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Datum Zeit Ort Vortrag
23.01.23 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 TBA
Peter Düben, European Centre for Medium-Range Weather Forecasts
21.11.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 + Zoom tba
Vanessa Trapp

14.11.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 tba
Martin Weiser, ZIB

07.11.22 15:00 In Zoom tba
Yahya Saleh

24.10.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 tba
Jonathan Hellwig

10.10.22 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Masterarbeit: Two-Component Model for Tracer Simulation
Sophie Externbrink
05.10.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Bachelorarbeit: Implizit-explizite Zeitschrittverfahren für die Maxey-Riley Gleichungen
Leon Schlegel
22.09.22 11:00 in Zoom Entwicklung einer dezentralen Geschwindigkeitsplanung auf einem autonomen Leader-Fahrzeug für ein sensorloses Intralogistikfahrzeug [Bachelorarbeit]
Selina Meier, Studiengang TM
12.09.22 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Ultra-kleine skalenfreie geometrische Netzwerke (Bachelorarbeit)
Nikolaus Rehberg
18.08.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Zentrale Grenzwertsätze im Random Connection Model
Franz Nestmann, Karlsruher Institut für Technologie (KIT), Fakultät für Mathematik, Institut für Stochastik
29.07.22 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Refinement of Jet simulations usingGenerative Adversarial Networks [Masterarbeit]
Shruthi Janardhan

At the Large Hadron Collider, the interaction of subatomic particles with matter lead to severalmillions of collisions every second. For each collision, upto thousands of particles are producedfollowing stochastic processes. The accurate description of these particles require thousands ofvariables, which leads to large data sets with high dimensionality. The interaction of particleswith the detectors (like Compact Muon Solenoid) are best simulated with the GEANT4 software.Alternatively, less precise but faster simulations are sometimes preferred to reach higher statisticalprecision. We present recent progresses of refinement of fast simulations with Machine Learningtechniques to enhance the quality of such fast simulations. We demonstrate the use of adversarialnetworks in the context of jet simulation using the Wasserstein distance metric. The architectureconsists of opposing networks, Refiner and Critic. A Refiner refines the distribution of the energyof the jets obtained with the fast simulation. The Critic is used to effectively differentiate betweenthe distributions of refined energy and the distribution obtained by the GEANT4 simulation. Weapply the technique to jet kinematics, when the response is close to Gaussian, first on toy data setsand then on realistic data sets
14.07.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Skeleta and shapes related to random tessellations
Daniel Hug, Karlsruher Institut für Technologie (KIT), Fakultät für Mathematik, Institut für Stochastik
11.07.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Spectral inequalities and observability with sensor sets of decaying density
Albrecht Seelmann, TU Dortmund, Fakultät für Mathematik

We discuss spectral inequalities and observability for the harmonic oscillator and more general Schrödinger operators with confinement potentials on the whole space. It turns out that the (super-)exponential decay of the corresponding eigenfunctions allows to consider sensor sets with a density that exhibits a certain decay. This, in particular, permits sensors with finite measure.
07.07.22 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 & Zoom Asymptotic-preserving and hybrid finite-volume/Monte-Carlo methods for kinetic equations in the plasma edge of a fusion reactor*
Giovanni Samaey, KU Leuven

Nuclear fusion reactor design crucially depends on numerical simulation. The plasma can usually be modeled using fluid equations (for mass, momentum and energy). However, the reactor also contains neutral (non-charged) particles (which are important in its operation), of which both the position and velocity distribution is important. This leads to a Boltzmann-type transport equation that needs to be discretised with a Monte Carlo method. In high-collisional regimes, the Monte Carlo simulation describing the evolution of neutral particles becomes prohibitively expensive, because each individual collision needs to be tracked.
In this presentation, we overview a number of approaches that can alleviate the computational burden associated with the high-collisional regime. One option is to avoid simulating each invididual collision. In the limit of infinite collision rate, the law of large numbers dictates the approach of an advection-diffusion like particle behaviour, in which the accumulated effect of an infinite amount of collisions is aggregated in a Brownian motion (diffusion). To maintain accuracy and remove exploding simulation costs in high-collisional regimes, one can define hybridized particles that exhibit both kinetic behaviour and diffusive behaviour depending on the local collisionality [3].
Additionally, we can reduce the number of Monte Carlo particles that needs to be simulated via the multilevel Monte Carlo method[5]. Finally, one can also reduce the variance of the simulation by using an approximate fluid model for the neutral particles, discretized with a finite volume methods. This deterministic simulation can be used as a control variate, allowing the Monte Carlo simulation to focus on solely the deviation of the kinetic model with respect to the approximate fluid model.
[1] KukushkinA.S.,PacherH.D.,KotovV.,PacherG.W.,andReiterD.(2011)FinalizingtheITERdivertordesign:thekeyroleofSOLPSmodeling Fusion Eng. Des. 86:2865-2873.
[2] ReiterD.,BaelmansM.,andBörner,P.(2005)TheEIRENEandB2-EIRENEcodes,FusionSci.Technol.47:172-186.
[3] MortierB.,SamaeyG.,BaelmansM.(2019)Kinetic-diffusionasymptotic-preservingMonteCarloalgorithmsforplasmaedgeneutralsimulation.
Contributions to Plasma Physics, in press.
[4] Horsten N., Samaey G., Baelmans M. (2019) Hybrid fluid-kinetic model for neutral particles in the plasma edge. Nuclear Materials and Energy
[5] Løvbak E., Samaey G., Vandewalle S. (2019) A multilevel Monte Carlo method for asymptotic-preserving particle schemes. Submitted. https://arxiv.org/abs/1907.04610.

Zoomlink: https://tuhh.zoom.us/j/84729171896?pwd=ODArbForaUxMM3Q3VTJsNG1kaVNYQT09
07.07.22 10:30 Big Blue Button Objektivierung des Fahrkomforts automatisierter Fahrzeuge [Masterarbeit]
Nele Thomsen
04.07.22 11:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Gaussian Kernel Ridge Regression using Matrix Decompositions for Preconditioning (Bachelorarbeit)
Ons Gharbia
01.07.22 09:00 TUHH, Raum B0.001 und in Zoom WARTESCHLANGENTHEORIE IN ROBOTISIERTEN LAGERHALTUNGSSYSTEMEN [Habilitationskolloquium]
Karsten Kruse

Aufgrund des zunehmenden Wachstums im E-Commerce-Sektor haben robotisierte Lagerhaltungs-
systeme – Robotic mobile fulfillment systems (RMFS) – für die Auftragsabwicklung in letzter Zeit
mehr Aufmerksamkeit erhalten. Dabei handelt es sich um eine neue Art von Lagerhaltungssyste-
men, bei denen nicht mehr Kommissionierer:innen in den Lagerbereich geschickt werden, um die
bestellten Artikel zu suchen und zu kommissionieren, sondern Roboter die Regale mit den bestell-
ten Artikeln aus dem Lagerbereich zu den Kommissionierstationen, auch Packstationen genannt,
tragen. An jeder Packstation steht eine Person – der oder die Kommissionierer:in (Packer:in) – die
die Artikel aus den Regalen nimmt und sie entsprechend der Kundenbestellung in Kartons verpackt.
Ein solches RMFS wirft viele Entscheidungsprobleme auf. Wir konzentrieren uns auf Entscheidun-
gen über die optimale Anzahl von Robotern. Wir modellieren das RMFS als ein Warteschlangen-
netzwerk, analysieren seine Stabilität und bestimmen die minimale Anzahl von Robotern für ein
stabiles System.
Dieser Vortrag basiert auf der gemeinsamen Arbeit [1] mit Sonja Otten, Ruslan Krenzler, Lin Xie
und Hans Daduna.

