Dozenten: | Jörg Liesen, Christian Mehl, Volker Mehrmann, Reinhard Nabben, Tatjana Stykel |
Koordination: | Agnieszka Międlar |
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 21.10.2010 | 10:15 | MA 376 |
--------------------- | Vorbesprechung |
Do 28.10.2010 | 10:15 | MA 376 |
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Do 04.11.2010 | 10:15 | MA 376 |
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Do 18.11.2010 | 10:15 | MA 376 |
Jens Möckel | Linear-Quadratic Gaussian Balancing for Model Reduction of Differential-Algebraic Systems (Abstract) |
im Anschluss | MA 376 |
Heiner Stilz | Convergence Bounds and True Convergence of Krylov Methods for Eigenvalue Computations (Abstract) | |
Do 25.11.2010 | 10:15 | MA 376 |
Jan Heiland | Boundary control of turbulent flow fields - I try linearizations and velocity decompositions for controller design (Abstract) |
Do 09.12.2010 | 10:15 | MA 376 |
Thorsten Rohwedder | The electronic Schrödinger equation and the continuous Coupled Cluster method (Abstract) |
Do 16.12.2010 | 10:15 | MA 376 |
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Do 06.01.2010 | 10:15 | MA 376 |
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Do 13.01.2010 | 10:15 | MA 376 |
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Do 20.01.2010 | 10:15 | MA 376 |
Ann-Kristin Baum | Networked based remodeling of large electrical and mechanical systems (Abstract) |
Do 27.01.2010 | 10:15 | MA 376 |
Olivier Séte | Functions of Matrices and Faber-Walsh-Polynomials (Abstract) |
im Anschluss | MA 376 |
André Gaul | Deflated and augmented Krylov subspace methods (Abstract) | |
Do 03.02.2011 | 10:15 | MA 376 |
Florian Goßler | Old and new condition number bounds for multilevel methods applied as preconditioner (Abstract) |
im Anschluss | MA 376 |
Phi Ha | Stability of Regular, Impulse-free Delay Differential-Algebraic Equations (Abstract) | |
Do 17.02.2011 | 10:45 | MA 376 |
Ina Thies | Krylov-Type Methods for Tensor Computations (paper by B. Savas and L. Eldén) (Abstract) |
Mo 28.02.2011 | 14:15 | MA 313 |
Sara Grundel | C^{2} Subdivision on Genus 0 Surfaces (Abstract) |
Oliver Rott (WIAS) | Modelling and stability of milling processes |
Interessenten sind herzlich eingeladen!
Weitere Vorträge siehe auch:
Abstract:
In this talk we consider Model Reduction for Differential-Algebraic Systems.
This kind of Systems appears in many practical applications. Technical and industrial developments have led to an increasement of the order of the considered System, while the number of its inputs and outputs have (typically) remained small - compared to the system order. Despite the accelerating computational speed, this enlargement of states cause difficulties like storage requirements and expensive computations. This motivates model order reduction that consists in approximating the considered (descriptor) system by a reduced-order system.
We will discuss linear-quadratic Gaussian (LQG) balanced truncation method, which based on the solutions of generalized algebraic Riccati equations and applies, in contrast to standard balanced truncation methods, even to systems, which are not asymptotically stable.
For this purpose we start with a short introduction to model order reduction and its main ideas. The main part of this talk is divided into two sections: On the one hand we consider generalized algebraic Riccati equations and some new solvability criteria in terms of system theoretic properties, on the other hand the LQG balanced truncation method is introduced. At the end, some numerically examples are presented.
Abstract:
A common application of Krylov methods is to approximate a certain desired invariant subspace of a matrix through a Krylov subspace. In this diploma thesis, the focus is on convergence of the "error" of the approximation - here, the angle between invariant subspace and Krylov subspace. A known error bound is compared to observed errors for earlier Krylov iterations and certain academic example matrices. These examples include Hermitean, similar to Hermitean, and defective matrices, and a matrix parametrizable from defective to non-defective.
Abstract:
The main task in designing a control setup for a dynamical system is the
synthesis of the so called controller. In many cases the controller itself is
a dynamical system of similar but less complex structure.
In my work I examine a model of a mixing process in a stirred tank, given by
the Navier-Stokes equations with turbulence modelling and transport equations
for the moments, that characterize quantities of the mixture.
In order to control the actual nonlinear system, I will derive a controller
for a linearized approximation and use it. The hope is, that if the
linearization is good, then this control will also perform in the original
system.
For the linearized system one can use the geometrical properties and a
decompositon of the rotating flow in the stirrer, to transform the boundary
control system into a distributed control. The transformation yields a
descriptor system with variable coefficients.
