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  • Articles: DFG German National Licenses  (11,657)
  • Electronic Resource  (11,657)
  • Engineering  (11,657)
  • Engineering General  (9,884)
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  • Articles: DFG German National Licenses  (11,657)
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  • Electronic Resource  (11,657)
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    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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  • 102
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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 8 Ill.
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  • 103
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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 1 Ill.
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  • 104
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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 3 Ill.
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  • 105
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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 1 Ill.
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  • 106
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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 1 Ill.
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  • 107
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    Chichester, West Sussex : Wiley-Blackwell
    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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  • 108
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    Chichester, West Sussex : Wiley-Blackwell
    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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  • 109
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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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  • 110
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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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  • 111
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    Chichester, West Sussex : Wiley-Blackwell
    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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  • 112
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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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  • 113
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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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  • 114
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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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  • 115
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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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  • 116
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    Chichester [u.a.] : Wiley-Blackwell
    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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  • 117
    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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  • 118
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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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  • 119
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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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  • 120
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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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  • 121
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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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  • 122
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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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  • 123
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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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  • 124
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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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  • 125
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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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  • 126
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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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  • 127
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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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  • 128
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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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  • 129
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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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  • 130
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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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    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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    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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    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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  • 134
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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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  • 135
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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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  • 136
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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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  • 137
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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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  • 138
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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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  • 139
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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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  • 140
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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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  • 141
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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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  • 142
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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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  • 143
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11 (1998), S. 69-84 
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    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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  • 144
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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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  • 146
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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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  • 147
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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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  • 148
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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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  • 149
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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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  • 150
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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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    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.
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  • 152
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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.
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  • 153
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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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  • 154
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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.
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  • 155
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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.
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  • 156
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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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  • 157
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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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    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.
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  • 159
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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
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    Notes: We consider numerical methods which exactly preserve the Gauss-Poisson equation when solving the charge conservation and Maxwell-Ampère's equations. Apart from the well-known leap-frog method, we present two situations where this property is verified, one with rectangular mesh and functions defined at the center of the cells, and one with a finite volume type of formulation on triangles. © 1998 John Wiley & Sons, Ltd.
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  • 160
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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.
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  • 161
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    Communications in Numerical Methods in Engineering 14 (1998), S. 43-49 
    ISSN: 1069-8299
    Keywords: lumped mass matrix ; Hermitian finite difference operators ; flexural wave propagation ; numeric velocity dispersion ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Hermitian finite difference operators are employed to formulate a new diagonal mass matrix for solving flexural wave propagation problems. The dynamic equilibrium for moments is considered. The consistency of the formulation is evident because these operators explicitly present second-order convergence. Numerical results indicate that the velocity dispersion is very close to the consistent mass matrix. © 1998 John Wiley & Sons, Ltd.
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  • 162
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    Communications in Numerical Methods in Engineering 14 (1998), S. 103-134 
    ISSN: 1069-8299
    Keywords: computational quantifier elimination ; edge crack ; feasibility (consistency) conditions ; fracture mechanics ; numerical methods in engineering ; parametric inequality constraints ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an attempt is made to show the usefulness of computational quantifier elimination (CQE) techniques in computer algebra inside classical numerical methods in engineering for the derivation of feasibility (consistency) conditions in problems with weakly parametric linear inequality constraints (with the parameters appearing only in their right-hand sides). A simple, but non-trivial, straight edge-crack problem in fracture mechanics under linear inequality constraints both on the applied loading along the crack faces and on the value of the stress intensity factor at the crack tip (associated with the Green/weight function method, numerical approximations and classical numerical integration) is used for an elementary illustration of the proposed approach. In this application, the method used tries to imitate the theoretical principle of the linear programming methods. The manually obtained related result is expressed as a disjunction of conjunctions of inequalities (as is frequently the case in similar CQE problems), and concrete numerical results are also displayed. The related influence of various approximations and the application of the trapezoidal quadrature rule are also considered in some detail. Further possibilities could concern the application of the approach to other numerical methods in engineering (such as to the finite and the boundary element methods, to singular and hypersingular integral equation methods, etc.) combined with efficient algorithms for linear inequality constraints such as the old Fourier and the recent Weispfenning elimination methods. © 1998 John Wiley & Sons, Ltd.
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  • 163
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    Communications in Numerical Methods in Engineering 14 (1998), S. 161-178 
    ISSN: 1069-8299
    Keywords: finite elements ; unsteady incompressible flows ; fractional-step ; equal-order-interpolation ; pQ2Q1 element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Implementation of an equal-order-interpolation velocity-pressure element pair is presented for the finite element solution of incompressible viscous flows. A fractional-step method is employed for temporal discretization. The element pair, also called a pseudo-biquadratic velocity/bilinear pressure element (pQ2Q1), consists of a bilinear pressure element and bilinear velocity elements defined on subdivisions of the pressure element. This pair satisfies the so-called ‘Ladyzhenskaya-Babuska-Brezzi’ condition. Considerable savings in computational cost are achieved due to the reduced number of elements for pressure. A modification of the element is realized for a better representation of curved surfaces. Two test cases, namely the lid-driven cavity flow and impulsively started circular cylinder in cross-flow, are used to assess the accuracy and efficiency of the element compared to a regular bilinear velocity-pressure (Q1Q1) element pair. Computational results presented show that the pQ2Q1 element solutions require less memory and CPU time compared to Q1Q1 element solutions, for at least the same accuracy. © 1998 John Wiley & Sons, Ltd.
