paper reports on computer-aided motion planning strategies to overcome this problem. Point-to-point motion designs are generated which not only connect prescribed start and end points of the robot motion, but also simultaneously return the satellite to its original attitude. Theoretical characterizations of some of those motion designs are presented, as well as numerical results. The computation time required to produce such motion designs is 1 or 2 min on a workstation. Thus, it can be practical to use these motion plans in space. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 143
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 823-864 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Description / Table of Contents: On présente dans cet article un certain nombre de résultats concernant le potentiel vecteur associé à une fonction à divergence nulle dans un ouvert borné de dimension trois. En particulier, plusieurs types de conditions aux limites sont proposés, pour lesquels on discute l'existence, l'unicité et la régularité du potentiel vecteur. On analyse la convergence d'une discrétisation par éléments finis de ces potentiels et on indique une application concernant l'approximation de fluides visqueux incompressibles.© 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
    Notes: This paper presents several results concerning the vector potential which can be associated with a divergence-free function in a bounded three-dimensional domain. Different types of boundary conditions are given, for which the existence, uniqueness and regularity of the potential are studied. This is applied firstly to the finite element discretization of these potentials and secondly to a new formulation of incompressible viscous flow problems.
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  • 144
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 865-882 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present an initial-boundary value problem of a quasilinear degenerate parabolic equation for the settling and consolidation of a flocculated suspension. The corresponding definition of generalized solutions is formulated. It is based on an entropy integral inequality in the sense of Kružkov. From this definition, jump and entropy conditions that have to be satisfied at discontinuities, and an entropy condition valid on one boundary of the computational domain are derived. The latter implies a set-valued reformulation of the original boundary condition. It is interpreted geometrically and characterized by the solution of an auxiliary hyperbolic Riemann problem. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 907-938 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work is devoted to prove the existence of weak solutions of the kinetic Vlasov-Poisson-Fokker-Planck system in bounded domains for attractive or repulsive forces. Absorbing and reflection-type boundary conditions are considered for the kinetic equation and zero values for the potential on the boundary. The existence of weak solutions is proved for bounded and integrable initial and boundary data with finite energy. The main difficulty of this problem is to obtain an existence theory for the linear equation. This fact is analysed using a variational technique and the theory of elliptic-parabolic equations of second order. The proof of existence for the initial-boundary value problems is carried out following a procedure of regularization and linearization of the problem. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 969-983 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the problem of the scattering by a periodic, inhomogeneous, penetrable medium. Using the Dirichlet-to-Neumann operator from the classical formulation of the problem we derive a variational equation and give regularity result to show the equivalence of both formulations. We present certain uniqueness results, which by the Fredholm alternative yield existence of the solution and its continuous dependence on the incoming wave. We prove existence of a solution for special incident waves even if there is no uniqueness. A result about analytical dependence of the solution on the wave number and the incident angle is given. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1015-1033 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study stationary and quasistationary solutions of the relativistic Vlasov-Maxwell system of plasma physics which have a special form introduced (in the classical setting) by Rudykh et al. [9, 10]. The actual construction of such solutions leads to semi-linear elliptic equations. Under suitable assumptions on the ansatz functions, we are able to solve these equations by a sub- and supersolution approach. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1035-1048 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider an initial boundary value problem for a non-linear differential system consisting of one equation of parabolic type coupled with a n × n semi-linear hyperbolic system of first order. This system of equations describes the compressible miscible displacement of n + 1 chemical species in a porous medium, in the absence of diffusion and dispersion. We assume the viscosity of the fluid mixture to be constant. We prove, in three space dimensions, the existence of a global weak solution with non-smooth initial data for the concentration. The proof is based on the artificial viscosity method together with a compensated compactness argument. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1149-1183 
