Christian Schröder

NLEVP: A Collection of Nonlinear Eigenvalue Problems

We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed specifically to have particular properties. A classification is given of polynomial eigenvalue problems according to their structural properties. Identifiers based on these and other properties can be used to extract particular types of problems from the collection. A brief description of each problem is given. NLEVP serves both to illustrate the tremendous variety of applications of nonlinear eigenvalue problems and to provide representative problems for testing, tuning, and benchmarking of algorithms and codes.

Implicit QR algorithms for palindromic and even eigenvalue problems

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques.

Nonlinear eigenvalue and frequency response problems in industrial practice

BackgroundWe discuss the numerical solution of large scale nonlinear eigenvalue problems and frequency response problems that arise in the analysis, simulation and optimization of acoustic fields. We report about the cooperation with the company SFE in Berlin. We present the challenges in the current industrial problems and the state-of-the-art of current methods.ResultsThe difficulties that arise with current off-the-shelf methods are discussed and several industrial examples are presented.ConclusionsIt is documented that industrial cooperation is by no means a one-way street of transfer from academia to industry but the challenges arising in industrial practice also lead to new mathematical questions which actually change the mathematical theory and methods.

Challenge diversity: New curricula in Natural Sciences, Computer Science and Engineering

Despite extensive social changes and intensive political efforts to establish equal opportunities, women are still a minority in the fields of natural sciences and technology studies, as well as in the related professional fields. At the same time, technologically oriented studies are not per se less interesting for women, but their motivation, specific interests, learning styles, goals and demands often vary significantly from those of men. The rather broad interests of women often are directly opposed by a unilateral, outdated, techno-centric learning-/training program, which is not only unattractive to women (and an increasingly high number of men), but also bypasses the actual demands of modern education and the job market. The complexity of global markets, social reference, economical objectives and ecological limits call for integrated thought and action, which has to be mirrored in interdisciplinary approaches. A change within the curricula towards a support of non-technological basics and social skills would thus not only support the interests of women and men but also follow the demands of economy. The Galilea project, located at the Berlin University of Technology, is developing several models of co-educative, gender-sensitive model-courses within the three areas: natural sciences, computer sciences and engineering.

Dissipativity Enforcement via Perturbation of Para-Hermitian Pencils

Dissipativity is an important property of individual systems that guarantees a stable interconnected system. However, due to errors in the modeling process weakly non-dissipative models may be constructed. This paper introduces an enhanced method to perturb a non-dissipative LTI system in order to enforce dissipativity using spectral perturbation results for para-Hermitian pencils. Compared to earlier algorithms the new method is applicable to a wider class of problems, it utilizes a simpler framework, and employs a larger class of allowable perturbations resulting in smaller perturbations. Moreover, system stability can be enforced as well. Numerical examples are provided to show the effectiveness of the new approach.Dissipativity is an important property of individual systems that guarantees a stable interconnected system. However, due to errors in the modeling process weakly non-dissipative models may be constructed. This paper introduces an enhanced method to perturb a non-dissipative LTI system in order to enforce dissipativity using spectral perturbation results for para-Hermitian pencils. Compared to earlier algorithms the new method is applicable to a wider class of problems, it utilizes a simpler framework, and employs a larger class of allowable perturbations resulting in smaller perturbations. Moreover, system stability can be enforced as well. Numerical examples are provided to show the effectiveness of the new approach.

A Jacobi–Davidson method for two‐real‐parameter nonlinear eigenvalue problems arising from delay‐differential equations

SUMMARY The critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real-valued critical delays; that is, complex critical delays, which have no physical meaning, are discarded. For large-scale problems, we propose new correction equations for a Newton-type or Jacobi–Davidson style method, which also forces real-valued critical delays. We present three different equations: one real-valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi–Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples for large-scale problems arising from PDEs. Copyright

Robustness of multi-mode control using tuned mass dampers for seismically excited structures

Robustness in multi-mode control of structures using tuned mass dampers (TMDs) is presented under seismic excitations. The robustness of the distributed multiple TMDs, i.e. d-MTMDs is compared with single TMD (STMD) and with multiple TMDs all installed at the top of the building (MTMDs-all.top). A 20-storey steel benchmark building subjected to earthquake ground motion is modeled, wherein stiffness and damping are considered with uncertainty in order to investigate the robustness of the STMD, MTMDs-all.top, and d-MTMDs. The d-MTMDs are distributed along the height of the building according to the mode shapes of the controlled and uncontrolled building. Monte-Carlo simulation is used to generate the uncertain stiffness and damping matrices of the 20-storey benchmark building. Parameters of the STMD, MTMDs-all.top, and d-MTMDs are optimized for each set of structural stiffness and damping matrices, and the probability distribution of the objective function is evaluated. The optimized parameters (mass ratio and damping ratio) are selected corresponding to the robust interval of the objective function calculated using the probability distribution. The results show that d-MTMDs perform satisfactorily even in the presence of the considered uncertainties and their performance is superior to that of the STMD and MTMDs-all.top in seismic response control of the structures.

Gender gap in technological disciplines: Societal causes and consequences

Despite extensive social changes and intensive political efforts to establish equal opportunities, women are still a minority in the fields of natural sciences and engineering both at universities and in the related professional fields. This low ratio leads to severe consequences both for women and society.

Natural Sciences in the Information Society: First experiences

The goal of the GALILEA project is to design and implement innovative programs and curricula, providing solutions to the changed job specifications for engineers and natural scientists and are capable of attracting more female students to these programs. In this article we outline the design, implementation and the first evaluation results of our pilot program, the bachelor course of “Natural Sciences in the Information Society” that started in the winter term of 2007/08.

Collaborative learning in teaching information management

In this paper, we present the course called ‘New Media in Education and Research’, which employs a blended learning approach. This course is a part of a new bachelors programme ‘Natural Sciences in the Information Society’ that is in place in TU Berlin. The main goal of this course is to provide the students with the appropriate information technology literacy that they will need during their studies and beyond. A more specific goal of the course is to train the students to collaborate in small groups. Tablet PCs with OneNote installed on it act as agents to communicate some of the technological aspects as well as soft skills in a blended learning scenario. We discuss the pedagogical and technological backgrounds of the course and we present the implementation of the course. We conclude with a review of our results and an outlook to future work.