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  • 164
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    Communications in Numerical Methods in Engineering 14 (1998), S. 839-847 
    ISSN: 1069-8299
    Keywords: coupled models of dynamic electroelasticity ; generalized solutions ; metrics weaker than L2 ; spectrum of a priori estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we deal with a model of coupled non-stationary electroelasticity with displacements and potential given on the boundary of a body. We construct a numerical scheme for modelling electromechanical interactions in the body, and present a spectrum of a priori estimates for the solution of this scheme. Such estimates allow us to prove the convergence of the scheme to a generalized solution of the differential problem from W22(QT) with the second order of accuracy in a weaker than L2 metric. © 1998 John Wiley & Sons, Ltd.
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  • 165
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    Communications in Numerical Methods in Engineering 14 (1998), S. 821-837 
    ISSN: 1069-8299
    Keywords: diagonally implicit Runge-Kutta methods ; parallelism ; stiffness ; stability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper we propose a parallel diagonal iteration process for solving a low-order implicit Runge-Kutta method of Lagrange type. The resulting scheme can be regarded as a parallel singly diagonally implicit Runge-Kutta (PSDIRK) method and it is strongly A-stable when the classical linear test model is used. On a two-processor computer, this method requires the solution of two implicit relations (sequential time units) per step and per processor. We compare our method with some sequential and parallel methods from the literature for solving linear as well as non-linear stiff problems and semidiscretized convection-diffusion equations. The numerical experiments show the behaviour of our method with regard to the other methods. © 1998 John Wiley & Sons, Ltd.
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  • 166
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    Communications in Numerical Methods in Engineering 14 (1998), S. 871-877 
    ISSN: 1069-8299
    Keywords: nearest neighbours ; Voronoi diagram ; Delaunay triangulation ; computational geometry ; algorithms ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the largest interior angle property of the Voronoi nearest neighbours and the Delaunay triangulation in two dimensions. It is indicated that each interior angle opposite to an edge of a Delaunay triangle is the largest of the interior angles opposite the same edge of all possible triangles on the same side. Based on this property, the algorithms for finding the Voronoi neighbours of a point (site) and for constructing the Delaunay triangulation are presented. The algorithms are especially useful for the meshless methods developed in recent years. © 1998 John Wiley & Sons, Ltd.
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  • 167
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    Communications in Numerical Methods in Engineering 14 (1998), S. 907-920 
    ISSN: 1069-8299
    Keywords: Stokes problem ; meshless ; MLS interpolant ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D problems and deformable domains. First, taking into consideration that Dirichlet boundary conditions are not applicable a posteriori as in finite elements, a variational weak formulation that includes all kinematic restrictions (Dirichlet and incompressibility) is derived. Then the discretized resultant equations using a moving least-squares (MLS) interpolant for velocity and pressure fields are presented. Finally, the performance of the MLS interpolation is analysed by comparing numerical and analytical solutions, paying attention to the selection of the polynomial degree for the basis function and its orthogonalization. Different aspects of numerical implementation are discussed. © 1998 John Wiley & Sons, Ltd.
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  • 168
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    Communications in Numerical Methods in Engineering 14 (1998), S. 921-930 
    ISSN: 1069-8299
    Keywords: non-linear Richards equation ; mixed-hybrid finite elements ; quasi-Newton methods ; fast-secant methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Groundwater flow in partially saturated porous media is modelled by using the non-linear Richards equation, which is discretized in the present work by using linear mixed-hybrid finite elements.The discretization produces an algebraic non-linear system, which can be solved by an iterative fixed-point algorithm, the Picard method. The convergence rate is linear, and may be too poor for practical applications. A superlinear convergence rate is obtained by considering a Broyden-type approach, based on the Shermann-Morrison formula.The local character of the Broyden method can be overcome by an accurate estimate of the initial solution, that is by appropriately initializing the computation via some (relaxed) Picard iterations. This strategy needs a convergence criterion to decide when switching from the Picard to the quasi-Newton method, which is crucial for the effectiveness of the scheme, as illustrated by some numerical experiments.We also consider the non-linear algebraic problem from a different viewpoint. Instead of applying the quasi-Newton method directly to such a non-linear system, we applied it to the non-linear function tied to the Picard scheme. Each function evaluation requested by such an algorithm corresponds to a local step of the Picard method, which is then used to compute a Broyden displacement. The present technique can be seen as an accelerated Picard algorithm.We compare the performances of these algorithms when applied to a stationary and a time-dependent benchmark problem. © 1998 John Wiley & Sons, Ltd.
