# Diplomanden- und Doktorandenseminar Numerische Mathematik WS 2010/2011

 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

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Datum Uhrzeit Raum Vortragende(r) Titel Vorläufige Terminplanung: Do 21.10.2010 10:15 MA 376 --------------------- Vorbesprechung Do 28.10.2010 10:15 MA 376 Do 04.11.2010 10:15 MA 376 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 Do 06.01.2010 10:15 MA 376 Do 13.01.2010 10:15 MA 376 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 C2 Subdivision on Genus 0 Surfaces (Abstract) Di 15.03.2011 11:00 MA 313 Oliver Rott (WIAS) Modelling and stability of milling processes

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Jens Möckel (TU Berlin)
Linear-Quadratic Gaussian Balancing for Model Reduction of Differential-Algebraic Systems
Thu 18.11.2010, 10:15 h in MA 376

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.

Heiner Stilz (TU Berlin)
Convergence Bounds and True Convergence of Krylov Methods for Eigenvalue Computations
Thu 18.11.2010, 10:15 h in MA 376

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.

Jan Heiland (TU Berlin)
Boundary control of turbulent flow fields - I try linearizations and velocity decompositions for controller design
Thu 25.11.2010, 10:15 h in MA 376

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.

Thorsten Rohwedder (TU Berlin)
The electronic Schrödinger equation and the continuous Coupled Cluster method
Thu 09.12.2010, 10:15 h in MA 376

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

Ann-Kristin Baum (TU Berlin)
Networked based remodeling of large electrical and mechanical systems
Thu 20.01.2011, 10:15 h in MA 376

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.

Olivier Séte (TU Berlin)
Functions of Matrices and Faber-Walsh-Polynomials
Thu 27.01.2011, 10:15 h in MA 376

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).

André Gaul (TU Berlin)
Deflated and augmented Krylov subspace methods
Thu 27.01.2011, 10:15 h in MA 376

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.

Florian Goßler (TU Berlin)
Old and new condition number bounds for multilevel methods applied as preconditioner
Thu 03.02.2011, 10:15 h in MA 376

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.

Phi Ha (TU Berlin)
Stability of Regular, Impulse-free Delay Differential-Algebraic Equations
Thu 03.02.2011, 10:15 h in MA 376

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.

Ina Thies (TU Berlin)
Krylov-Type Methods for Tensor Computations (paper by B. Savas and L. Eldén)
Thu 17.02.2011,10:45 h in MA 376

Abstract:
In my talk I will present the paper "Krylov-Type Methods for Tensor Computations" by Berkant Savas and Lars Eldén (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.

Sandra Grundel
C2 Subdivision on Genus 0 Surfaces
Mo 28.02.2011, 14:15 h in MA 313

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 C2 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