    ISSN: 0170-4214
    Keywords: free boundary fluid motion ; Cauchy problem ; Hamilton structure ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Cauchy problem for the motion of a liquid drop under surface tension is solved locally in time on the basis of a general abstract existence theorem for Hamiltonian systems which seems to be of interest also in other areas. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1227-1232 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a reaction-diffusion system with a full matrix of diffusion coefficients satisfying a balance law on a bounded domain with no-flux boundary conditions. We demonstrate that global solutions exist for polynomial reaction terms provided some conditions on the diffusion coefficients are satisfied. The proof makes use of comparison results and Solonnikov's estimates concerning linear parabolic equations in Banach spaces. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1269-1286 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider homogeneous solutions of the Vlasov-Fokker-Planck equation in plasma theory proving that they reach the equilibrium with a time exponential rate in various norms. By Csiszar-Kullback inequality, strong L1-convergence is a consequence of the ‘sharp’ exponential decay of relative entropy and relative Fisher information. To prove exponential strong decay in Sobolev spaces Hk, k ≥ 0, we take into account the smoothing effect of the Fokker-Planck kernel. Finally, we prove that in a metric for probability distributions recently introduced in [9] and studied in [4, 14] the decay towards equilibrium is exponential at a rate depending on the number of moments bounded initially. Uniform bounds on the solution in various norms are then combined, by interpolation inequalities, with the convergence in this weak metric, to recover the optimal rate of decay in Sobolev spaces. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1297-1342 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of the paper is to provide the mathematical foundation of effective numerical algorithms for the optimal design of periodic binary gratings. Special attention is paid to reliable methods for the computation of diffraction efficiencies and of the gradients of certain functionals with respect to the parameters of the non-smooth grating profile. The methods are based on a generalized finite element discretization of strongly elliptic variational formulations of quasi-periodic transmission problems for the Helmholtz equation in a bounded domain coupled with boundary integral representations in the exterior. We prove uniqueness and existence results for quite general situations and analyse the convergence of the numerical solutions. Furthermore, explicit formulas for the partial derivatives of the reflection and transmission coefficients with respect to the parameters of a binary grating profile are derived. Finally, we briefly discuss the implementation of the generalized finite element method for solving direct and adjoint diffraction problems and present some numerical results. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1441-1465 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the inverse backscattering problem for Maxwell's equations in a non-magnetic inhomogeneous medium, i.e. the magnetic permeability is a fixed constant. We show that the electric permittivity ε is uniquely determined by the trace of the backscattering kernel S(s, -θ, θ) for all s∊∝, θ∊S2 provided that it is a priori close to a constant. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1379-1398 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with a non-linear inverse problem of identification of unknown boundaries, on which the prescribed conditions are of Signorini type. We first prove an identifiability result, in both frameworks of thermal and elastic testing. Local Lipschitz stability of the solutions with respect to the boundary measurements is also established, in case of unknown boundaries which are parts of C1, β Jordan curves, with β〉0. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1495-1517 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Inverse problems for identification of the four memory kernels in one-dimensional linear thermoviscoelasticity are reduced to a system of non-linear Volterra integral equations using Fourier's method for solving the direct problem. To this system of equations the contraction principle in weighted norms is applied. In this way global in time existence of a solution to the inverse problems is proved and stability estimates for it are derived. In analogous way inverse problems for the memory kernels in linear poroviscoelasticity can be handled. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 153-166 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Most methods for the numerical calculation of inverse Laplace transformations f(t) = L-1[F(s)] have serious limitations concerning the class of functions F(s) that can be inverted or the achievable accuracy. The procedures described in the paper can be used to invert rational as well as irrational or transcendental functions of the complex variable s. The required accuracy of the results can be enhanced without changing the algorithm, only at the cost of a longer computation time. The described methods were verified with many examples including transients in lumped/distributed systems with sections of lossy multiconductor transmission lines or with distributed RC elements. © 1998 John Wiley & Sons, Ltd.