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  • 169
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    Communications in Numerical Methods in Engineering 14 (1998), S. 897-906 
    ISSN: 1069-8299
    Keywords: preconditioning ; conjugate gradient ; finite elements ; shells ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Preconditioned Krylov subspace methods have proved to be efficient in solving large, sparse linear systems in many areas of scientific computing. The success of these methods in many cases is due to the existence of good preconditioning techniques. In problems of structural mechanics, like the analysis of heat transfer and deformation of solid bodies, iterative solution of the linear equation system can result in a significant reduction of computing time. Also many preconditioning techniques can be applied to these problems, thus facilitating the choice of an optimal preconditioning on the particular computer architecture available.However, in the analysis of thin shells the situation is not so transparent. It is well known that the stiffness matrices generated by the FE discretization of thin shells are very ill-conditioned. Thus, many preconditioning techniques fail to converge or they converge too slowly to be competitive with direct solvers. In this study, the performance of some general preconditioning techniques on shell problems is examined. © 1998 John Wiley & Sons, Ltd.
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  • 170
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    Communications in Numerical Methods in Engineering 14 (1998), S. 959-961 
    ISSN: 1069-8299
    Keywords: Stokes problem ; finite element ; eigensystems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of mixed finite element methods in discretizing the Stokes equations leads to systems involving the so-called pressure matrix. Some new spectral properties of this important matrix are here presented for the Q1-P0 element. © 1998 John Wiley & Sons, Ltd.
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  • 171
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    Communications in Numerical Methods in Engineering 14 (1998), S. 381-392 
    ISSN: 1069-8299
    Keywords: porous medium ; fluid flow ; electromechanical coupling ; FEM ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider a coupled problem of the deformation of a porous solid, flow of a compressible fluid and the electrical field in the mixture. The governing equations consist of balance of the linear momentum of solid and of fluid, continuity equations of the fluid and current density, and a generalized form of Darcy's law which includes electrokinetic coupling. The compressibility of the solid and the fluid are taken into account. We transform these equations to the corresponding finite element relations by employing the principle of virtual work and the Galerkin procedure. The nodal point variables in our general formulation are displacements of solid, fluid pore pressure, relative velocity of the fluid and electrical potential. Derivation of the FE equations is presented for small displacements and elastic solid, which can further be generalized to large displacements and inelastic behaviour of the solid skeleton.According to this formulation we can include general boundary conditions for the solid, relative velocity of the fluid, fluid pressure, current density and electrical potential. The dynamic-type non-symmetric system of equations is solved through the Newmark procedure, while in the case of neglect of inertial terms we use the Euler method.Numerical examples, solved by our general-purpose FE package PAK, are taken from biomechanics. The results are compared with those available in the literature, demonstrating the correctness and generality of the procedure presented. © 1998 John Wiley & Sons, Ltd.
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  • 172
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    Communications in Numerical Methods in Engineering 14 (1998), S. 397-407 
    ISSN: 1069-8299
    Keywords: 3D mesh generation ; adaptive refinement ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive finite element (FE) method for the solution of three-dimensional elasto-static problems is described. The computational domain is represented by an assembly of tetrahedral elements and the mesh adaptation is achieved by a 3D bisection method using an error estimator procedure coupled with an automatic 3D mesh generator. The performance of the method is demonstrated using a number of examples. © 1998 John Wiley & Sons, Ltd.
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  • 173
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    Communications in Numerical Methods in Engineering 14 (1998), S. 429-436 
    ISSN: 1069-8299
    Keywords: stress intensity factor (SIF) ; singular finite element ; double cracks ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Using the quasi-compatible finite element method advanced by Zhichao and Lisu (1990), the influence of the size of a plate with double cracks on the stress intensity factor is studied. Many numerical computations are carried out and various data, curves and formulae are given. It is shown clearly how the stress intensity factors of double cracks are affected by the size of the cracked body. © 1998 John Wiley & Sons, Ltd.
