Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations

New methods for computing eigenvectors of symmetric block tridiagonal matrices based on twisted block factorizations are explored. The relation of the block where two twisted factorizations meet to an eigenvector of the block tridiagonal matrix is reviewed. Based on this, several new algorithmic strategies for computing the eigenvector efficiently are motivated and designed. The underlying idea is to determine a good starting vector for an inverse iteration process from the twisted block factorizations such that a good eigenvector approximation can be computed with a single step of inverse iteration.     

Analysis of free-edge effects by boundary finite element method

The scaled boundary finite element method is a novel semi-analytical analysis technique that combines the advantages of the finite element method and the boundary element method. Only a part of the boundary of the considered domain has to be discretized but nevertheless the method is solely finite element based. The governing equations are solved in the so-called scaling direction analytically, whereas a finite element approximation of the solution is performed in the circumferential directions, which form the boundary of the considered domain. Thus, the numerical effort can be reduced considerably when handling stress concentration problems such as e.g. the free-edge effect in laminated plates. In order to analyze the free-edge effect in a semi-infinite half plane, some kinematic coupling equations have to be introduced, that not only couple the degrees of freedom on the boundary, but also within the non-discretized domain. The implementation of kinematic coupling equations within the method is presented. Finally, the efficiency of the new approach is shown in some benchmark examples. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Boundary Finite Element Method for the Efficient Computation of Orders and Modes of Three-Dimensional Stress Singularities

In this contribution the B oundary F inite E lement M ethod (BFEM) is employed for the computation of the orders of stress singularities for several three-dimensional stress concentration problems in linear elastic fracture mechanics. The BFEM combines the advantages of both the FEM and the BEM: while only a discretization on a structural boundary is required, the actual surface mesh consists of standard displacement based finite elements. In contrast to the BEM, no fundamental solution is required. The BFEM is an ef.cient analysis tool which leads to highly accurate results with significantly lesser computational effort when compared to e.g. standard FEM procedures. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On parabolic systems with variational structure

We prove global existence of strong solutions for two-dimensional parabolic systems of variational flow type subject to the one-sided condition.     

Glühdrahtexperimente mit den Systemen Pt/O2, Ir/O2, Pt/Cl2, Pt/Br und Rh/Br

Glowing Filament Experiments with the Systems Pt/O₂, Ir/O₂, Pt/Cl₂, Pt/Br, and Rh/Br Reactions of glowing filaments of platinum and iridium with oxygen confirmed the usefulness of the method for the determination of the formulae of the volatile compounds (PtO₂, IrO₃) under equilibrium conditions. The afterwards made experiments with glowing filaments of platinum with Cl₂ at 1300 K and with platinum and rhodium with Br at 1900 K under equilibrium conditions lead to the formation of PtCl₂, PtBr, and RhBr.     

Types of likelihood maxima in mixture models and their implication on the performance of tests

In two-component mixtures of exponential distributions, different strategies for starting the likelihood maximization algorithm converge to different types of maxima. The power of an LR test of homogeneity against such a mixture strongly depends on the considered strategy, and global maximization need not result in the largest power. An explanation is given on basis of a systematic investigation of the likelihood function in a large number of simulations, using a variety of diagnostic tools. Thereby, we also gain a deeper insight into the properties of the samples that generate particular types of solutions of the likelihood equation. In particular, “spurious solutions” often occur; these are mainly responsible for the fact that global maximization may not result in a statistically meaningful estimator. Removing the smallest elements of a sample may drastically increase the power of previously inferior strategies. This research has been supported by a grant from the Deutsche Forschungsgemeinschaft.     

Einstein and Cosmic Physics

The article gives an overview on Albert Einstein's activity in relation to geophysics. Various aspects of his fundamental investigations and their significance for geophysical research are discussed.