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  • 157
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 158
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 167-181 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: In this study, a software package is described which has been developed for the simulation of detection and tracking in surface wave high frequency (SW-HF) radars. The aim is to investigate the problems related to detection and tracking of surface targets at beyond the horizon ranges. In SW-HF radars target detection and tracking involves stochastic features such as target RCS fluctuations, atmospheric, galactic and/or man-made ambient interference components, and the sea clutter with the dominant resonant Bragg returns which affect target detection are all incorporated in the package. In the model, first, terrain data are fed into the simulator by means of a specially designed graphical user interface. Then, a scenario is prepared where the radar's location, coverage and operational parameters can be defined, together with different targets and their sailing routes. The radial propagation paths for angular resolution cells are extracted from the terrain data with the lengths of (possible) sea-island transitions. The surface wave path losses are calculated over the smooth spherical earth's surface with finite conductivity. Surface roughness and mixed-path propagation effects are also included in these calculations. The target detection is performed in the frequency domain after calculation of the noise floor, signal to noise (SNR) and clutter to noise (CNR) ratios. Since SW-HF radars yield coarse range and azimuth but accurate velocity measurements, different Kalman filter techniques are applied for the target tracking, and algorithms are added to improve the track-measurement data correlation. Various simulation tests are performed and the results are presented. © 1998 John Wiley & Sons, Ltd.
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  • 159
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 187-187 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: No abstract
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  • 160
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 273-274 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: No Abstract
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  • 161
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 255-257 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: We re-examine the potential drop method to give a direct estimation of the absolute error in transmission-line matrix (TLM) diffusion modelling. In particular, the open-circuit boundary is taken into account. Promising results are presented with a structure relevant to thermal analysis of semiconductor devices. © 1998 John Wiley & Sons, Ltd.
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  • 162
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 259-271 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: There is a class of material processing simulators which require solution of the diffusion equation over a surface which is evolving due to some physical or chemical process related to the concentration of the diffusing species. Because of its explicit and unconditionally stable nature, the transmission line matrix (TLM) method is well suited to efficiently solve the diffusion equation in these instances. However, the methodology for using TLM on a dynamic problem space is not well established.This paper describes the development of algorithms to handle the insertion, deletion and motion of TLM nodes along the one-dimensional surface of a two-dimensional thin film process simulator called GROFILMS. These routines are completely compatible with concurrent time scaling to increase computational efficiency. Central to this development is the use of an asymmetric TLM cell which provides more flexibility for representation and minimizes the disturbance effects of these nodal operations. The scaling routines apply conservation of charge and continuity of current into the affected region to recompute the scattered or the incident pulses as a result of the evolving network. Verification of these results through comparison with known analytic solutions is achieved where possible. © 1998 John Wiley & Sons, Ltd.
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  • 163
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 277-287 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The solution of Maxwell's equations is considered using the finite difference time domain (FDTD) method and the client-server software paradigm on a heterogeneous network of distributed computers. The performance of compilers is evaluated and the PVM 3.3 message-passing harness, in both its conventional and TCP mode of operation, is compared with direct calls to the lesser known TCP/IP routines on the operating system. An example is given showing the impact of using different floating-point representations, in each subdomain, when computing field updates. As far as we are aware to date, there has been no discussion of the actual content of the communication between concurrent FDTD processes; accordingly we have defined one such protocol. © 1998 John Wiley & Sons, Ltd.
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  • 164
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 307-316 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper presents an FE modelling approach for the calculation of transient eddy currents in thin conductive layers, where the complexity of the geometry prohibits both a detailed FE modelling and the use of analytical tools. The method allows an estimation of the maximum values of eddy currents at a highly reduced modelling effort and the use of a commercial FE software package. A prerequisite is a slowly varying magnetic field that can be assumed to be unaffected by the eddy currents. It is shown that neither the source of the magnetic field nor the insulating environment has to be modelled. The model is built up exclusively from 2D elements and is excited via the magnetic vector potential. The spatial distribution of the latter is calculated separately in a magnetostatic calculation based on Biot-Savart's law. It is then applied in time-varying form as a dynamic boundary condition at every node of the model. The method was applied to a simple problem for which the results of a detailed FE calculation were available, to document its validity. Further numerical results are presented for the plasma vessel and the heat radiation shield of the Wendelstein 7-X fusion experiment in the case of an emergency discharge. © 1998 John Wiley & Sons, Ltd.