[1] Otten, S., Krenzler, R., Xie, L., Daduna, H., und Kruse, K. Analysis of semi-open queueing
networks using lost customers approximation with an application to robotic mobile fulfilment
systems, OR Spectrum, 1–46, 2021. DOI: 10.1007/s00291-021-00662-9.
27.06.22 15:00 Zoom Recent investigations on spectral sets and Crouzeix’s conjecture
Felix Schwenninger, via Zoom

We discuss recent developments around approaches to Crouzeix's conjecture, the statement that the numerical range is a 2 spectral set for any complex square matrix. This includes spectral constants for specific classes of operators.

20.06.22 15:00 Zoom An efficient numerical method for the Maxey-Riley equation
Julio Urizarna Carasa

The Maxey-Riley Equation (MRE) models the motion of a finite-sized, spherical particle moving in a fluid. Applications using the MRE are, for example, the study of the spread of Coronavirus particles in a room, the formation of clouds and the so-called marine snow. The MRE is a second-order, implicit integro-differential equation with a singular kernel at initial time. For over 35 years, researchers used approximations and numerical schemes with high storage requirements or ignored the integral term, although its impact can be relevant. A major break-through was reached in 2019, when Prasath et al. mapped the MRE to a time-dependent Robin-type boundary condition of the 1D Heat equation, thus removing the requirement to store the full history. They provided an implicit integral form of the solution by using the so-called Fokas method that could be later solved with numerical scheme and a nonlinear solver. While Prasath et al.’s method can deliver numerical solutions of very high accuracy, the need to evaluate nested integrals makes it computationally costly and it becomes impractical for computing trajectories of a large number of particles. In the talk, we will present a finite differences approach that it is not only storage efficient but also much faster. We will compare our approach to both Prasath et al.’s method as well as a to the numerical schemes developed by A. Daitche in 2013 for direct integration of the original Maxey-Riley equation with integral term.
16.06.22 15:00 Online Solving the traveling salesman problem via deep reinforcement learning [Masterarbeit]
Darius Schaub
13.06.22 15:00 Zoom tba - cancelled
Riccardo Morandin, TU Berlin
10.06.22 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 und Zoom Planung und Optimierung von Schnittpfaden für dynamisch begrenzte Kinematiken bzgl. Ausschussreduktion [Masterarbeit]
Constantin Riß
30.05.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Spectral deferred correction methods for second-order problems
Ikrom Akramov

Spectral deferred corrections (SDC) is an iterative method for the numerical solution of ordinary differential equations. It can be interpreted as a Picard iteration for the collocation problem, preconditioned with a low order method. SDC has been studied for first order problems, using explicit, implicit or implicit-explicit Euler as preconditioner. It has been shown that SDC can achieve arbitrary high order of accuracy and possesses good stability properties.

In this talk, we will present an analysis of the convergence and stability properties of the SDC method when applied to second-order ODEs and using velocity-Verlet as preconditioner. While a variant of this method called Boris-SDC for the Lorentz equation has been investigated, no general analysis of its properties for general second order problems exists.

We will show that the order of convergence depends on whether the force on the right hand side of the system depends on velocity (like in the Lorentz equation) or not (like in the undamped harmonic oscillator). Moreover, we also show that the SDC iteration is stable under certain conditions. We compare its stability domain with that of the Picard iteration and validate our theoretical analysis in numerical examples.
23.05.22 15:00 Zoom On observability estimates for semigroups in Banach spaces
Dennis Gallaun

In this talk, I would like to present the main results of my PhD thesis.
We study a general method to obtain observability estimates for control systems in infinite dimensional spaces by combining an uncertainty principle and a dissipation estimate. Contrary to previous results obtained in the context of Hilbert spaces, we obtain conditions for observability in Banach spaces, allow for more general asymptotic behavior in the assumptions, and retain explicit estimates on the observability constant.
Our approach has applications, e.g., to control systems on non-reflexive spaces and anomalous diffusion operators.
Further, we derive duality results that connect observability estimates to controllability and stabilizability properties. As an application, we study controllability properties of systems given by fractional powers of elliptic differential operators with constant coefficients in $L_p(\mathbb{R}^d)$ for $p\in [1,\infty)$ and thick control sets.

09.05.22 15:00 Zoom Resilience in Spectral Deferred Corrections
Thomas Baumann, FZ Jülich

Advancement in computational speed is nowadays gained by using more processing units rather than faster ones.
Faults in the processing units caused by numerous sources including radiation and aging have been neglected in the past.
However, the increasing size of HPC machines makes them more susceptible and it is important to develop a resilience strategy to avoid losing millions of CPU hours.
Parallel-in-time methods target the very largest of computers and are hence required to come with algorithm-based fault tolerance.
We look here at spectral deferred corrections (SDC), which is a time marching scheme that is at the heart of parallel-in-time methods such as PFASST.
Due to its iterative nature, there is ample opportunity to plug in computationally inexpensive fault tolerance schemes, many of which are also easy to implement.
We experimentally examine the capability of various strategies to recover from single bit flips in time serial SDC, which will later be applied to parallel-in-time methods.

02.05.22 15:00 Zoom Robot manipulation in real-time, in the real-world, and under uncertainty.*
Wisdom Agboh, University of Leeds

Robots have the potential to disrupt many aspects of our lives, from healthcare to manufacturing. To realize this potential, a key challenge is real-time robot manipulation. Given a task, how can a robot quickly generate a motion plan to successfully complete it? How can the robot react in real-time to potential uncertainties in the real-world as it executes its plan? In this talk, we will overview recent developments at the University of Leeds, to realize real-time robot manipulation. These will include parallel-in-time integration methods that leverage parallel computing to significantly speed-up physics predictions for various robot manipulation tasks. It will also include learning-based and optimal control-based methods for robots to handle real-world uncertainties in object pose estimation and model parameters. We hope these recent advances will help accelerate the next generation of intelligent robots.