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  • 174
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    Communications in Numerical Methods in Engineering 14 (1998), S. 463-472 
    ISSN: 1069-8299
    Keywords: multibody systems ; non-linear analysis ; static equilibrium ; constrained optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents four different approaches to the solution of the non-linear static-equilibrium problem in complex linkages, including rigid and elastic elements. The error function is based on the potential of the system, and includes rigid elements by means of non-linear constraints. To this end use is made of Lagrange multipliers, along with the primal-dual method, penalty functions and weighted stiffness, comparisons being made between them. A Newton-Raphson method is used in seeking function minima for equilibrium positions. This procedure is also directly applicable to the other linkage and multibody position problems. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1109-1117 
    ISSN: 1069-8299
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The symmetry present in Green's functions is exploited to significantly reduce the matrix assembly time for a Galerkin boundary integral analysis. A relatively simple modification of the standard Galerkin implementation for computing the non-singular integrals yields a 20-30 per cent decrease in computation time. This faster Galerkin method is developed for both singular and hypersingular equations, and applied to symmetric-Galerkin implementations in two dimensions for the Laplace equation and for orthotropic elasticity. In three dimensions, the modified algorithm has been implemented for the singular equation for the Laplace and elastodynamics equations. Comparison timing results for standard and modified algorithms are presented. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1097-1108 
    ISSN: 1069-8299
    Keywords: grid generation ; finite point method ; mesh free techniques ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm to construct boundary-conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point distance and an initial triangulation of the surface. Borrowing a key concept from advancing front grid generators, one point at a time is removed and, if possible, surrounded by admissible new points. This operation is repeated until no active points are left. Timings show that the scheme is about an order of magnitude faster than volume grid generators based on the advancing front technique, making it possible to generate large (〉106) yet optimal clouds of points in a matter of minutes on a workstation. Several examples are included that demonstrate the capabilities of the technique. Copyright © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 671-679 
    ISSN: 1069-8299
    Keywords: advection-diffusion ; semi-Lagrangian ; stability ; accuracy ; QUICKEST ; DISCUS ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the incorporation of diffusive transport into the original semi-Lagrangian DISCUS algorithm for pure advection. An explicit treatment of diffusion is adopted following the approach used in the QUICKEST algorithm for advection-diffusion. The semi-Lagrangian treatment of the advection term relaxes the small time step restriction normally associated with Eulerian treatments of advection, but the Eulerian treatment of the diffusion term imposes conventional limitations on the scheme. Numerical experiments of advection-diffusion, however, indicate that DISCUS has advantages over the QUICKEST scheme for advection-diffusion in three key areas: stability, accuracy and computational efficiency. © 1998 John Wiley & Sons, Ltd.
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  • 178
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    Communications in Numerical Methods in Engineering 14 (1998), S. 709-717 
    ISSN: 1069-8299
    Keywords: fluid dynamics ; multiphase-flow ; lattice gases ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Nearly all CFD methods can be considered as discretization methods for partial differential equations, such as finite difference, finite volume, finite element, spectral or boundary integral element methods. Virtually unrecognized by the scientific mainstream in computational fluid dynamics (CFD) during the last decade, a completely different approach to flow simulation has been developed in computational physics.The basic idea of lattice-gas solvers (LGS) goes back to the cellular automation concept of John von Neumann. LGS use objects (‘cells’), being extremely simple compared to finite boxes or finite elements. The state of a cell is usually described by only a few bits therefore often two orders of magnitude more cells are used for a simulation with LGS than ‘elements’ in a finite element computation. LGS are explicit time-stepping procedures; no equation systems have to be solved. Thus every time-step is extremely cheap in terms of CPU power compared to standard procedures, yet again much shorter time-steps have to be used. LGS are inherently parallel and are suitable to coarse-grain as well as to fine-grain parallelization.The paper will discuss some advantages and disadvantages of lattice-gas solvers and present LG simulation results of two-phase flow with moving boundaries on a microscope scale for a two-dimensional test geometry of randomly distributed equally sized disks where the effect of surface tension on the steady-state saturation will be demonstrated. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1155-1170 
    ISSN: 1069-8299
    Keywords: shell problem ; Naghdi model ; finite elements ; mixed elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this work is the construction of some special finite elements for the numerical solution of Naghdi cylindrical shell problems. The standard numerical approximation of the shell problem is subjected to the shear and membrane locking phenomenon, i.e. the numerical solution degenerates for low thickness. The most common way to avoid locking is the use of modified bilinear forms to describe the shear and membrane energy of the shell. In this paper we build a family of special finite elements that still follow the above strategy by introducing a linear operator that reduces the influence both of the shear and membrane energy terms. The main idea comes from the non-standard mixed interpolated tensorial components (MITC) formulation for Reissner-Mindlin plates. The performance of the new elements is then tested for solving benchmark problems involving very thin shells. The results show both the properties of convergence and robustness. Copyright © 1998 John Wiley & Sons, Ltd.
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    Numerical Linear Algebra with Applications 5 (1998), S. 219-247 
    ISSN: 1070-5325
    Keywords: non-linear programming ; sparse problems ; equality constraints ; inexact Newton method ; augmented Lagrangian function ; indefinite systems ; indefinite preconditioners ; conjugate gradient method ; residual smoothing ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An inexact Newton algorithm for large sparse equality constrained non-linear programming problems is proposed. This algorithm is based on an indefinitely preconditioned smoothed conjugate gradient method applied to the linear KKT system and uses a simple augmented Lagrangian merit function for Armijo type stepsize selection. Most attention is devoted to the termination of the CG method, guaranteeing sufficient descent in every iteration and decreasing the number of required CG iterations, and especially, to the choice of a suitable preconditioner. We investigate four preconditioners, which have 2 × 2 block structure, and prove theoretically their good properties. The efficiency of the inexact Newton algorithm, together with a comparison of various preconditioners and strategies, is demonstrated by using a large collection of test problems. © 1998 John Wiley & Sons, Ltd.