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  • 165
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 55-68 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Multiresolution time domain (MRTD) analysis is applied directly to Maxwell's equations to model inhomogeneous dielectric material. In our approach, scaling and wavelet functions are used as a complete basis for the method of moments. The MRTD scheme is used to analyze different types of resonant cavity structures with varying dielectric perturbations in one, two and three dimensions. The results presented here agree very well with those obtained by FDTD, FEM and integral equation methods. MRTD allows for considerable savings in memory and computation time in comparison to FDTD, while maintaining the same accuracy of the results. © 1998 John Wiley & Sons, Ltd.
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  • 166
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 1-1 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: No Abstract
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  • 167
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 105-121 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper describes a computationally efficient diakoptic algorithm for the solution of closed-mesh electrical network equations. The algorithm is designed for use with time-varying and/or discontinuous equations describing limited size power supply systems, allowing them to be torn into smaller subdivisions in a manner that is independent of their structure. The efficiency of the algorithm is demonstrated by comparing its performance with that obtained when using a more conventional sparse matrix technique, on the basis of the number of floating point operations required for the solution of a range of typical network problems. Mention is made of the parallel processes inherent in the resultant equation structure. © 1998 John Wiley & Sons, Ltd.
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  • 168
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 131-131 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: No Abstract
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  • 169
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 221-229 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper presents a physical-mathematical model for abrupt heterojunction transistors and its solution using numerical methods with application to InP/InGaAs HBTs. The physical model is based on the combination of the drift-diffusion transport model in the bulk with thermionic emission and tunnelling transmission through the emitter-base interface. Fermi-Dirac statistics and bandgap narrowing distribution between the valence and conduction bands are considered in the model. A compact formulation is used that makes it easy to take into account other effects such as the non-parabolic nature of the bands or the presence of various subbands in the conduction process. The simulator has been implemented for distributed memory multicomputers, making use of the MPI message-passing standard library. In order to accelerate the solution process of the linear system, iterative methods with parallel incomplete factorization-based preconditioners have been used. © 1998 John Wiley & Sons, Ltd.
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  • 170
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 273-273 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: No Abstract
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  • 171
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 233-242 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The propagation factors of buried microstrip lines are considered. The associated eigenvalue problems are solved by the edge-based vectorial finite element method (VFEM). To improve the higher-order VFEM solutions, the problem infinite domain is truncated by second-order absorbing boundary conditions (ABCs). This reduces the number of unknowns and, consequently, the numerical effort. Owing to the many advantages of both the edge-based VFEM and the second-order ABCs, this full-wave method is implemented by a general computer program for solving unbounded domain problems involving complex geometries and inhomogeneous media. The examples presented show the validity of this technique. © 1998 John Wiley & Sons, Ltd.
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  • 172
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 243-254 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Various local absorbing boundary conditions are implemented in the TLM method and their corresponding reflections are compared as a waveguide termination. The instability in different ABCs is discussed and reflections from the terminating walls are computed. An improvement for the matched termination wall is proposed and reflection of this absorbing condition is compared with ordinary matched termination. © 1998 John Wiley & Sons, Ltd.
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  • 173
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 317-318 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: No Abstract
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  • 174
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 289-298 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Oscillatory flow present in the melt during InSb single crystal growth using an RF-heating Czochralski method has been numerically investigated by means of the finite difference method using the HSMAC algorithm. The thermal boundary conditions required for the numerical simulation model were obtained experimentally by measuring the temperature profile along the crucible of a Czochralski system by means of thermocouples mounted in the crucible. Results of numerical simulations showed that the use of a third-order upwind discretization scheme was necessary to catch the oscillatory behaviour of the fluid flow in the melt. It was shown that this oscillatory behaviour strongly depends on the crystal rotation rate. Indeed, the oscillation period increases when the crystal rotation rate is above a critical rotation rate. In order to avoid such oscillations, crystal rotation rates lower than this critical value of crystal rotation rate must be selected for the growth of high quality crystals free of striations. © 1998 John Wiley & Sons, Ltd.