Zoomlink: https://tuhh.zoom.us/j/85353626407?pwd=MEIzeTEvY3dRTmtYZjFWUHJaVll4UT09

Meeting ID: 853 5362 6407
Passcode: 045209
25.04.22 15:00 Zoom Component sizes of scale-free inhomogeneous random graphs
Matthias Lienau

The Norros-Reittu model is an inhomogeneous random multigraph that exhibits the so-called scale-free or power-law behaviour, which is observed in real-world complex networks. We study the component sizes of the Norros-Reittu model in the subcritical regime, i.e. in the abscence of a giant component, and show convergence of the point process of the component sizes to a Poisson process. It is planned to derive similar results for other models such as the random connection model.
11.04.22 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 & Zoom Introductory Talk: Boundary layer enriched Hybrid Discontinuous Galerkin Methods for Convection dominated flow
Abdul Qadir Ibrahim

The thesis deals with boundary layer enrichment of convection dominated flow problems using the Hybrid Discontinuous Galerkin Method. It aims to introduce an appropriate and computationally efficient Hybrid Discontinuous Galerkin formulation for the most important model problems of incompressible fluid flow, namely the convection-diffusion equation.The main contribution is the derivation, discussion and analysis of the Enriched Finite elementSpace using non-polynomial spaces (specifically boundary layer functions) for both the Discontinuous Galerkin Methods and the Hybrid Discontinuous Galerkin Method. We evaluate the robustness (i.e linear stability as well as reasonable linear systems) and accuracy of this method using various analytical and realistic problems and compare the results to those obtained using the standard (H)DG method. Numerical results are provided to contrast the Enriched (H)DG methods with standard (H)DG approaches.
31.03.22 16:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Understanding Double Descent in Neural Networks [Bachelorarbeit]
Marvin Steinmeister
29.03.22 10:00 Zoom Random Walks and Tridiagonal Matrices [Masterarbeit]
Luis Weber, TM
23.02.22 10:30 Zoom Untersuchung statistischer Vorhersagealgorithmen für Offshore Wetter-Zeitreihen [Bachelorarbeit]
Sebastian Eberle
22.02.22 15:00 Online Forecasting the shipped volume using a neural network model based on a booking data driven pick-up approach [Masterarbeit]
Gordon Lisch
15.02.22 13:00 online Machine Learning of Gradient-based Optimization Methods [Bachelorarbeit]
Leonard Schröter
14.02.22 15:00 Online Training MobileNetV2 on ImageNet with different activation functions [Projektarbeit]
Abdul Bostan
09.02.22 12:15 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Uniform Turán density
Samuel Mohr

In the early 1980s, Erd\H{o}s and S\'os initiated the study of the classical Tur\'an problem with a uniformity condition: the uniform Tur\'an density of a hypergraph $H$ is the infimum over all $d$ for which any sufficiently large hypergraph with the property that all its linear-size subhyperghraphs have density at least $d$ contains $H$. In particular, they raise the questions of determining the uniform Tur\'an densities of $K_4^{(3)-}$ and $K_4^{(3)}$. The former question was solved only recently in [Israel J. Math. 211 (2016), 349--366] and [J. Eur. Math. Soc. 20 (2018), 1139--1159], while the latter still remains open for almost 40 years.
In addition to $K_4^{(3)-}$, the only $3$-uniform hypergraphs whose uniform Tur\'an density is known are those with zero uniform Tur\'an density classified by Reiher, R\"odl and Schacht~[J. London Math. Soc. 97 (2018), 77--97] and a specific family with uniform Tur\'an density equal to $1/27$.

In this talk, we give an introduction to the concept of uniform Tur\'an densities, present a way to obtain lower bounds using color schemes, and give a glimpse of the proof for determining the uniform Turán density of the tight $3$-uniform cycle $C_\ell^{(3)}$, $\ell\ge 5$.
07.02.22 15:00 Zoom Observability for the (anisotropic) Hermite semigroup from finite volume or decaying sensor sets*
Ivan Veselic, TU Dortmund, Fakultät für Mathematik, Lehrstuhl LSIX

We study the observability and null control problem for
the semigroup generated by the harmonic oscillator
and the partial harmonic oscillator.
We identify sensor sets which ensure null controlabillity
improving and unifying previous results for such problems.
In particular, it is possible to observe the Hermite semigroup
from finite volume sensor sets.
This is joint work with A.Dicke and A. Seelmann.
04.02.22 13:30 Zoom (same as coffee chat) Second Order Information in Neural Network Training
Lina Fesefeldt

Since I am new to our institute, I will start by introducing myself and presenting the results of my master thesis on second order information in
neural network training.

Traditionally, neural networks are trained using gradient-based optimization methods like Adagrad or Adam. Using second order methods might result in faster convergence (e.g. locally quadratic convergence in Newton's method). Furthermore, curvature information can provide some insight into the optimization process and help to characterize the cost function of a neural network.

For large problems, applying Newton's method and Quasi-Newton-methods to the cost function of a neural net is only possible through implicit Hessian-vector-products. For this reason, Krvlov subspace methods are particularly well suited for solving the linear system with the Hessian that appears in Newton's method. Krylov subspace methods use matrix-vector-products instead of operating on the full matrix.

Two data sets are used: The first one is constructed to allow the exact calculation (except for rounding errors) of the Hessian and its eigenvalues. Here, we observe that the largest eigenvalue can be approximated with a small number of steps of a Krylov subspace method and with high accuracy. The second data set is the famous MNIST data set for handwritten digit classification. For MNIST and the given computational resources, we cannot calculate the full Hessian of the cost function. Instead, the Krylov subspace method is used to approximate eigenvalues from implicitly calculated Hessian-vector-products. On both data sets, the largest eigenvalue can be observed to be coupled to the value of the cost function.

An inexact Quasi-Newton-method and the L-BFGS method are used to train a neural network on both data sets.

Furthermore, I will talk about first ideas for my dissertation on nonlinear finite element methods with applications in ship structural design.
28.01.22 13:30 Zoom Discontinuous Galerkin Spectral Element Methods - Space-Time Formulations and Efficient Solvers
Lea Miko Versbach

We are interested in constructing cheap and efficient implicit high order
solvers for compressible turbulent
flow problems. These problems arise for
example in the design of next generation jet engines, air frames, wind tur-
bines or star formation. A suitable high order discretization for these prob-
lems are discontinuous Galerkin spectral element methods (DG-SEM). In
this talk we discuss challenges of solvers for DG-SEM discretizations in space
combined with implicit time-stepping methods.
One option to yield implicit DG-SEM solvers is to apply a space-time
DG-SEM discretization, i.e. discretizing space and time simultaneously with
DG-SEM. We present two approaches for the formulation and implementa-
tion of space-time DG-SEM: Either time is treated as an additional coor-
dinate direction and the Galerkin procedure is applied to the entire prob-
lem. Alternatively, the method of lines is used with DG-SEM in space and
the fully implicit Runge-Kutta method Lobatto IIIC in time. The two ap-
proaches are mathematically equivalent in the sense that they lead to the
same discrete solution. However, in practice they differ in several important
respects, including the terminology used to the describe them, the struc-
ture of the resulting software, and the interaction with nonlinear solvers.
We present challenges and merits of the two approaches and show their im-
pact on numerical tests using implementations based on the Distributed and
Unified Numerics Environment (DUNE).
Another option to construct implicit DG-SEM solvers is the classical
method of lines approach. The spatial directions are discretized with DG-
SEM and any implicit time-stepping method can be applied to the resulting
ODE. This yields large nonlinear systems and a solver has to be chosen
carefully. We suggest to use a preconditioned Jacobian-free Newton-Krylov
method. The challenge here is to construct a preconditioner without con-
structing the Jacobian of the spatial discretization. Our idea is to make use
of a simplified replacement operator for the DG operator and a multigrid
method. We discuss the idea of our suggested preconditioner and present
numerical results to show the potential of this preconditioning technique.

