Diplomanden- und Doktorandenseminar
Numerische Mathematik SS 2009


Dozenten: Jörg Liesen, Volker Mehrmann, Reinhard Nabben
Koordination:Agnieszka Miedlar
LV-Termine:Do 10-12 in MA 376
Inhalt: Vorträge von Diplomanden, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen

Vorläufige Terminplanung:
 
Datum Uhrzeit Raum Vortragende(r) Titel
Do 16.04.2009 10:15 MA 376
 
--------------------- Vorbesprechung
Do 23.04.2009 10:15 MA 376
 
 Safique Ahmad Pseudospectra, critical points and multiple eigenvalues of matrix polynomials (Abstract)
Do 30.04.2009 10:15 MA 376
 
 Prof. Dr. Erik S. Van Vleck
(Univ. Kansas, USA)
The Error in QR Integration and Applications (Abstract)
Do 07.05.2009 10:15 MA 376
 
 Ann-Kristin Baum Numerical methods in the simulation of transient magnetic fields (Abstract)
Do 14.05.2009 10:15 MA 376
 
 Jan Heiland Distributed Control of Semidiscretized Oseen Equation (Abstract)
Do 28.05.2009 10:15 MA 376
 
 Tobias Brüll Linear Dissipative Systems and the Behavioral Approach (Abstract)
im Anschluss MA 376
 
 Sander Wahls Control Approach to Joint Suppression of Intersymbol and Cochannel Interference in Frequency Selective MIMO Channels (Abstract)
Do 11.06.2009 10:15 MA 376
 
 Tobias Baumgarten Eigenvalue path-following for large scale second order systems (Abstract)
im Anschluss MA 376
 
 Matthias Miltenberger The IDR method for solving large nonsymmetric parameterized linear systems (Abstract)
Do 18.06.2009 10:15 MA 376
 
 Phi Ha On the positivity of strangeness-free descriptor systems (Abstract)
im Anschluss MA 376
 
 Dr. Vu Hoang Linh
(Hanoi National Univ. and TU Berlin)
Maximal stability bound for generalized singularly perturbed systems (Abstract)
Do 25.06.2009 10:15 MA 376
 
 Lisa Poppe TBA (Abstract)
Do 02.07.2009 10:15 MA 376
 
 Elena Teidelt Numerical Solutions of Eigenvalue Problems Arising from Noise Control Problems (Abstract)
im Anschluss MA 376
 
 Jens Möckel Computation of Sacker-Sell spectral intervals for DAE-systems (Abstract)
Do 02.07.2009 17:30
(extra)
MA 645 
 Markus Stammberger
(TU Hamburg-Harburg)
AMLS für Fluid-Struktur-Interaktionsprobleme (Abstract)
Do 16.07.2009 10:15 MA 376
 
 Aziz Salih Numerical solution of algebraic Lur'e equation using the Newton method (Abstract)

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Abstracts zu den Vorträgen:


Safique Ahmad (TU Berlin)
Pseudospectra, critical points and multiple eigenvalues of matrix polynomials
Thu 23.04.2009, 10:15 h in MA 376

Abstract:
In this talk we will discuss a general framework for perturbation analysis of matrix polynomials. The framework so developed provides a convenient setting for analyzing pseudospectra of matrix polynomials and parallels the well developed framework that exists for pseudospectra of matrices. We provide a general definition of pseudospectra of matrix polynomials from which the pseudospectra of matrix polynomials well known in the literature follow as special cases. We analyze critical points of backward errors of approximate eigenvalues of matrix polynomials and show that each critical point is a multiple eigenvalue of an appropriately perturbed polynomial. We show that common boundary points of components of pseudospectra of matrix polynomials are critical points. In particular, we show that a minimal critical point can be read off from the pseudospectra of matrix polynomials. Hence we show that a solution of Wilkinson's problem for matrix polynomials can be read off from the pseudospectra of matrix polynomials.
We will also discuss a general framework for the construction of nearest defective matrix pencils to a diagonal pencil with various examples.


Ann-Kristin Baum (TU Berlin)
Numerical methods in the simulation of transient magnetic fields
Thu 07.05.2009, 10:15 in MA 376

Abstract:

The aim of this talk is to give overview of the simulation of transient magnetic fields with a special regard to the conservation of physical and continuous features in the process of discretization.
Starting from the physical aspects of the magneto-quasistatic Maxwell Equations, curl-conforming Finite Elements and implicit Runge-Kutta methods are motivated and presented as suitable methods for an efficient discretization of the magneto-quasistatic potential equation.
In particular, the stability inheritance in the process of time discretization is analyzed analytically and tested numerically, including a comparison of implicit and linear-implicit Runge-Kutta methods.


Jan Heiland (TU Berlin)
Distributed Control of Semidiscretized Oseen Equation
Thu 14.05.2009, 10:15 in MA 376

Abstract:

The primary goal of this diploma thesis is to capture the input/output (i/o) behaviour of a physical system governed by the linear Oseen equations in a closed mathematical formulation to enable an effective application of distributed control. A practical approach is to discretize the spaces of the input and output functions to obtain an approximating matrix representation of the i/o operator. For an adaptive procedure error estimates by means of an analytical form of the i/o map are important.
Considering the semidiscretized Oseen equation as a linear differential algebraic equation (DAE) with constant coefficients, one has an explicit solution formula. If applied to a system with a control term, it can function as the base for a closed-form i/o map. The DAE approach admits a wide range of spatial discretization methods, a special focus lies on mixed q1p0 finite elements. The investigation is accompanied and backed by numerical tests.
In my talk I will give a short summary of the topic and present theoretical results as well as outcomes of the numerical simulation.