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    Numerical Linear Algebra with Applications 5 (1998), S. 253-274 
    ISSN: 1070-5325
    Keywords: stochastic matrix ; aggregation/disaggregation iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An aggregation/disaggregation iterative algorithm for computing stationary probability vectors of stochastic matrices is analysed. Two convergence results are presented. First, it is shown that fast, global convergence can be achieved provided that a sufficiently high number of relaxations is performed on the fine level. Second, local convergence is shown to take place with just one relaxation performed on the fine level. The convergence proofs are general and require no assumptions on the magnitude of off-diagonal elements (blocks). Furthermore, a relationship between the errors on the fine and on the coarse level is described. To illustrate the theory, the results of some numerical experiments are presented. © 1998 John Wiley & Sons, Ltd.
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    Numerical Linear Algebra with Applications 5 (1998), S. 321-345 
    ISSN: 1070-5325
    Keywords: second order elliptic problems ; Dirichlet boundary conditions ; mixed finite elements ; preconditioning ; domain embedding ; auxiliary space method ; non-conforming finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study block diagonal preconditioners for mixed systems derived from the Dirichlet problems for second order elliptic equations. The main purpose is to discuss how an embedding of the original computational domain into a simpler extended can be utilized in this case. We show that a family of uniform preconditioners for the corresponding problem on the extended, or fictitious, domain leads directly to uniform preconditioners for the original problem. This is in contrast to the situation for the standard finite element method, where the domain embedding approach for the Dirichlet problem is less obvious. Copyright © 1999 John Wiley & Sons, Ltd.
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    Numerical Linear Algebra with Applications 5 (1998), S. 377-399 
    ISSN: 1070-5325
    Keywords: iterative methods ; operator trigonometry ; anti-eigenvector ; Dirichlet problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The new operator-trigonometric theory for iterative linear solvers is illustrated by working out its details for the classical model problem for numerical partial differential equations: the Dirichlet problem on the unit square. Copyright © 1999 John Wiley & Sons, Ltd.
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    Numerical Linear Algebra with Applications 5 (1998), S. 363-376 
    ISSN: 1070-5325
    Keywords: convergence ; multigrid ; sparse grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The convergence behaviour of solution algorithms is investigated for the anisotropic Poisson problem on partially ordered, sparse families of regular grids in 3D. In order to study multilevel techniques on sparse families of grids, first we consider the convergence of a two-level algorithm that applies semi-coarsening successively in each of the coordinate directions. This algorithm shows good convergence, but recursive application of the successive semi-coarsening is not sufficiently efficient. Therefore we introduce another algorithm, which uses collective 3D semi-coarsened coarse grid corrections. The convergence behaviour of this collective version is worse, due to the lack of correspondence between the solutions on the different grids. By solving for the trivial solution we demonstrate that a good convergence behaviour of the collective version of the algorithm can be retained when the different solutions are sufficiently coherent. In order to solve also non-trivial problems, we develop a defect correction process. This algorithm makes use of hierarchical smoothing in order to deal with the problems related to the lack of coherence between the solutions on the different grids. Now good convergence rates are obtained also for non-trivial solutions. All convergence results are obtained for two-level processes. The results show convergence rates which are bounded, independent of the discretisation level and of the anisotropy in the problem. Copyright © 1999 John Wiley & Sons, Ltd.
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  • 185
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    Numerical Linear Algebra with Applications 5 (1998), S. 475-482 
    ISSN: 1070-5325
    Keywords: nearest doubly stochastic matrix ; alternating projections ; first moment ; normal cone ; RC1 ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let T be an arbitrary n × n matrix with real entries. We consider the set of all matrices with a given complex number as an eigenvalue, as well as being given the corresponding left and right eigenvectors. We find the closest matrix A, in Frobenius norm, in this set to the matrix T. The normal cone to a matrix in this set is also obtained. We then investigate the problem of determining the closest ‘doubly stochastic’ (i.e., Ae = e and eT A = eT, but not necessarily non-negative) matrix A to T, subject to the constraints ${\bf e}_{1}^{\rm T} A^{k} {\bf e}_{1} = {\bf e}_{1}^{\rm T}T^{k}{\bf e}_{1}$, for k = 1, 2, … A complete solution is obtained via alternating projections on convex sets for the case k = 1, including when the matrix is non-negative. Copyright © 1999 John Wiley & Sons, Ltd.
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  • 186
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    Numerical Linear Algebra with Applications 5 (1998), S. 483-509 
    ISSN: 1070-5325
    Keywords: sparse linear systems ; symmetric positive definite matrices ; iterative solvers ; incomplete factorization preconditionings ; conjugate gradients ; K-condition number ; unsymmetric positive definite matrices ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new matrix decomposition of the form A = UTU + UTR + RTU is proposed and investigated, where U is an upper triangular matrix (an approximation to the exact Cholesky factor U0), and R is a strictly upper triangular error matrix (with small elements and the fill-in limited by that of U0). For an arbitrary symmetric positive matrix A such a decomposition always exists and can be efficiently constructed; however it is not unique, and is determined by the choice of an involved truncation rule. An analysis of both spectral and K-condition numbers is given for the preconditioned matrix M = U-T AU-1 and a comparison is made with the RIC preconditioning proposed by Ajiz and Jennings. A concept of approximation order of an incomplete factorization is introduced and it is shown that RIC is the first order method, whereas the proposed method is of second order. The idea underlying the proposed method is also applicable to the analysis of CGNE-type methods for general non-singular matrices and approximate LU factorizations of non-symmetric positive definite matrices. Practical use of the preconditioning techniques developed is discussed and illustrated by an extensive set of numerical examples. Copyright © 1999 John Wiley & Sons, Ltd.
