Overlapping Schwarz and Spectral Element Methods for Linear Elasticity and Elastic Waves

The classical overlapping Schwarz algorithm is here extended to the spectral element discretization of linear elastic problems, for both homogeneous and heterogeneous compressible materials. The algorithm solves iteratively the resulting preconditioned system of linear equations by the conjugate gradient or GMRES methods. The overlapping Schwarz preconditioned technique is then applied to the numerical approximation of elastic waves with spectral elements methods in space and implicit Newmark time advancing schemes. The results of several numerical experiments, for both elastostatic and elastodynamic problems, show that the convergence rate of the proposed preconditioning algorithm is independent of the number of spectral elements (scalability), is independent of the spectral degree in case of generous overlap, otherwise it depends inversely on the overlap size. Some results on the convergence properties of the spectral element approximation combined with Newmark schemes for elastic waves are also presented.     

RFID im Blickpunkt wirtschaftlicher Überlegungen

Diese Recherche zeigt, dass sich die Bedeutung, die dem Thema RFID in den Medien und der ?ffentlichen Diskussion derzeit beigemessen wird, auch in der Anzahl der im Internet zu findenden Seiten niederschl?gt. Dabei bewegt sich die Qualit?t der betrachteten Angebote überwiegend auf einem hohen Niveau, was vor allem auf Seiten der kommerziellen Anbieter nicht weiter verwundert, da es sich bei RFID doch um einen zunehmend st?rker umk?mpften Markt handelt, auf dem es hei?t, potenzielle Kunden für sich zu akquirieren. Es darf mit Spannung erwartet werden, wie sich das Informationsangebot wandelt, wenn tats?chlich das prognostizierte exponentielle Wachstum des RFID-Marktes eintritt.     

Grenzen der Anwendbarkeit der Theorie der analytischen Signale

Zusammenfassung Bei der praktischen Anwendung der analytischen Signale ist es erforderlich, die Ermittlung der Hilbert-Transformation numerisch durchzuführen. Dazu wurden u.a. Verfahren von H.W. Schü?ler, R. Unbehauen und G. Wunsch vorgeschlagen. In der Arbeit werden allgemeine Ergebnisse zur numerischen Umsetzung der Hilbert-Transformation dargestellt. Es wird gezeigt, da? alle praktisch realisierbaren Verfahren für bestimmte Signale divergieren. Damit ist es m?glich, die in der Experimentalphysik schon l?nger bekannten Schwierigkeiten bei der Umsetzung der Hilbert-Transformation zu erkl?ren.     

Transient elastic waves in a half-space: comparison of the DBIE-method with the method of generalized ray

Summary The two-dimensional problem of wave propagation in an elastic half-space is studied by the DBIEM (Direct Boundary Integral Equation Method) combined with the finite difference procedure applied to the time variable. The present hybrid formulation employs the fundamental solution depending neither on the frequency nor on the time variable. Time records of surface responses of the half-space are computed and compared with those obtained by the numerical evaluation of exact analytical solutions to this problem.     

Vibration of doubly-curved shallow shells

Summary This paper presents the free vibration of thin doubly-curved shallow shells of rectangular planform. The study covers wide combinations of free, simply supported and clamped boundary conditions. Both positive and negative Gaussian curvatures (spherical and hyperbolic paraboloidal shells resepectively) are considered. Thepb-2 Ritz energy based approach, along with the in-plane and transverse deflections assumed in the form of a product of mathematically complete two-dimensional orthogonal polynomials and a basic function, is employed to model the vibratory characteristic of these shells. Numerical results have been established through convergence study and comparison with published data from the open literature. Extensive sets of new results for various ranges of aspect ratio, curvature ratio andx- andy-shallowness ratios have been presented for future reference.     

On compressible subsonic flow between impeller and casing of radial-flow compressors with superposed throughflow

Summary Subject of this paper is the numerical investigation of the flow between impeller and casing of compressors of radial construction. The solution procedure is based on implicite difference equations, in which parameters of material such as heat conductivity, viscosity and density are variable. Because of the assumption of low density, laminar flow conditions are assumed. The computation method makes possible the determination of the torque coefficient as a function of Reynolds-and Mach number as well as of geometry and superposed throughflow.With 3 Figures     

Computing hysteresis points of nonlinear equations depending on two parameters

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of theQ-quadratically convergent method.     

IV-Controlling in einem Systemhaus

This paper analyses the characteristics of software houses as service providers. The tasks of internal IT-services are determined from these characteristics and a reporting system for the IT-controlling is outlined. The concept results from the analysis of one of the 25 largest German software houses. The paper concludes with a case study of the fiscal year 2000 IT-controlling report of the above-mentioned firm.