Diplomanden- und Doktorandenseminar
Numerische Mathematik WS 2008/09

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 16.10.2008 10:15 MA 376
--------------------- Vorbesprechung
Do 23.10.2008 10:15 MA 376
Christian Schröder Iterative Refinement of the Palindromic Schur Form (Abstract)
Do 13.11.2008 11:00 MA 376
Tobias Brüll A different approach to distributions (Abstract)
Do 20.11.2008 10:15 MA 376
Agnieszka Miedlar Adaptive solution of elliptic PDE-eigenvalue problems (Abstract)
Do 27.11.2008 10:15 MA 376
--------------------- ---------------------
Do 04.12.2008 10:15 MA 376
Jan Heiland Distributed Control of Semidiscretized Oseen Equation (Abstract)
im Anschluss MA 376
Volker Mehrmann AG Besprechung
Do 11.12.2008 10:15 MA 376
Joscha Gedicke A posteriori error control for nonsymmetric eigenvalue problems (Abstract)
Do 18.12.2008 10:15 MA 376
Florian Goßler An introduction in primal and dual substructuring methods (Abstract)
Do 08.01.2009 10:15 MA 376
Michael Karow Structured Pseudospectra and the condition of a nonderogatory eigenvalue (Abstract)
Do 15.01.2009 10:15 MA 376
Maciek Korzec (WIAS) The Pang and Huang model for quantum dots growth (Abstract)
Do 22.01.2009 10:15 MA 376
--------------------- ---------------------
Do 29.01.2009 10:15 MA 376
Niels Hartanto Spectral Properties of a class of Analytic Operator Functions with Selfadjoint Coefficients (Abstract)
im Anschluss MA 376
Nenad Moraca Norm bounds for matrix inverses (Abstract)
Do 05.02.2009 10:15 MA 376
Ninoslav Truhar Damping optimization of linear vibrating systems and related problems (Abstract)
im Anschluss MA 376
Lisa Poppe Derivative Arrays and the Behavior Approach for DAEs with Time-Delays (Abstract)

Interessenten sind herzlich eingeladen!

Weitere Vorträge siehe auch:


Abstracts zu den Vorträgen:

Christian Schröder (TU Berlin)
Iterative Refinement of the Palindromic Schur Form
Thu 23.10.2008, 10:15 h in MA 376

Let A be a dense square complex matrix. A palindromic eigenvalue problem is of the form A*x=lambda*A'*x, where A' is the transpose of A. One possibility to solve this structured eigenvalue problem is to find a unitary square matrix Q such that Q'*A*Q is in anti triangular form. In this talk it is assumed that A is already close to antitriangular form. A method is presented to iteratively drive the elements above the anti diagonal to zero. Applications are mixed precision arithmetic, corrections of unstable algorithms and subspace tracking for palindromic eigenvalue problems.

Tobias Brüll (TU Berlin)
A different approach to distributions
Thu 13.11.2008, 10:15 h in MA 376

In continuous-time control theory one frequently has to deal with inputs that are step functions like, for example, the Heaviside function. If, however, the system description is not an ordinary differential equation but a differential-algebraic equation of higher index the concept of solution for such systems can not be generalized in a trivial way. To handle such systems, typically, distributions are introduced in the sense of "Schwartz, L. (1950−1951), Théorie des distributions" where a distribution is defined to be a continuous and linear mapping from some test function space into the real numbers. In this talk a different, more algebraic approach will be presented.

Agnieszka Miedlar (TU Berlin)
Adaptive solution of elliptic PDE-eigenvalue problems
Thu 20.11.2008, 10:15 h in MA 376

We consider a new adaptive finite element algorithm for elliptic eigenvalue problems. The accuracy of the method is guaranteed by using a posteriori estimators based on the backward error analysis. In this talk we will show error estimates and numerical examples for model problem together with theoretical analysis. Additionally some further ideas of improving our method will be discussed.

Jan Heiland (TU Berlin)
Distributed Control of Semidiscretized Oseen Equation
Thu 04.12.2008, 10:15 h in MA 376

The higher-ranking goal of the 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 of maximum interest. 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 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 an insight into the problem definition, present current results, and address upcoming issues.

Joscha Gedicke (HU Berlin)
A posteriori error control for nonsymmetric eigenvalue problems
Thu 11.12.2008, 10:15 h in MA 376

A posteriori error estimators for non symmetric eigenvalue problems of PDE's have been first studied by [Heuveline and Rannacher, A posteriori error control for finite element approximations of elliptic eigenvalue problems, 2001]. In this talk error estimates for the eigenvalue error of a simple convection-diffusion problem will be shortly derived using the variational formulation rather than the non linear ansatz of Becker and Rannacher. In addition error estimators for the eigenvalue error based on averaging techniques are developed. In the case of linear P1 finite elements and piecewise constant coefficients, reduced error estimates of the residual and averaging error estimators are presented. Moreover several DWR techniques are compared numerically and two new weighted error estimators are proposed. The first new estimator utilises an auxiliary Raviard-Thomas solution and the second uses the averaging techniques in combination with the ideas of DWR.

Florian Goßler (TU Berlin)
An introduction in primal and dual substructuring methods
Thu 18.12.2008, 10:15 h in MA 376

Substructuring methods are among the most popular and widely used methods for the solution of systems of linear algebraic equations obtained by finite element discretization of second order elliptic problems. In the talk, I first give a brief review of dual (FETI, FETI_DP, P-FETI, P-FETI-DP) and primal (BDD, BDDC) methods and then discuss some equivalences between primal and dual substructuring preconditioners.

Maciek Korzec (WIAS)
The Pang and Huang model for quantum dots growth
Thu 15.01.2009, 10:15 h in MA 376

Modeling and numerical simulation of quantum dots growth received a good deal of attention in recent years. One new continuum model that is capable of showing effects that can be observed in experiments, such as reasonable length scales or flat regions between the dots which contain a thin ''wetting'' layer, has been derived by Pang and Huang [1]. In this talk I present the derivation of the model, discuss some of the general mathematical basics that are needed to obtain it and show how a possible pseudospectral method can be applied to numerically approximate the solutions. Since the simulated dots are not pyramidal in its form as observed in the most common Si/Ge quantum dots system [2], I extend the surface tension to be anisotropic and compute needed terms for further simulations.

[1] Y. Pang and R. Huang, ''Nonlinear effect of stress and wetting on surface evolution of epitaxial thin films'', Phys. Rev. B 74, 075413, 2006

[2] J. Drucker, ''Self-Assembling Ge(Si)/Si(001)'', IEEE J. Quantum Electronics 38/8, 975-987, 2002

Niels Hartanto (TU Berlin)
Spectral Properties of a class of Analytic Operator Functions with Selfadjoint Coefficients
Thu 29.01.2009, 10:15 h in MA 376

From the Perron-Frobenius theorem it is known that the peripheral spectrum of a nonnegative irreducible matrix A consists of h eigenvalues which are arranged according to the h-th roots of unity where h is the index of imprimitivity of A. A similar result has been given by H. K. Wimmer for a monic matrix polynomials with hermitian coefficients and its spectrum contained in the closed unit disc.
In this talk a generalization of Wimmer's result for some Operator Functions G which are analytic on an annulus is derived, i.e. for r>0, v \neq 0 the set M(r,v)={z \in C : G(z)=0, |z|=r} is described under some additional assumption on G(r). It turns out, that it makes an essential difference if M(r,v) contains elements for which the order of z/r as a root of unity is odd or not.

Impressum Agnieszka Miedlar 03.02.2009