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  • 187
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    Numerical Linear Algebra with Applications 5 (1998), S. 123-139 
    ISSN: 1070-5325
    Keywords: elasticity problem ; separate displacement component ; preconditioned conjugate gradient method ; parallel algorithm ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The discretized linear elasticity problem is solved by the preconditioned conjugate gradient (pcg) method. Mainly we consider the linear isotropic case but we also comment on the more general linear orthotropic problem. The preconditioner is based on the separate displacement component (sdc) part of the equations of elasticity. The preconditioning system consists of two or three subsystems (in two or three dimensions) also called inner systems, each of which is solved by the incomplete factorization pcg-method, i.e., we perform inner iterations. A finite element discretization and node numbering giving a high degree of partial parallelism with equal processor load for the solution of these systems by the MIC(0) pcg method is presented. In general, the incomplete factorization requires an M-matrix. This property is studied for the elasticity problem. The rate of convergence of the pcg-method is analysed for different preconditionings based on the sdc-part of the elasticity equations. In the following two parts of this trilogy we will focus more on parallelism and implementation aspects. © 1998 John Wiley & Sons, Ltd.
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  • 188
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 1-26 
    ISSN: 1082-5010
    Keywords: anisotropy ; failure criterion ; schist ; sedimentary rock ; rock joints ; laboratory testing ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is devoted to the assessment of some representative failure criteria in the framework of modelling the failure behaviour of strongly anisotropic geomaterials. Experimental data concerning the failure behaviour of a typical strongly anisotropic rock; the schist of Angers are first presented. Nine widely used failure criteria are then selected and classified into three groups, the mathematical continuous models, the empirical continuous models and the discontinuous weakness planes based models. This classification is made up according to the main assumptions and techniques used in each criterion to describe the strength anisotropy. The calibration of each one is carried out with respect to the laboratory data of Angers schist. Qualitative and quantitative comparisons between the selected criteria and with the experimental data are provided. © 1998 John Wiley & Sons, Ltd.
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  • 189
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 89-103 
    ISSN: 1082-5010
    Keywords: transversely isotropic material ; elliptic paraboloid failure surface ; strength differential effect ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A coordinate-free formulation of a failure criterion for transversely isotropic solids is proposed. In the three-dimensional stress space the criterion is represented by an elliptic paraboloid. The anisotropic form of the proposed criterion is based on generalization of the second invariant of the deviatoric stress and of the mean stress obtained through the introduction of a unique fourth-order tensor. For isotropic conditions, the criterion reduces to the Mises-Schleicher failure condition. It is shown that the criterion satisfactorily predicts the strength anisotropy of transversely isotropic rocks subjected to an axisymmetric stress state. The procedure for the identification of the parameters of the criterion from a few simple laboratory tests is outlined. © 1998 John Wiley & Sons, Ltd.
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  • 190
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 27-39 
    ISSN: 1082-5010
    Keywords: creep ; effective spring concept ; Kelvin chain model ; load bearing volume ; micromechanical model ; relaxation ; softening spring ; solidification ; tension softening ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An analytical constitutive model similar to the Kelvin chain rheological model associated with solidification theory, is developed for time-dependent tension softening of ageing materials like concrete. The stiffness of spring elements is allowed to vary with time via a function of load bearing volume fraction as in the solidification theory. The development of cracks reduces the load bearing volume fraction with time, so that the overall behaviour of springs is a softening type. A reduction in the load bearing volume with time ensures a gradual reduction in the spring stiffness without violating prescribed retardation times. In some circumstances, depending on the boundary conditions, the stress in a structure can remain unchanged over a period of time. During this period, any cracks in the structure will continue to experience an increased opening due to creep. In other parts of the structure, again depending on the boundary conditions, the crack opening displacements may remain unchanged over a period of time, so that the stress will relax over these parts of the structure. In a large concrete structure, creep and relaxation may be taking place simultaneously in different parts or in the same part but at different times. There is thus a need for a visco-elastic tension softening model for ageing concrete that will cater for both creep and relaxation. © 1998 John Wiley & Sons, Ltd.
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  • 191
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 41-63 
    ISSN: 1082-5010
    Keywords: elastoplasticity ; damage ; bonded geomaterials ; triaxial testing ; intact and remoulded specimen ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In order to model the various phenomena which govern the mechanical response of bonded geomaterials under monotonic loadings, an elastoplastic model coupled with an elastic model with damage was developed, taking into account both the frictional and cohesive aspects of these materials. First, the principles at the base of the model are presented, as well as the physical meaning of the parameters which were used in the elastic model with damage. In order to illustrate the capabilities of the model to reproduce the mechanical behaviour of bonded geomaterials, we simulated triaxial tests on various materials: a deep cemented clay, whose heterogeneity from one specimen to another appeared mainly due to the calcium carbonate content; an assembly of sintered glass balls; and an artificially cemented sand. In this last example, various initial mean stresses allowed us to enlighten the brittle-ductile transition which was modelled by introducing the mean confining pressure in the damage evolution law. We demonstrated that the parameters of each part of the model could be adapted to reproduce the observed general trends. For weak bonds, the elastoplastic part played the predominant role, whereas for strong bonds, the elastic part with damage governed the mechanical behaviour. © 1998 John Wiley & Sons, Ltd.
