|Dozenten:||Jörg Liesen, Volker Mehrmann, Reinhard Nabben|
|LV-Termine:||Do 10-12 in MA 376|
|Inhalt:||Vorträge von Diplomanden, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen|
|Vorschau Sommersemester 2010:|
|Do 15.10.2009||10:15||MA 376
|Do 22.10.2009||10:15||MA 376
||Matthias Miltenberger||The IDR method for solving large nonsymmetric parameterized linear systems (Abstract)|
|im Anschluss||MA 376
||Tobias Brüll||Optimal control of behavior systems (Abstract)|
|Do 05.11.2009||10:15||MA 376
||Robert Luce||Taking advantage of short chains in sparse triangular substitution (Abstract)|
|im Anschluss||MA 376
||Agnieszka Międlar||A homotopy approach for the adaptive solution of PDE-eigenvalue problems (Abstract)|
|Do 19.11.2009||10:15||MA 376
||Phi Ha||Positive descriptor systems — Introduction and first steps (Abstract)|
|im Anschluss||MA 376
||Timo Reis||Lur'e Equations and Even Matrix Pencils (Abstract)|
|Do 26.11.2009||10:15||MA 376
|| Prof. Serkan Gugercin
|Optimal Model Reduction by Interpolation (Abstract)|
|Do 03.12.2009||10:15||MA 376
||Safique Ahmad||Perturbation analysis for structured matrix polynomials in the solution of matrix equations (Abstract)|
|Do 10.12.2009||10:15||MA 376
||Ann-Kristin Baum||Positivity preserving discretizations for linear problems - the constant coefficient case (Abstract)|
|Do 17.12.2009||10:15||MA 376
||André Gaul||Domain Decomposition Method for a Finite Element Algorithm for Image Segmentation (Abstract)|
|im Anschluss||MA 376
||Jan Heiland||Control of drop size distributions in liquid/liquid dispersions (Abstract)|
|Do 14.01.2010||10:15||MA 376
|| Prof. Ivan Slapnicar
(University of Split)
|On the spectra of Fibonacci-like operators and modeling invasions by fungal pathogens (Abstract)|
|Do 21.01.2010||10:15||MA 376
||Jens Möckel||Methods for computing Sacker-Sell spectral intervals for linear differential-algebraic equations (Abstract)|
|im Anschluss||MA 376
||Florian Goßler||An introduction in quantum chromodynamics and why numerical analysis is needed (Abstract)|
|Do 11.02.2010||10:15||MA 313
|| Prof. Nick Trefethen FRS
|Who invented the great numerical algorithms? (Abstract)|
Interessenten sind herzlich eingeladen!
Weitere Vorträge siehe auch:
Abstracts zu den Vorträgen:
This presentation is on the results of my Diploma thesis. Thereby I showed how to combine recycling techniques with two methods of the IDR family in order to accelerate the solution of a sequence of linear systems. IDR methods are quite new and therefore lack thorough analysis. Hence, working with them is rather difficult. Besides, I will present how IDR methods - especially the idea of recycling information - could be enhanced further.
In this talk a very general form of the infinite-horizon linear quadratic control problem is considered, i.e., we will consider quadratic cost functionals which involve not only the state and input-variables but also derivatives of the state and input-variables of arbitrary order under constraints given by linear systems of higher order. We will examine two preliminary results which relate the linear quadratic control problem to an optimality system, which is given through a special even matrix polynomial. Also we will see that the notion of dissipativity (when introduced in the proper way) is equivalent to the solvability of the linear quadratic control problem.
Triangular matrices correspond naturally to partially ordered sets. We discuss a technique for the solution of sparse triangular linear systems that takes advantage of sparse solutions and short poset height. Applications and preliminary numerical results will be given.
We introduce a new adaptive finite element algorithm for PDE-eigenvalue problems combined with a homotopy approach to determine a few eigenpairs of non-selfadjoint eigenvalue problems for PDEs. In order to reduce the complexity while retaining good accuracy for symmetric problems the adaptive algorithms with guaranteed computable bounds in the algebraic part are used. However, large, sparse non-symmetric real matrices may have complex eigenvalues, occurring as complex conjugate pairs. Unfortunately, in this case the min-max theorem does not hold and we are not able to use standard eigenvalue solvers without additional information about the spectrum. The homotopy method allow us to control the convergence process and detect whether a conjugate pair appeared. Our new algorithm combines those two techniques to solve non-selfadjoint eigenvalue problems with desired accuracy and reasonable complexity.
This is a joint work with J. Gedicke.