Vortrag (PDF, 73KB)

27.01.22 13:00 Zoom Reinforcement Learning von Parametern für Runge-Kutta Methode [Bachelorarbeit]
Finn Sommer


Meeting-ID: 825 1648 6683
Kenncode: 329040
25.01.22 17:00 Zoom Schleifen und Mehrfachkanten im Konfigurationsmodell [Bachelorarbeit]
Happy Khairunnisa Sariyanto
24.01.22 15:00 zoom A new approach to the hot spots conjecture
Dr. Jonathan Rohleder, Stockholm University, Sweden

It is a conjecture going back to J. Rauch (1974) that the hottest and coldest spots in an insulated homogeneous medium such as an insulated plate of metal should converge to the boundary, for "most" initial heat distributions, as time tends to infinity. This so-called hot spots conjecture can be phrased alternatively as follows: the eigenfunction(s) corresponding to the first non-zero eigenvalue of the Neumann Laplacian on a Euclidean domain should take its maximum and minimum on the boundary only. This has been proven to be false for certain domains with holes, but it was shown to hold for several classes of simply connected or convex planar domains. One of the most recent advances is the proof for all triangles given by Judge and Mondal (Annals of Math. 2020). The conjecture remains open in general for simply connected or at least convex domains. In this talk we provide a new approach to the conjecture. It is based on a non-standard variational principle for the eigenvalues of the Neumann and Dirichlet Laplacians.

Jonathan Rohleder is an associate professor at Stockholm University, Sweden. His work focusses on spectral theory.
17.01.22 15:00 Zoom Solution of the vibrational Schrödinger equation using neural networks [Masterarbeit]
Jannik Eggers
07.01.22 13:30 zoom Behavior of Nonlinear Water Waves in the Presence of Random Wind Forcing
Leo Dostal

Specific solutions of the nonlinear Schrödinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is whether these solutions also exist in the presence of gusty wind. Using the method of multiple scales, a nonlinear Schrödinger equation is obtained for the case of wind-forced weakly nonlinear deep water waves. Thereby, the wind forcing is modeled as a stochastic process. This leads to a stochastic nonlinear Schrödinger equation, which is calculated for different wind regimes. For the case of wind forcing which is either random in time or random in space, it is shown that breather-type solutions such as the Peregrine breather occur even in strong gusty wind conditions.
06.01.22 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Bachelorarbeit: Task-basierte Implementierung von Parareal mittels torcpy
Florentine Meerjanssen, Institut für Mathematik
17.12.21 13:30 Zoom Low-Rank Updates for Schur Complement Preconditioners
Rebekka Beddig

Atmospheric dynamics can be described by the Boussinesq approximation which models bouyancy-driven fluid flows. Its simulation involves the repeated solution of the Navier-Stokes equations. This requires numerical solution methods for the dense Schur complement. In this talk, we will be concerned with Schur complement preconditioners. Furthermore, we will discuss a low-rank update for the Schur complement preconditioners. The update method is based on the error between the preconditioned Schur complement and the identity. It will be illustrated with some numerical results.
10.12.21 13:30 Zoom A Block Householder Based Algorithm for the QR Decomposition of Hierarchical Matrices
Vincent Griem

Hierarchical Matrices are dense but data-sparse matrices that use low-rank factorisations of suitable submatrices to allow for storage with linear-polylogarithmic complexity. Furthermore, efficient approximations of matrix operations like matrix-vector and matrix-matrix multiplication, matrix inversion and LU decomposition are available. There are several approaches for the computation of QR factorisations in the hierarchical matrix format, however, they suffer from numerical drawbacks that limit their use in many applications. In this talk, I will present a new approach based on block Householder transformations that improves upon some of those problems. To prevent unnecessary high ranks in the resulting factors and increase speed as well as accuracy the algorithm meticulously tracks for which intermediate results low-rank factorisations are available.

I will try to keep things as simple as possible and give a short introduction to hierarchical matrices as well. Previous knowledge of them is not necessary to understand the basic ideas and main obstacles of the new algorithm. I will focus on aspects, that I haven't talked about yet in similar talks in the past, mainly on how a cost estimate is possible although the hierarchical structure of the resulting QR decomposition is step-wise created during the algorithm and not defined beforehand.
30.11.21 17:15 Online via Zoom Statistische Analyse von Fehlern in Schachpartien [Bachelorarbeit]
Paul Roth
29.11.21 15:00 Online & E3.074 (talk via zoom) Local pressure-correction for flow problems
Malte Braack, Christian-Albrechts-Universität zu Kiel

We present a novel local pressure correction method for incompressible fluid flows. Pressure correction methods
decouple the velocity and pressure components of the time-dependent Navier-Stokes equations and lead to a sequence of elliptic partial differential equations for both components instead of a saddle point problem. In some situations, the equations
for the velocity components are solved explicitly (with time step restrictions) and thus the elliptic pressure problem remains to be the most expensive step. Here, we employ a multiscale procedure for the solution of the Poisson problem related to pressure. The procedure replaces the global Poisson problem by local Poisson problems on subregions.We propose a new Robin-type boundary condition design for the
local Poisson problems, which contains a coarse approximation of the global Poisson problem. Accordingly, no further communication between subregions is necessary and the method is perfectly adapted for parallel computations. Numerical experiments regarding a known analytical solution and flow around cylinder benchmarks show the effectivity of this new local pressure correction method.
22.11.21 15:00 E3.074 & zoom (talk via zoom) A Hybrid Approach for Data-based Models Using a Least-squares Regression*
Malin Lachmann

An increased use of renewable energy could significantly contribute to decelerate climate change but cannot be realized easily since most renewable energy sources underlie volatile availability. Using of storage devices and scheduling consumers to times when energy is available can increase the amount of renewable energy that is used. For this purpose, adequate models that forecast the energy generation and consumption as well as the behavior of storage devices are essential. We present a computationally efficient modeling approach based on a least-squares problem that is extended by a hybrid model approach based on kmeans clustering and evaluate it on real-world data at the examples of modeling the state of charge of a battery storage and the temperature inside a milk cooling tank. The experiments indicate that the hybrid approach leads to better forecasting results, especially if the devices show a more complicated behavior. Furthermore, we investigate whether the behavior of the models is qualitatively realistic and find that the battery model fulfills this requirement and is thus suitable for the application in a smart energy management system. Even though forecasts for the hybrid milk cooling model have low error values, further steps need to be taken to avoid undesired effects when using this model in such a sophisticated system.
19.11.21 13:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 + Zoom Shearlet-based Approach to Dynamic Computed Tomography
Thorben Abel

I will introduce myself and present the topic of my master thesis.