Tobias Brüll (TU Berlin)
Linear Dissipative Systems and the Behavioral Approach
Thu 28.05.2009, 10:15 in MA 376

Abstract:

In this talk we are going to investigate dissipative systems theory with the help of the behavioral approach. Both topics (the behavioral approach and dissipative systems theory as well as their interconnection) have already thoroughly been studied by J. C. Willems et al. Here we will look at the most simple version of the theory of Willems et al. and then show how dissipativity of such systems can also be handled computationally with the help of structured matrix pencils.


Sander Wahls (TU Berlin)
Control Approach to Joint Suppression of Intersymbol and Cochannel Interference in Frequency Selective MIMO Channels
Thu 28.05.2009, 10:15 in MA 376

Abstract:

We consider a common problem in wireless communications, i.e., recovery of signals which have been compromised by intersymbol as well as cochannel interference. Intersymbol interference (ISI) occurs due to the multipath nature of the wireless channel, where multiple echos of the transmitted signals arrive at the receiver through various paths at various times and superpose. On the other hand, cochannel interference (CCI) occurs when multiple users are simultaneously transmitting on the same frequency. In this talk, we will derive the optimal linear equalizer to jointly suppress ISI and CCI. The main idea will be to reformulate this problem as a linear system inversion problem with frequency weighted H2 norm criterion. The equivalent system inversion problem is then solved using tools from H2 optimal control.


Tobias Brüll (TU Berlin)
Linear Dissipative Systems and the Behavioral Approach
Thu 28.05.2009, 10:15 in MA 376

Abstract:

In this talk we are going to investigate dissipative systems theory with the help of the behavioral approach. Both topics (the behavioral approach and dissipative systems theory as well as their interconnection) have already thoroughly been studied by J. C. Willems et al. Here we will look at the most simple version of the theory of Willems et al. and then show how dissipativity of such systems can also be handled computationally with the help of structured matrix pencils.


Tobias Baumgarten (TU Berlin)

Thu 11.06.2009, 10:15 in MA 376

Abstract:

The final goal of the diploma thesis is, to detect all eigenvalues and vectors of large scale second order system in a specified area in C. Therefore I will use a homotopy method over the damping matrix D, starting with the eigenvalues and vectors of the undamped system. For the path-following problem we have to consider perturbation and bifurcation theory as well as general eigenanalysis. In this talk I will give short introduction into the topic and summarize the parts I already implemented as well as the prospective problems. Also I will show some numerical results.


Matthias Miltenberger (TU Berlin)

Thu 11.06.2009, 10:15 in MA 376

Abstract:

This presentation is on the family of IDR methods as a technique to solve large nonsymmetric linear systems of equations. In contrast to other options IDR methods do not require any special features of the matrix. When dealing with a sequence of similar systems of equations, Krylov recycling techniques, that exploit similarities between them, can be very useful. The aim of my Diploma thesis is the development of a combination of both..


Dr. Vu Hoang Linh (Hanoi National Univ. and TU Berlin)

Thu 18.06.2009, 10:15 in MA 376

Abstract:

This talk is concerned with computable formulas for the maximal stability bound for an implicit system of linear differential equations which contains an uncertain small parameter in the leading term. Sufficient conditions are given for the robust stability of the system, i.e., the system is asymptotically stable for all sufficiently small parameter values. To find the maximal stability bound of the systems, the time-domain method is used. This leads to generalized eigenvalue problems. Details of the numerical algorithms and some illustrative examples are given.


Elena Teidelt
Numerical Solutions of Eigenvalue Problems Arising from Noise Control Problems
Thu 02.07.2009, 10:15 in MA 376

Abstract:

As part of my diploma thesis, I implemented and still implement a program for SFE GmbH Berlin, which solves large scale generalized eigenvalue problems. In this talk, I will introduce the specific kind of generalized eigenvalue problems arising in acoustics and structural mechanics as well as sketch the implemented algorithms. A focus of my talk will lie on the difficulties of writing robust and fast software for well known, but large scale problems. This is done by evaluating the numerical results of the implemented solver, which show that a standard Arnoldi method is not suitable for fast software.


Jens Möckel
Computation of Sacker-Sell spectral intervals for DAE-systems
Thu 02.07.2009, 10:15 in MA 376

Abstract:

The aim of my master thesis is to check stability of linear DAEs with timedependent and regular coefficient matrices. This could be achieved by using Sacker-Sell spectral intervals (as well as Lyapunov spectral intervals). The idea to obtain these spectral sets is to transforme the DAE in a reduced system. If the fundamental solution matrix of this reduced system is integrally separated, one could use the associated underlying ODE of this system to determine the spectral intervals of the DAE. Furthermore, it has to be considered, how these spectral sets behave under pertubations. In this talk, I will give an introduction on the spectral theory for DAE systems as well as the main ideas for two algorithms, which computes the wanted intervals.


Aziz Salih
Numerical solution of algebraic Lur'e equation using the Newton method
Thu 16.07.2009, 10:15 in MA 376

Abstract:

As the subject of my diploma-thesis, I have to solve algebraic Lur'e equations that arise in the process of model order reduction of descriptor systems. In my talk, I will give some introductions in model order reduction and how Newton's method is used to solve nonlinear algebraic equations, as well as some results and numerical examples of MATLAB-routines that compute the solution of the Lur'e equations.


Impressum Agnieszka Miedlar 09.07.2009