In this talk, we will discuss the problem for positive descriptor systems with time-varying coefficients. First we give a short introduction on different approaches to positive descriptor systems. Afterwards, the positivity of linear state-space systems will be considered. Finally, some first results about descriptor systems will be presented.
Lur'e equations are a generalization of algebraic Riccati equations and they arise in linear-quadratic optimal control problems which are singular in the input.
It is well-known that there is a one-to-one correspondence between the solutions of Riccati equations and Lagrangian disconjugate eigenspaces of a certain Hamiltonian matrix.
The aim of this talk is to generalize this concept to Lur'e equations. We are led to the consideration of deflating subspaces of even matrix pencils.
The solution of matrix equations in control leads to eigenvalue problems for structured matrix polynomials. In this work we propose a general framework for the structured perturbation analysis of several classes of structured matrix polynomials in homogeneous form, including complex symmetric, skew-symmetric, even and odd matrix polynomials. We introduce structured backward errors for approximate eigenvalues and eigenvectors and we construct minimal structured perturbations such that an approximate eigenpair is an exact eigenpair of an appropriately perturbed matrix polynomial. This work extends previous work for the non-homogeneous case (we include infinite eigenvalues) and we show that the structured backward errors improve the known unstructured backward errors with various examples.
In this talk, first results about positivity preserving discretizations for DAEs are presented and an outlook of the future work is given. For ODEs, positivity preservation has already been investigated in the context of semi-discretized Advection-Diffusion-Equations or dissipative ODEs.
For linear ODEs with constant coefficients, positivity and its preservation is characterized by the notion of Z- and M-Matrices and Absolute Monotonic Functions. Analyzing this argumentation and extending the relevant definitions to Matrix pairs, these criteria are straightforward generalized to linear DAEs. In conlusion, an outline of those topics will be given, that have to be adressed in order to establish positive discretizations of linear, timevariable and non-linear DAEs.
Computer-based image segmentation is a common task when analyzing and classifying images in an automated way. We will present a finite element algorithm for image segmentation based on a level set formulation of the Mumford-Shah functional. The algorithm will be combined with a domain decomposition method which enables us to compute segmentations of large datasets like high-resolution microscope or satellite scans on multi-core CPUs and high-performance distributed parallel computers rapidly. Numerical results including scaling behavior will be shown.
The project presented is dedicated to the control of drop size distributions in stirred liquid/liquid dispersions which are of major importance in chemical industries. The design of reactors requires usually expensive experimental investigations. Mathematical modelling, model based simulation and control are often the only feasible approach to achieve the technological goals. For the complex process of formation of drop size distributions (DSD) in a stirred tank such mathematical methods are currently not available. The global long-term perspective of the project is to develop model based methods for the prediction of the complex process of DSD formation in stirred liquid/liquid dispersions in a stirred tank. The technological vision is to be able to achieve a desired average drop size and a defined size distribution, using control parameters such as the stirrer speed. There a specific stirrer setup is investigated analytically, numerically and by means of experiments.
In my talk I will present the concret physical setup, introduce the underlying mathematical model and address solution and implementation approaches. The model is given by a coupling of the k-e equations for the flow and a population balance equation (PBE) describing the dispersed phase. To soften the high computational loads of a direct numerical solution of the PBE the method of moments (MOM) will be used for the simulations. In view of PID-control or system identification an interface between the flow/PBE solver and Matlab is implemented.
This talk will present the main points of my master thesis. First, I will give a short introduction to the extension of concepts like Bohl exponents and Sacker-Sell spectrum from ordinary differential equations to linear differential-algebraic equations. Based on this theoretical background I will describe different ideas, how to compute this spectrum. In particular, used numerical integration methods and the effect of several parameters will be discussed. In the end, some numerical results will be given.
In physics, fundamental interactions are the ways that the simplest particles in the universe interact with one other. The four known fundamental interactions are electromagnetism, strong interaction, weak interaction and gravitation. In this talk quantum chromodynamics (QCD) which is a theory of the strong interaction is introduced. The theory is based on quantum electrodynamics (QED) which is the best understood theory of interaction. Later on it is shown why numerical analysis is needed in QCD and why perturbation theory can't be used (as in other theories (e.g. QED)).
This talk identifies thirty of the great algorithms of numerical analysis, from Gaussian elimination to automatic differentiation, and asks in each case, who were the main inventors? Were they mathematicians or engineers, academics or industrialists? The story is full of pictures and anecdotes, with some surprises along the way.
|Impressum||Agnieszka Miedlar 05.02.2010|