Computed Tomography (CT) is a standard procedure in clinical imaging. In dynamic CT, several CT scans are made to make a process inside the patient visible. Therefore, the X-ray exposure to the patient is relatively high during such a survey. Thus, it is desirable to lower the X-ray exposure to the patient.

In my thesis I investigated an approach which requires only sparse angular sampling for every scan. In order to be able to reconstruct the image anyway, I used a shearlet system combined with an $\ell^1$-regularization. I compared different shearlet systems and checked for different parameters the impact on the results. I used both simulated data as well as real CT data for the tests.
11.11.21 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Informationen zweiter Ordnung im Training neuronaler Netze [Masterarbeit]
Eva Lina Fesefeldt
08.11.21 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 & Zoom How Stein met Malliavin in Paris and what happened next: non-linear approximation, limit theorems, chaos and the first four moments
Simon Campese

Back in 2009, both Stein's method - a probabilistic technique to derive quantitative limit theorems - and Malliavin calculus - a stochastic version of the calculus of variations - had already established themselves as standard tools in their respective domain, even though both were discovered quite recently in 1972 and 1978, respectively. Then they started an innocent liaison in Paris which quickly developed into a very strong bond (despite numerous affairs), leading to fame and success both in- and outside the probabilistic community. This bond is today known as the Malliavin-Stein approach.

I will highlight some exciting parts of this story, also attributing a fair share of time to yet unwritten chapters (i.e. open problems). Mathematically, this will feature non-linear approximation, limit theorems (central and non-central), stochastic processes, chaos, Markov generators, non-commutative probability theory and the first four moments. Catering to the fact that probabilists are in the minority in our department, things will also be presented from a functional analytic point of view.

The talk will mostly be informal and understandable by non-specialists.
08.11.21 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Physics-informed neural networks for reconstructing flow velocity fields [Bachelorarbeit]
Michel Krispin
05.11.21 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 + Zoom Coupling Methods in Probability Theory
Hermann Thorisson, Department of Mathematics, University of Iceland

Coupling means the joint construction of two or more random variables, processes, or any random objects. The aim of the construction could be to deduce properties of the individual objects, or to gain insight into distributional relations between them, or to simulate a particular object. It has been called The Probabilistic Method since it is not based on methods from other fields of mathematics.

In this talk we shall consider some basic examples such as the Poisson approximation, stochastic domination, Markov chains and Brownian motion, and perfect simulation
01.11.21 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Approximating Evolution Equations with Random Coefficients
Katharina Klioba

Solving evolution equations with random coefficients numerically requires discretizing in space, time and of random parameters. As numerical methods for all three discretisations are well-known, it is natural to ask under which conditions they can be combined. In this talk, we discuss this question with a special emphasis on preservation of strong convergence rates.

A common approach to spatial discretization consists of solving the weak formulation on finite-dimensional approximating spaces. We present a novel quantified version of the Trotter-Kato theorem in this setting, yielding rates of strong convergence under a joint condition on properties of the corresponding form and the approximating spaces.

This is joint work with Christian Seifert.
25.10.21 15:00 Raum 3.074 & Zoom (same link as coffee chat) A Parareal Algorithm for Shallow Water Equations
Judith Angel

The trend towards massively parallel high-performance computers requires the development of parallel algorithms to employ their computational power.
The Parareal algorithm computes the solution of time-dependent problems parallel in time, meaning that approximations to the solution at different times are computed simultaneously. In this talk, we will focus on hyperbolic one-dimensional problems, where a combination of Parareal and a discontinuous Galerkin method will be used. The practical use and challenges of this method will be illustrated by means of a Python implementation for shallow water equations and corresponding numerical results.
21.10.21 15:00 Zoom (see below for link) The quest for the cortical algorithm*
Dr. Helmut Linde, Merck KGaA, Darmstadt, Germany

How will the next generation of Artificial Intelligence (AI) look like? Comparing today's AI algorithms with biological intelligence, one of the most remarkable differences is the ability of the human brain to somehow understand the 'essence' of things: A small child can easily identify any type of object after having seen only a few examples or recognize a song even when played on different instruments or in a different key. In other words: Brains are able to create abstract concepts of real-world entities - and today's algorithms are not.

With today's AI largely being based on neuron models already invented by the mid of last century, I will argue that we should take a new look at the brain to find inspiration for the next generation of machine learning algorithms. Even though there is still only a very limited understanding of how the brain works computationally, I'll explain why there is hope that we can reverse-engineer some of its algorithmic principles and implement them in a computer. I'll explain why a highly interdisciplinary approach is required from neuroscience, computer science, mathematics and physics to make progress in this question.

The talk will be held on Zoom:
Meeting-ID: 868 3621 0324
Kenncode: 521014
21.10.21 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 und Zoom Non-autonomous Desch-Schappacher perturbations
Christian Budde, North-West University, Potchefstroom, South Africa

For many processes in sciences, the coefficients of the partial differential equation describing a dynamical system as well as the boundary conditions of it may vary with time. In such cases one speaks of non-autonomous (or time-varying) evolution equations. From an operator theoretical point of view one considers families of Banach space operators which depend on the time parameter and studies the associated non-autonomous abstract Cauchy problem. We consider time-dependent Desch-Schappacher perturbations of non-autonomous abstract Cauchy problems and apply our result to non-autonomous uniformly strongly elliptic differential operators on Lp -spaces. This is joint work with Christian Seifert (TUHH).
18.10.21 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 & Zoom Methods in Quantum Optimal Transport
Dennis Schmeckpeper

I will introduce myself and present the topic of my master thesis.

A fundamental principle in developing the Theory of Quantum Mechanics is to take
well-studied concepts from the Theory of Classical Mechanics and to define
analogues in the quantum mechanical setting.
One such important tool in Classical Mechanics is the theory of optimal
transport and in particular the Wasserstein distance.