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  • 175
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 299-306 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The application of the FDTD algorithm on generalized non-orthogonal meshes, following the basic ideas of Holland (1983), has been investigated by many authors for several years now, and detailed dispersion analysis as well as convergence studies have been published. Already in 1992 also a general stability criterion was given for the time integration using the standard leap-frog scheme (Lee et al.). Many authors, however, still propose some damped time stepping algorithms to work around unexpected instabilities in the discretization method. In this paper the origin of this type of instability is revealed, and a technique to obtain a stable discretization of Maxwell's equations on non-orthogonal grids is proposed. To obtain more insight into the stability properties of the method, it is reformulated according to the matrix-vector notation of the Finite Integration Technique. © 1998 John Wiley & Sons, Ltd.
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  • 176
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 123-130 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper presents the electrode separation method for the boundary condition of a-Si TFT mixed-level simulation. The Poisson equation and the continuity equation are formulated into equivalent circuits. So, a circuit simulator can be used to handle the two-dimensional numerical simulation of a-Si TFT. The boundary condition problem between a semiconductor and an external circuit is solved by the electrode separation method. An electrode is separated into two nodes to fit Kirchhoff's current law and the semiconductor equations, respectively. A simple a-Si TFT/LCD circuit is taken as an example for the electrode separation method. For mixed-level simulation this technique is very useful. © 1998 John Wiley & Sons, Ltd.
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  • 177
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 133-151 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Most traditional theories of speech production are currently based on plane waves. However, it is well known that, for acoustic waveguides, higher acoustical modes start to propagate and can become predominant above cut-on frequencies. This paper thus presents the transmission line matrix method, a numerical method initially designed for electromagnetic waves, and its adaptation to acoustic waveguides. The method, and in particular the representation of boundary conditions, is validated by comparison with known analytical theories. It is then used to show the dramatic effect of higher order modes upon the radiation characteristics of uniform ducts, as well as the importance of source location. Finally, first applications to bent and bifurcating rectangular ducts are presented, and the transfer function of a vowel [a] is shown to display frequency patterns typical of those measured on human subjects and that cannot be explained by one-dimensional propagation only. © 1998 John Wiley & Sons, Ltd.
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  • 178
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 189-205 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The atomic mixing model that forms the basis of the IMPETUS software is described in detail. The model simulates the mixing and particle emission that occurs when a solid is bombarded with energetic particles, such as in SIMS or SNMS. The methods employed for computing the deposition of the bombarding particles and their energies along with the modelling of the particle yield and the surface recession speed are described.The material volume concentrations are governed by a set of partial differential equations. A description of the finite element method that is employed for their solution is given. Results from the application of IMPETUS II to a number of typical structures are given. © 1998 John Wiley & Sons, Ltd.
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  • 179
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 207-219 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The IMPETUS II code simulates the atomic mixing and particle emission that occurs when a solid is bombarded by energetic particles (as in SIMS or SNMS). The underlying model consists of a system of partial differential equations that are solved by a finite difference method (FDM). Special techniques are also employed to model thin layers and sharp interfaces, to deal efficiently with wide homogeneous layers (when the solution is tending to a steady state), to model linear diffusion in order to smooth the sharp interfaces before they enter to domain of the FDM.In this paper the special techniques are described in detail. Results from test problems, demonstrating these techniques, are shown. An algorithm that describes the way the IMPETUS II code is structured is given. © 1998 John Wiley & Sons, Ltd.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 3-19 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper presents an efficient space domain integral formulation of planar dielectric structures based on the concepts of multiresolution analysis (MRA) theory. Battle-Lemarie multiresolution expansions are utilized in the moment method solution of a volume integral equation for the unknown electric field. The generation of sparse moment matrices is explained in view of the cancellation property of wavelet basis functions. The formulation is then applied to two- and three-dimensional dielectric structures including waveguides and resonators, and the numerical results and consequences of matrix sparsity are discussed in detail. © 1998 John Wiley & Sons, Ltd.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 21-40 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: An efficient wavelet-packet-based time-frequency technique is proposed in this paper. This technique has found applications in inverse synthetic aperture radar (ISAR). It combines the Wigner-Ville distribution (WVD) of each sub-band signal partitioned from an input signal by the wavelet-packet transform (WPT). These distributions are used to estimate the parameters in Doppler processing. Similar parametric compensation is carried out in range processing so that a specific scatterer is focused in both range and cross-range. The end result uses the Fourier imaging method to obtain a high-resolution radar image. This technique is primarily based on estimation and compensation of the Doppler scattering parameters of the dominant scatterers for improved focus. It can be of great value to the scattering-oriented ISAR imaging. © 1998 John Wiley & Sons, Ltd.