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  • 192
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 65-87 
    ISSN: 1082-5010
    Keywords: elastoplasticity ; sand ; constitutive modelling ; controllability ; instability ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper investigates the possibility of the occurrence of a multiplicity of homogeneous responses of soil specimens under the same incremental loading, and the associated non-controllability of the imposed loading path.It is shown that for non-associated elastoplastic strain-hardening constitutive laws, such a possibility exists even in the hardening regime. Only when the stiffness matrix is positive-definite is the incremental solution unique for any loading programme.A particular constitutive model is chosen and the shape of the loci of non-uniqueness is calculated for various loading programmes. It is shown that the conditions for the occurrence of a shear band and of a peak of the deviator stress in a triaxial undrained test can be seen as special cases of the theory presented. Accordingly, the so-called ‘instability line’ concept in undrained conditions is generalized. © 1998 by John Wiley & Sons, Ltd.
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  • 193
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 105-125 
    ISSN: 1082-5010
    Keywords: localization ; non-local damage ; Perzyna viscoplasticity ; mesh adaptivity ; Arbitrary Lagrangian-Eulerian technique ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The computational modelling of localization of deformation in cohesive-frictional materials must be carried out in a proper, accurate and efficient manner. A proper solution can be obtained by using an enriched material description such as a non-local damage model or Perzyna's viscoplasticity model. However, still a large number of finite elements is needed for an accurate description of the localization zone. To improve efficiency, mesh adaption is applied here by means of the Arbitrary Lagrangian-Eulerian (ALE) technique. The ALE technique must typically be applied in combination with an enriched material model. Otherwise, the use of a standard model gives a zero-width solution of the localization zone and therefore remeshing results in a continuing decrease of finite element size. Implementation of this method requires the addition of convective forces in the equations of motion, transport of the state variables and the formulation of a remeshing strategy. The remeshing strategy heavily determines the success of the ALE method. Three examples of wave propagation have been treated and it is shown that a suitable remeshing strategy in combination with an enriched material model leads to proper, accurate and efficient analyses of the localization process. © 1998 John Wiley & Sons. Ltd.
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  • 194
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 127-153 
    ISSN: 1082-5010
    Keywords: constitutive equations ; post-localization behaviour ; large strain ; interface model ; bifurcation ; shear band ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper addresses developments on a constitutive model able to describe the post-localized behaviour of structures composed by geomaterials. The behaviour of the shear band is defined by means of a specific non-linear constitutive equation in the framework of large strain. Concept of ‘consistency’ of this model with the CLoE model from which it is derived at the onset of localization is discussed. During the post-localization regime this model evolves in a specific way by introducing the concept of critical void ratio. After some recalls about the CLoE framework and about a Rice bifurcation analysis involving CLoE models, the basic concepts of the Daphnis model are introduced. The last part of this paper is devoted to numerical results on an initially homogeneous frictionless biaxial test. The behaviour of the sample is modelled by means of a plane Mohr Coulomb model defined in the CLoE framework and its associated Daphnis model is used to characterize the specific behaviour of the shear band in the post-localization regime. © 1998 John Wiley & Sons, Ltd.
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  • 195
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 155-180 
    ISSN: 1082-5010
    Keywords: reinforced concrete ; bond model ; plasticity ; interface ; yield surface ; modelling ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The development of an interface, non-associative, plasticity model for bond between ribbed, steel bars and concrete is discussed. The model relates average local slip and radial dilation to average bond shear stress and radial confinement stress. The model partially accounts for the response of the damaged, finite-thickness region around the bar - the bond zone. The model is developed for standard steel bars that are initially unstrained. With simplifying assumptions, data for the components of a plasticity law are extracted from a key set of experimental results. In this paper, we emphasize the development of an expression for the yield surface for monotonic loading. While the forms of the model's components are empirically derived, they qualitatively reflect the mechanics of the mechanical interaction of ribbed bars with the adjacent concrete. A characteristic length, related to the rib pattern, helps quantify this interaction. The mechanics of the bond are difficult to characterize in a simple form, but the calibrated model only requires four physical properties and reproduces with acceptable accuracy experimental results with various levels of radial confinement stress. Model refinements are suggested for future work. © 1998 John Wiley & Sons, Ltd.