In my thesis I studied the mathematical objects needed to translate
the concepts of the optimal transport problem to the realm of Quantum
Mechanics. In particular,
one wants to establish a relation between density matrices (trace-class operators
of trace one) and
probability measures. This can be done by the so-called
(generalized) Toeplitz operators and the (generalized) Husimi

After I give a brief introduction into both the Optimal Transport and Quantum
Mechanics I will introduce both
the Toeplitz operators and the Husimi transform and discuss some of their
30.09.21 16:00 TUHH, Gebäude D, 1.021 und Zoom Maker-Breaker Spiele über mehrere Runden [Bachelorarbeit TM]
Juri Barkey
30.09.21 15:00 Zoom Varianten von Toucher-Isolator Spielen auf Graphen [Bachelorarbeit TM]
Leon Speidel
30.09.21 14:00 Zoom Über die Erdös-Hajnal-Vermutung [Bachelorarbeit TM]
Luis Fernando Fernandez Salvador
30.09.21 11:00 Online Trainierbare Aktivierungsfunktionen in neuronalen Netzen [Projektarbeit]
Firaz Khokhar
24.09.21 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 and via Zoom Boundedness and Compactness of Toeplitz+Hankel Operators
Raffael Hagger, University of Reading / Christian-Albrechts-Universität zu Kiel

Suppose that $A$ is a bounded linear operator on the Hardy space $H^p$ that satisfies
\[\langle Az^j,z^k \rangle = a_{k-j} \quad (j,k \in \mathbb{N}_0)\]
for some sequence of complex numbers $\{a_n\}_{n \in \mathbb{Z}}$. By the Brown--Halmos theorem, $A$ must be a Toeplitz operator with bounded symbol, that is, $\{a_n\}_{n \in \mathbb{Z}}$ is the Fourier sequence of a bounded function. Likewise, Nehari's theorem shows that if $A$ satisfies $\langle Az^j,z^k \rangle = a_{k+j+1}$ instead, then $A$ is equal to a Hankel operator with bounded symbol. These results were proven in the 50's and 60's and have become classical in the theory of Hardy spaces.

More recently, due to some applications in mathematical physics, there has been a lot of interest in so-called Toeplitz+Hankel operators. Quite simply put, a Toeplitz+Hankel operator is the sum of a Toeplitz operator $T(a)$ and a Hankel operator $H(b)$. Now clearly, if both $T(a)$ and $H(b)$ are bounded, then $A = T(a)+H(b)$ is necessarily bounded as well. It is therefore natural to ask whether the converse is also true or if the ``unboundedness'' of $T(a)$ and $H(b)$ can somehow cancel out. I will elaborate on this question and present a Brown--Halmos type result for Toeplitz+Hankel operators for both the Hardy spaces $H^p$ and the sequence spaces $\ell^p(\mathbb{N}_0)$. A similar characterization for compactness will be obtained as well.

Based on joint work with Torsten Ehrhardt and Jani Virtanen.
21.09.21 11:00 Zoom (Zugangsdaten im Einladungstext) New Combinatorial Proofs for Enumeration Problems and Random Anchored Structures
Alexander Haupt

Hallo liebe Institutsmitarbeiter*innen,

anbei der offizielle Einladungstext zum Promotionsvortrag von Alexander Haupt:


Sehr geehrte Damen und Herren,

im Rahmen seines Promotionsverfahrens wird

Herr M. Sc. Alexander Michael Haupt

einen kombinierten Live-Online-Vortrag mit dem Titel

„New Combinatorial Proofs for Enumeration Problems and Random Anchored Structures“

halten. Der Vortrag findet statt am

Dienstag, dem 21. September 2021 um 11:00 Uhr.

Zu diesem universitätsöffentlichen Vortrag lade ich Sie herzlich ein.

Aufgrund der aktuell geltenden Regelungen können Interessierte nur per Zoom am Vortrag teilnehmen. Bitte benutzen Sie hierzu die folgenden Zugangsdaten:


Meeting-ID: 883 5322 0627
Kenncode: 747604

Mit freundlichen Grüßen
Prof. Dr. Matthias Schulte

(Vorsitzender des Prüfungsausschusses)
21.09.21 10:00 Zoom (URL kommt per Email) Der Quarter-Laplace als schneller Filter zur kantenerhaltenden Glättung in Bildern
Leif Jensen, [Bachelorarbeit TM]
19.08.21 14:00 Zoom Preferential Placement - ein neuer Ansatz für zufällige Graphen (Bachelorarbeit)
Nils Koch
16.08.21 15:00 Zoom Anwendungsbezogene automatisierte Optimierung von Parametern einer digitalen Industriekamera [Masterarbeit]
Jonas Eckhoff
16.08.21 14:00 Zoom Bilaterale Filter [Masterarbeit]
Thanh Hung Le
26.07.21 13:00 Zoom Gesichterkennung und Tensorenfaktorisierung (Bachelorarbeit)
Moritz Pirk
23.07.21 11:00 Zoom & Am Schwarzenberg-Campus 3 (E), Raum 3.074 Modifizierte Block-Gram-Schmidt Orthogonalisierung (Bachelorarbeit)
Finn Heck
20.07.21 10:00 Zoom Numerical Methods for the Rotating Shallow Water Equations with Bathymetry (Bachelor Arbeit)
Joshua Lampert
12.07.21 15:00 zoom L^{p}-extrapolation of non-local operators
Patrick Tolksdorf, Institut für Mathematik an der Johannes Gutenberg-Universität Mainz

In this talk, we discuss non-local operators like elliptic integrodifferential operators of fractional type
Au := p.v. \int_{\mathbb{R}^d} \frac{u(x) - u(y)}{|x-y|^{d+2\alpha}}dy \quad \quad (1)
or the Stokes operator with bounded measurable coefficients $\mu$, formally given by
Au := -div( \mu \nabla u ) + \nabla \phi, \quad div(u) = 0 \; in \; \mathbb{R}^d. \quad \quad (2)
These operators satisfy $L^{2}$-resolvent estimates of the form
|| \lambda ( \lambda + A )^{-1} f ||_{L^2} \leq C || f ||_{L^2} \quad (f \in L^2(\mathbb{R^d}))
for $\lambda$ in some complex sector $\left\{z \in \mathbb{C} \smallsetminus {0} : | arg(z) | < \theta \right\}$. We describe how analogues of such a resolvent estimate can be established in $L^{p}$ by virtue of certain non-local Caccioppoli inequalities. Such estimates build the foundation for many important functional analytic properties of these operators like maximal $L^{q}$-regularity.

More precisely, we establish resolvent estimates in $L^{p}$ for $p$ satisfying
\left|\frac{1}{p} - \frac{1}{2} \right| < \frac{\alpha}{d}
in the case (1) and
\left|\frac{1}{p} - \frac{1}{2}\right| < \frac{1}{d} \quad \quad (3)
in the case (2). This resembles a well-known situation for elliptic systems in divergence form with $L^{\infty}$-coefficients. Here, important estimates like Gaussian upper bounds for the semigroup cease to exist and the $L^{p}$-extrapolation has be concluded by other means. In particular, for elliptic systems one can establish resolvent bounds for numbers p that satisfy (3) and if $d \geq 3$, Davies constructed examples which show that corresponding resolvent bounds do not hold for numbers $1 < p < \infty$ that satisfy
\left|\frac{1}{p} - \frac{1}{2} \right| > \frac{1}{d}.
These elliptic results give an indication that the result for the Stokes operator with $L^{\infty}$-coefficients is optimal as well.
05.07.21 15:00 Zoom (same as Coffee Chat) Integral input-to-state stability of unbounded bilinear control systems
René Hosfeld