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  • 182
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 41-54 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The local support and vanishing moment property of wavelet bases have been recently used to obtain a sparse matrix representation of integral equations in the spatial domain. In this paper, an application of the cubic spline and the corresponding semi-orthogonal wavelets in the spectral domain is proposed for the evaluation of the reflection coefficient for open/short transmission lines. Because of the nearly optimal time (space)-frequency (wavenumber)-window product of the cubic spline and wavelet, the double spectral integrals appearing in the formulation can be computed more efficiently than with the commonly used piecewise sinusoidal (PWS) or triangular basis functions. It is shown that the time-frequency-window product of the triangular and PWS function are close to each other, whereas those of the cubic spline/wavelet are close to 0·5, the lowest possible value corresponding to functions of Gaussian class. Both the PWS and wavelet bases are applied to microstrip and coplanar waveguides with isotropic and anisotropic substrates, and the results are compared with published theoretical and experimental data. It is observed that even though the number of splines/wavelets required for an accurate representation of the current distribution in the transmission line is almost twice as high as the number of PWS functions, the overall computation time decreases significantly in the former case. © 1998 John Wiley & Sons, Ltd.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 69-84 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The use of wavelet expansions in numerical solutions of electromagnetic frequency-domain integral equation formulations is steadily growing. In this paper we review the recently suggested impedance matrix compression (IMC) method for a more effective integration of wavelet-based transforms into existing numerical solvers. The difference between the IMC method and the previous approaches to applying wavelets in computational electromagnetics is twofold. Firstly, the transformation is effected by means of a digital filtering approach. This approach renders the transform algorithm adaptive and facilitates the derivation of a basis which best suits the problem at hand. Secondly, the conventional thresholding procedure applied to the impedance matrix is substituted for by a compression process in which only the significant terms in the expansion of the (yet-unknown) current are retained and hence a substantially smaller number of coefficients has to be determined. A few numerical results are included to demonstrate the advantages of the presented method over the currently used ones. The feasibility of ensuring a slow growth in the number of unknowns even when there is a rapid increase in the problem complexity is shown by an illustrative example. © 1998 John Wiley & Sons, Ltd.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 87-103 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: An efficient novel algorithm is introduced for ground wave propagation problems. First, ground wave propagation characteristics for a vertically polarized short electric dipole over a smooth spherical earth are reviewed, reducing the vector electromagnetic problem for the three-dimensional spherical geometry to an equivalent two-dimensional rectilinear scalar potential problem which is solved by spectral analysis and synthesis. Alternative evaluations of the spectral integral yield ray optical and normal mode solutions, which are conventionally referred to as the Norton and Wait formulations, respectively. Combining these formulations in an efficient manner yields a hybrid algorithm which is constructed so as to account adaptively for the characteristics of ground wave propagation in interference, intermediate and diffraction regions (including mixed paths) for various source and/or receiver heights. Numerical comparisons are made with reference results obtained via the parabolic equation (PE) method, in parametric ranges where PE is reliable; this permits assessment of the effectiveness of the hybrid approach. © 1998 John Wiley & Sons, Ltd.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 183-184 
    ISSN: 0894-3370
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: No Abstract
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  • 186
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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  • 187
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 188
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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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  • 189
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 190
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 191
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 6 Ill.
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  • 192
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 1 Ill.
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  • 193
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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  • 194
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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.
    Additional Material: 6 Ill.
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  • 195
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 7 Ill.
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  • 196
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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  • 197
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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  • 198
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 3 Ill.
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  • 199
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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  • 200
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 4 Ill.
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