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:
Abstract:
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.
Abstract:
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.
Abstract:
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.
Abstract:
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.
Abstract:
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 P_{1} 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.
Abstract:
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.
Abstract:
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
Abstract:
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 |