We study integral input-to-state stability of bilinear systems with
unbounded control operators and derive natural sufficient conditions. The
results are applied to a bilinearly controlled Fokker-Planck equation.
28.06.21 15:00 Zoom Some peculiar (and not very well known) aspects of Gauss quadrature rules*
Thibaut Lunet, Université de Genève

Gauss quadrature rules are nowadays not only a powerful tool to compute integrals in many scientific applications, but also a numerical method that most people in the scientific community at least heard of at some point in there life.
Even if they are not the only tool to compute integral numerically, they provide the possibility to integrate any function multiplied by a given weight function (or measure), by estimating the integral of the product using a weighted sum of the function evaluations at given values (nodes).
Classical measures are well known (e.g Legendre, Chebyshev, Laguerre, Hermite), and their associated quadrature rules are well studied and documented in the literature.
While some measures allow to estimate integrals over infinite intervals (e.g Laguerre or Hermite), others also allow to integrate a function with singularities (e.g Chebyshev of the first, third and fourth kind).
However, the use of non-classical measures for specific applications can also be considered, and even this is not often used in the community, many algorithms exist to compute the nodes and weights of those quadrature rules.
In this talk we will give a quick overview of those algorithms, their efficiency, numerical stability, and some current challenge that still need to be solved.
Furthermore, under some conditions, all Gauss quadrature rules share some common properties, in particular when considering a large number of nodes.
We will give a quick overview of those common asymptotic properties, and show how they can be generalized to other applications (e.g barycentric Lagrange interpolation).
While some of those properties have been proven in particular cases, we will present some situations where they have not been proved theoretically yet, or still need to be verified.
21.06.21 15:00 Zoom Can Spectral Deferred Correction methods improve Numerical Weather Prediction?
Joscha Fregin

Atmospheric motion covers a broad range of time- and spatial scales. Low and high pressure systems can influence us for days or even weeks and they extend up to hundreds of kilometers. In contrast, sound waves pass by in seconds with wavelengths of centimeters to meters. Implicit-explicit (IMEX) time stepping methods can help to avoid drastic limitations on the time step induced by the variety of scales without requiring computationally expensive fully nonlinear implicit solves. I will introduce Spectral Deferred Correction (SDC) methods as a strong competitor to currently used schemes. They allow an easy construction of high order schemes in contrast to e.g IMEX Runge-Kutta methods which require a growing number of coupling conditions with increasing order.
14.06.21 15:00 Zoom (Same as Coffee Chat) (A)periodic Schrödinger Operators
Riko Ukena

Discrete Schrödinger operators are used to describe systems in theoretical solid-state physics.
In this talk we consider discrete Schödinger operators with both periodic and aperiodic potentials. We analyse spectral properties of these operators and find conditions for the applicability of the so-called "finite section method" that allows us to approximate solutions of systems involving discrete Schrödinger operators.
11.06.21 15:00 Zoom (same as Coffee Chat) On convergence rates of form-induced semigroup approximation
Katharina Klioba

Solving evolution equations numerically requires discretizing both in time and in space. However, these two problems can be treated seperately. A common approach to spatial discretization relies on solving the weak formulation on finite-dimensional subspaces. On a semigroup level, this corresponds to approximating a semigroup by semigroups on finite-dimensional subspaces. For practical applications, quantifying the convergence speed is essential. This can be achieved by the quantified version of the Trotter-Kato theorem presented in this talk. Rates of strong convergence are obtained on dense subspaces under a joint condition on properties of both the form and the approximating spaces. An outlook to evolution equations with random coefficients and their polynomial chaos approximation will be given as well as a generalization allowing to treat the Dirichlet-to-Neumann operator.
10.06.21 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Algorithmische Ansätze für kürzeste Wege mit wenigen Farbwechseln im Hyperwürfel (Bachelorarbeit)
Tim Meyer

Zoom Link folgt.
31.05.21 15:00 Zoom(Same as Coffee Chat) Preconditioning of saddle point problems
Jonas Grams

In many problems, like the discretized Stokes or Navier-Stokes equation, linear systems of saddle point type arise. Since the condition number for such problems can grow unbounded, as the number of unknowns grows, good preconditioners are key for solving such problems fast.

In this talk I will introduce some general preconditioning techniques for saddle point problems, and how to apply them to the discretized Stokes and Navier-Stokes equation
26.05.21 15:00 Zoom Coupling Conditions for the BGK Equation and Associated Macroscopic Equations on Networks.
Ikrom Akramov

In this talk, we examine linearized kinetic BGK equation in 1D velocity dimension. It is closely related to the Maxwell-Boltzmann equation for gas dynamics. The equation that we are interested is obtained by linearization of the equation around Maxwellian. We discuss the kinetic and macroscopic equations and the boundary and coupling conditions for this equation.

Furthermore, we will drive coupling conditions for macroscopic equations on different network and compare the solutions with Maxwell and half-moment approximations. Moreover, the macroscopic equations on the network with the different Knudsen numbers are numerically compared with each other.
17.05.21 15:00 Zoom: Image reconstruction from scattered Radon data by weighted kernel functions
Kristof Albrecht

Positive definite kernel functions are powerful tools, which can be used to solve a variety of mathematical problems. One possible application of kernel-based methods is the reconstruction of images from scattered Radon data, which is described in [1]. More precisely, the authors introduced weighted kernel functions to solve the reconstruction problem via generalized interpolation. Although the reconstruction method was quite competitive in comparison to standard Fourier-based methods, a detailed discussion on well-posedness and stability was mainly missing.

In this talk, I will explain the basics of kernel-based generalized interpolation and discuss the well-posedness of the proposed reconstruction method. Like most kernel-based methods, the reconstruction method also suffers from bad condition numbers. I will show how to apply well-known stabilization methods from standard Lagrangian interpolation to the generalized case to improve the stability significantly.

[1] S. De Marchi, A. Iske, G. Santin. Image reconstruction from scattered Radon data by weighted kernel functions. Calcolo 55, 2018.
05.05.21 15:00 BBB Training of YOLO with altered activation function [Bachelorarbeitsvortrag]
Minh An Pham
03.05.21 15:00 Zoom Hypothesis tests in regression models with long-range dependence
Matthias Lienau, Institute of Mathematics, Chair of Stochastics

In my inaugural talk I would like to introduce myself and present the topic of my master thesis. To this end, I will first provide a brief introduction to empirical processes and long-range dependence. Afterwards, we consider the problem of testing the equality of two non-parametric regression functions. Finally, we provide a goodness of fit test for the error distribution.
26.04.21 15:00 Zoom Inertial Particles in a viscous fluid: The Maxey-Riley equation.
Julio Urizarna

The characterisation of the dynamics of a small inertial particle in a viscous fluid is a problem that dates to Stokes[1], back in 1851. Since his first attempt, many have tried and several formulas have been obtained for different types of flows, as well
as more general cases; however, the scientific community did not agree in a general formula until 1983, when M. Maxey and J. Riley[2] obtained a formula from first principles. This formula includes an integro-differential term, called the Basset History term, which
requires information for the whole history of the particle dynamics and creates difficulties in the numerical implementation due to fast increasing storage requeriments.
In the last decade, the Maxey-Riley formula has drawn the interest of many mathematicians and so, local and global existence and uniqueness of mild solutions have been proved ([3] & [4]). Nevertheless, a method to bypass the history term and obtain the trajectory
of the particle remained unknown until the publication of an accurate solution method by S.Ganga Prasath et al (2019) [5].
In this presentation I will analyse the Maxey Riley equation and will identify the core ideas within S. Ganga Prasath's method to solve the Maxey Riley equation as well as its implementation for certain fluid flows.