In my talk I am going to give a comprehensive explanation and motivation of
the underlying physical problem and the mathematical model. I will explain
the linearization procedure and the flow decomposition. If time permits I
will show how the descriptor system is obtained and address the theory
regarding controller design of such systems.
Abstract:
Many properties of atoms, molecules and solid states are described quite
accurately by solutions $\Psi$ of the electronic Schrödinger equation
$H\Psi = E\Psi$, an extremely high-dimensional operator eigenvalue equation for the
Hamiltonian $H$ of the system under consideration. Of utmost interest is often
the smallest eigenvalue of $H$ and the corresponding eigenfunction,
giving the ground state energy and the electronic wave function
describing the ground state, respectively.
In the first part of this talk, a review on the
electronic Schrödinger equation and the typical problems that arise when
dealing with this equation is given. I will then given then introduce the Coupled Cluster method, a method that is standardly used in quantum chemistry for highly accurate calculations.
Coupled Cluster (CC) is standardly formulated as an ansatz for the
approximation of the Galerkin solution of the Schrödinger equation
within a given discretisation [1]. I will show how this ansatz can be extended to infinite dimensional spaces, thus obtaining
an equivalent reformulation of the original, continuous Schrödinger
equation in terms of a root equation for a nonlinear operator, and present some results that can be derived in this setting.
[1] R. Schneider, Num. Math. 113, 3, 2009.
/homes/numerik/miedlar
Abstract:
Large electrical and mechanical systems occurring in engineering are
typically modeled by network lists that arise from a graph theoretical
description of the considered system.
This ansatz provides a systematic way to assemble the governing system of
differential-algebraic equations (DAE), but, due to redundancies and
dependencies of some variables, these equations usually contain extra
algebraic constraints involving derivatives of input functions.
To carry out an efficient and precise numerical simulation, these hidden
equations must be available to avoid discretization errors and drift-off
phenomena and to prescribe consistent initial values.
In my talk, I will introduce to the idea of Bond Graph Modeling and will
show how the topology of these Graphs can be exploited to detect the
hidden constraints.
This is a joint work with Timo Reis.
Abstract:
We consider the expression f(A), where A is a complex square Matrix and f
a function analytic on the spectrum of A. The problem is then to compute an
approximation g(A) of f(A) and to estimate the error in a given norm.
For this purpose, we introduce the concept of Faber-Walsh-Polynomials, which
lead to an approximation of f by polynomials which have some of the good
properties of Taylor series (especially fast and uniform convergence to f).
Abstract:
We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Deflation ``removes'' certain parts from the operator while augmentation adds another subspace to the Krylov subspace. We analyze known deflation and augmentation strategies for CG, GMRes and MinRes by mathematically characterizing the equivalence of certain approaches. Furthermore, our analysis reveals how breakdowns in the recently proposed RMinRes method can be avoided.
Abstract:
In this talk we consider the inheritance of different types of spectral equivalence in algebraic
multilevel methods. This leads to new condition number bounds for multilevel methods applied as preconditioner.
For specific C.B.S. constants we show that the new bounds improve well-known bounds.
Abstract:
The aim of this talk is to analyze the stability of regular, impulse-free delay differential-algebraic equation E\dot{x}(t)=A_0 x(t) + A_1 x(t-h) + f(t). In the first part of the talk, under some assumptions, the structure of matrix triple (E,A_0,A_1) will be considered. Then, based on Lyapunov-Krasovskii functional method, we shall derive some sufficient stability conditions in terms of linear matrix inequalities.
Abstract:
In my talk I will present the paper "Krylov-Type Methods for Tensor Computations" by Berkant Savas and Lars EldÃ©n (submitted to LAA in May 2010). Here, "tensor" means multidimensional array. Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. These tensor Krylov methods are intended for the computation of low-rank approximations of large and sparse tensors.
Abstract:
Subdivision Surfaces are ideally suited for applications in geometric
modeling in the graphics community and are widely used. Despite their
success in computer graphics, subdivision methods have not made a
similar impact in the engineering community, where the requirements
for surface quality are more demanding than those of the entertainment
industry. One of the problems is that Subdivision Surfaces have
curvature singularities or flat spots. It has been thought impossible to
find a Subdivision Scheme that has C^{2} smoothness without being too
cumbersome. However, by restricting the approach to a certain class of
surfaces it \textit{is} possible. We explain the details of the development
of this scheme and its curvature properties. The scheme can be used in
various different applications. One of the advantages over other
methods is that it is multi-scale in nature.
Impressum | Agnieszka Międlar 26.01.2011 |