Dozenten: | Jörg Liesen, Christian Mehl, Volker Mehrmann, Reinhard Nabben |
Koordination: | Christian Mehl |
LV-Termine: | Do 10:15-11:45 in MA 376 |
Inhalt: | Vorträge von Diplomanden, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen |
Vollständige Terminplanung: | ||||
Datum | Uhrzeit | Raum | Vortragende(r) | Titel |
---|---|---|---|---|
Do 19.10.2006 | 10:15 | MA 376 |
Vorbesprechung | |
Do 26.10.2006 | 10:15 | MA 376 |
Martin Bodestedt | A first perturbation result for the modified nodal analysis coupled with non-stationary drift-diffusion (Abstract) |
Do 2.11.2006 | 10:15 | MA 376 |
Stephan Trenn
(TU Ilmenau) |
Distributional DAEs (Abstract) |
Do 9.11.2006 | 10:15 | MA 376 |
Jok Tang (TU Delft) |
Deflation method applied on 3-D bubbly flow problems (Abstract) |
Do 16.11.2006 | 10:15 | MA 376 |
Falk Ebert | Proper Orthogonal Decomposition for DAEs (Abstract) |
Do 23.11.2006 | 10:15 | MA 376 |
Christian Schröder | Passivity of LTI systems (Abstract) |
Do 7.12.2006 | 10:00 | MA 376 |
Sadegh Jokar | Exact and Approximate Minimal Support Solutions of Underdetermined Linear Equation Systems (Abstract) |
Do 7.12.2006 | im An- schluss |
MA 376 |
Lena Wunderlich | An Introduction to Hybrid DAEs (Abstract) |
Do 18.1.2007 | 10:15 | MA 376 |
Lisa Poppe | An Introduction to H∞-control (Abstract) |
Do 25.1.2007 | 10:15 | MA 376 |
Volker Mehrmann | Linearization of matrix polynomials/first order formulations of DAEs - A new point of view (Abstract) |
Do 1.2.2007 | 10:00 | MA 376 |
Timo Reis | Passivity-Preserving Model Reduction of Descriptor Systems (Abstract) |
Do 1.2.2007 | im An- schluss |
MA 376 |
Elena Virnik | A generalisation of the Perron-Frobenius Theorem (Abstract) |
Interessenten sind herzlich eingeladen!
Weitere Vorträge siehe auch:
Abstracts zu den Vorträgen:
Abstract:
We investigate an integrated circuit model coupling the modified nodal
analysis (MNA) equations
the non-stationary drift-diffusion equations. By considering
perturbations only in the MNA equations we could obtain the first
perturbation estimate for this partial differential algebraic equation
(PDAE). It is assumed that the linear circuit without the semiconductor
branch is of index 1, that the diode contacts are connected by a
capacitive path and that the semiconductor region is a one-dimensional.
Abstract:
It will be motivated that differential algebraic equations DAEs with
piecewise analytical coefficients are a nice setup for considering initial
value problems as well as switched systems. On the other hand it is well
known that for a complete solution theory of DAEs generalized functions
(i.e. distributions) are needed. The aim of this talk is to give an overview
how DAEs with piecewise analytical coefficients can be embedded in the
distributional setup.
Abstract:
Simulating bubbly flows is a very popular topic in CFD and it receives a lot
of attention in various research projects in the last decades. The bubbly
flows are governed by the Navier-Stokes equations. In many popular operator
splitting formulations for these equations, solving the singular SPSD
linear
system Ax=b coming from the Poisson equation with discontinuous
coefficients
takes the most computational time. Standard Krylov solvers like conjugate
gradient (cg) method with any preconditioner appear to converge very
slowly.
We present a method based on cg by adding a so-called deflation technique to accelerate the iteration process significantly. Using some numerical linear algebra, we give theoretical results to illustrate that the deflation technique can indeed be applied on bubbly flow problems. Finally, some 3-D numerical experiments with bubbles an droplets will be presented in order to show that the deflation method works very well by considering both the number of iterations and the computational time.
Abstract:
Proper orthogonal decomposition aka. POD aka. principal component
analysis aka. Karhuenen-Loewe expansion has been used in data
representation and compression for a long time. By means of a
Gelerkin projection they can be employed in the model order reduction
of nonlinear ODEs. The simple approach, however, fails when dealing
with differential-algebraic equations. There the state-reduction must
be applied to the inherent dynamic system only. We will present a
general introduction to the POD method and show why it fails for
DAEs. A POD method adapted to DAEs will be presented together with
related issues such as computation of the relevant projection
subspaces.
Abstract:
We will give a definition of passivity of LTI systems and explain how to
determine, if a given system is passive. Furthermore, we will discuss an
algorithm to perturb a given system to make it passive. Finally, numerical
examples are presented.
Abstract:
Many complex dynamical systems in different application areas are switched
or hybrid systems, i.e. the mathematical model itself may change with
time, depending on certain indicators. In this talk we consider the modeling
and numerical simulation of hybrid differential-algebraic systems.
We deal with certain difficulties as index changes after mode switching events
or the computation of consistent initial values after mode changes.
Abstract:
In this talk an introduction to H∞-control is given. First the
control problem for ODEs is introduced and it is shown how the conditions
for the existence of a controller can be obtained. In the second part we
show how the ODE techniques can be used to approach the H∞-control
problem for descriptor systems and discuss different methods for this class of problems.
Abstract:
We will discuss a new concept for linearization of matrix polynomials
and first order formulations of DAEs. This new approach allows to
reduce the lengths of Jordan chains associated with singular parts
or infinte eigenvalues and is in line with the approach used
for first order formulations in multiboy dynamics.
This is joint work with Ralph Byers and Hongguo Xu.
Abstract:
We will present a method for the model reduction of passive descriptor
system
such that the reduced order model remains to be passive. As a concrete
application, we discuss the equations from the modified nodal analysis of
electrical circuits.
Abstract:
We present a new extension of the well-known
Perron-Frobenius theorem to regular matrix pairs (E,A) that has a number
of advantages over previous extensions.
The new extension is based on projector chains and is motivated from
the solution of positive descriptor
systems. We give an extensive introduction to the underlying topics and
present examples where the new condition holds, whereas conditions
in previous literature are not satisfied.
Impressum | Christian Mehl 7.2.2007 |