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  • 196
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 181-205 
    ISSN: 1082-5010
    Keywords: cemented ; carbide ; finite ; element ; compaction ; sintering ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We have developed a tool for simulating the press cycle and the sintering cycle of cemented carbides. A constitutive model for compaction and tensile fracture has been implemented in the explicit FE programme LS-DYNA2D, and it has been tuned to experiments of hydrostatic compression, uniaxial strain and conventional triaxial compression. The programme simulates the complete compaction cycle in a robust manner. Friction against the tooling is properly taken into account. We have further developed a constitutive model for the stress-free solid-state sintering to also account for a mechanical stress field. The sintering model is based on physical concepts, diffusion parameters, free surface energy, dimensions of carbide grains, etc. of the constituents, and was tuned to successfully simulate the unloaded and loaded sintering of simple specimens. The models of compaction and sintering have a common set of state variables, such that after the compaction cycle, and at raising the temperature the sintering starts out with proper account of the residual stress field. Finally, the potential of the model is demonstrated by simulating the production cycle of a simple WC-Co tool piece until sintering to 75% of full density. The final geometrical shape of the specimen is compared to experimental data. © 1998 John Wiley & Sons, Ltd.
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  • 197
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 229-256 
    ISSN: 1082-5010
    Keywords: finite element method ; viscous constitutive equations ; time-discrete scheme ; stability ; superstability ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The general framework of the paper deals with the finite element modelling of mechanical problems involving viscous materials such as bitumen or bituminous concrete. Its aim is to present a second-order-accurate discrete scheme which remains unconditionally superstable when used for the time discretization of the linear and non-linear viscoelastic constitutive equations considered. After stating the space- and time-continuous mechanical problem we focus on the time discretization of these equations, considering three different schemes. For both of them sufficiently small values of the time step are required in order to ensure the superstability, whereas the third remains unconditionally superstable. Eventually, some numerical results are presented. © 1998 John Wiley & Sons, Ltd.
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  • 198
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 257-276 
    ISSN: 1082-5010
    Keywords: impacts ; structural damage ; discrete element method ; dynamic loading ; scabbing ; perforation ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Impacts of rigid spherical nose shaped missiles on concrete beams are simulated with a discrete element method. The history of the structural damage of the beam is followed from the very first crushing and fracturing processes to the ultimate fragmentation step. Spalling, scabbing, penetration and perforation events are characterized and compared with real test cases of the civil engineering industry. It is found that these phenomena depend not only on the kinetic energy of the missile as predicted by some recent empirical laws but also on its momentum. This means that the dynamic impact loading time is determinant in the scabbing and perforation thicknesses. When the numerical data is plotted against the empirical rules determined from experimental data, the fit is good although the model is two dimensional. © 1998 John Wiley & Sons, Ltd.
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  • 199
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 207-228 
    ISSN: 1082-5010
    Keywords: jointed rock masses ; stability ; failure ; yield design ; homogenization ; strength anisotropy ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Conceived as a potential alternative to the methods usually employed for evaluating the stability of jointed rock masses, the homogenization approach developed in this paper stems from the intuitive idea that, from a macroscopic point of view, a rock mass intersected by a regular network of joint surfaces may be perceived as a homogeneous continuum. The failure criterion of such an equivalent medium is theoretically determined from the knowledge of the failure conditions of the individual constituents, namely the intact rock matrix and joint interfaces. Owing to the existence of privileged material directions associated with the joint orientation distribution, this criterion turns out to be of the anisotropic frictional type, as shown by the closed-form expression obtained in the particular case of two mutually orthogonal joint sets. This criterion is then applied to the investigation of two illustrative engineering problems: the calculation of the load-bearing capacity of a shallow foundation on a jointed rock half-space and the stability analysis of an excavation. Both problems are handled by means of the kinematic method of yield design, making use of the previously determined macroscopic failure condition. The upper bound estimates thus derived appear to be significantly better than those obtained from a direct analysis in which the intact rock matrix and joints are considered separately. In spite of some limitations regarding its range of applicability, which are underlined throughout the paper, the homogenization approach may constitute an appropriate general framework for the design of densely jointed rock structures. © 1998 John Wiley & Sons, Ltd.
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    Mechanics of Cohesive-frictional Materials 3 (1998), S. 277-290 
    ISSN: 1082-5010
    Keywords: experimental analysis ; slabs on soil ; reinforced concrete ; steel fibres ; fracture energy ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The cracking control of plain concrete slabs on soil foundation requires the execution of joints with mechanisms of load transfer between adjacent panels. These joints increase the construction costs and, often, are the source of local damage and loss of service performance. Slabs reinforced with steel wire mesh have been used in order to increase the load-carrying capacity and to enhance the cracking control. However, the use of this conventional reinforcement increases the costs, mainly due to labour time spent on the arrangement and positioning of the reinforcement.Fibre-reinforced concrete is a recent material well fitted for applications in industrial floors on soil foundation. The cost of fibres is compensated by a faster construction process and a reduction in the number of expansion joints. The fatigue, impact and flexural strength are significantly improved when steel fibres are added to the concrete mix.The work developed aims to contribute to the on going research effort to clarify the behaviour of fibre-reinforced concrete slabs on soil foundation. For this purpose, an experimental and numerical investigation were carried out. The present article deals basically with the experimental work developed, describing the tests performed and discussing the main results obtained. © 1998 John Wiley & Sons, Ltd.
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