[1] Stokes, G. G. (1851). On the effect of the internal friction of fluids on the motion of pendulums.
[2] Maxey, M. R., & Riley, J. J. (1983). Equation of motion for a small rigid sphere in a nonuniform flow. The Physics of Fluids, 26(4), 883-889.
[3] Farazmand, M., & Haller, G. (2015). The Maxey–Riley equation: Existence, uniqueness and regularity of solutions. Nonlinear Analysis: Real World Applications, 22, 98-106.
[4] Langlois, G. P., Farazmand, M., & Haller, G. (2015). Asymptotic dynamics of inertial particles with memory. Journal of nonlinear science, 25(6), 1225-1255.
[5] Prasath, S. G., Vasan, V., & Govindarajan, R. (2019). Accurate solution method for the Maxey–Riley equation, and the effects of Basset history. Journal of Fluid Mechanics, 868, 428-460.
12.04.21 15:00 Zoom Malliavin calculus and Malliavin-Stein method
Vanessa Trapp

In this talk, I would like to introduce myself and the topic of my master thesis "Malliavin calculus and Malliavin-Stein method".
As indicated by its name, this talk provides a basic overview of the Malliavin calculus and its operators in the case where the underlying process is an isonormal Gaussian process. After this introduction, it is shown how the Malliavin calculus can be combined with Stein's method for the purpose of one-dimensional normal approximation and, particularly, for the derivation of generalized central limit theorems.
30.03.21 13:00 BBB Banachs Hyperebenen-Problem (Bachelorarbeitsvortrag)
Max Levermann
16.03.21 16:00 Online Einfluss von Batch-Normalisierung für verschiedene Aktivierungsfunktionen [Bachelorarbeitsvortrag]
Moritz Seefeldt
16.03.21 15:00 Online Relation between Activation Function and Weight Initialization in Neural Networks [Bachelorarbeitsvortrag]
Erich Doclaf
15.03.21 15:00 Zoom meeting A semi-implicit meshfree/particle scheme for the shallow water equations*
Dr. Adeleke Bankole, Institute of Mathematics, Hamburg University

This presentation introduces the semi-implicit Smoothed Particle Hydrodynamics (SPH)
scheme [1] for the shallow water equations following the semi-implicit finite volume and finite
difference approach of Casulli [2]. In standard explicit numerical methods, there is often a severe
limitation on the time step due to the stability restriction imposed by the CFL condition. To this
effect, a semi-implicit SPH scheme is derived, which leads to an unconditionally stable method.
The discrete momentum equation is substituted into the discrete continuity equation to obtain
a symmetric positive definite linear system for the free surface elevation. The resulting system
can be easily solved by a matrix-free conjugate gradient method. Once the new free surface
location is known, the velocity at the new time level can be directly computed and the particle
positions can subsequently be updated. We further discuss a nonlinear algorithm for treating
wetting/drying problems. We derive a mildly nonlinear system for the discrete free surface
elevation from the shallow water equations by taking into consideration a correct mass balance
in wet regions and in transition regions, i.e. the regions from wet particles to dry particles
and those from dry particles to wet particles. The scheme is validated on a two dimensional
inviscid hydrostatic free surface flows for the two dimensional shallow water equations and
wetting/drying test problem.

[1] A.O. Bankole, A. Iske, T. Rung, M. Dumbser, A meshfree semi-implicit Smoothed Particle
Hydrodynamics method for free surface flow. Meshfree Methods for Partial Differential
Equations VIII, M. Griebel and M.A. Schweitzer (eds.), Springer LNCSE, Vol. 115, pp.
35-52 (2017).
[2] V. Casulli, Semi-Implicit Finite Difference Methods for the Two-Dimensional Shallow
Water Equations. Jour. of Comp. Phys., Vol 86. pp. 56-74 (1990).
25.02.21 09:00 BBB Mündliche Prüfung zur Dissertation: Fractional Powers of Linear Operators in Locally Convex Vector Spaces
Jan Meichsner
24.02.21 14:00 Online Neuronale Netzwerke mit (approximativ) orthonormalen Gewichtsmatrizen [Bachelorarbeitsvortrag]
Marco Zabel
18.02.21 13:00 Zoom Habilitationskolloquium: „Polynomial Chaos Expansion“
Christian Seifert

Meeting-ID: 820 3979 6993
Passwort: 694649
15.02.21 15:00 Zoom, Link per Mail Verified solution of ODEs by Taylor models implemented in MATLAB/INTLAB
Dr Florian Bünger, Institute for Reliable Computing

Solving differential equations rigorously is a main and vigorous topic in the
field of verified computation. Here, solving rigorously means that a computer
program supplies an approximate solution along with error bounds that respect
all numerical as well as all rounding errors that occurred during the computation.
An exact solution is proved to be enclosed within these rigorous bounds.
In this context so-called Taylor models have been used successfully for solving
ordinary differential equations (ODEs) rigorously. Implementations are COSY INFINITY [1], FLOW [2], ODEIntegretor [3], and RIOT [4]. Here, COSY INFINITY
developed by Berz and Makino and their group is the most advanced
implementation. Recently, we implemented the Taylor model approach in MATLAB/

We give a short introduction to Taylor models, their rigorous arithmetic,
and the Taylor model method for enclosing solutions of ordinary differential
equations in a verified manner. We only treat initial value problems
$y_0 = f(t,y)$, $y(t_0) = y_0$
where the initial value $y_0$ may be an interval vector. For specific ODEs we demonstrate
how to use and call our verified ODE solver. This is designed to be very
similar to calling MATLAB's non-verified ODE solvers like ode45. Finally, results
and run times are compared to those of COSY INFINITY, RIOT and Lohner's
classical AWA.

[1] M. Berz, K. Makino, COSY INFINITY: www.bt.pa.msu.edu/index_cosy.htm
[2] X. Chen, Reachability analysis of non-linear hybrid systems using Taylor models,
Dissertation RWTH Aachen, 2015. FLOW: https://flowstar.org/dowloads/
[3] T. Dzetkulic, Rigorous integration of non-linear ordinary differential equations in
Chebyshev basis, Numer. Algor. 69, 183-205, 2015.
ODEintegrator: https://sourceforge.net/projects/odeintegrator
[4] I. Eble, Über Taylor-Modelle, Dissertation at Karlsruhe Inst. of Technology, 2007.
RIOT: www.math.kit.edu/ianm1/~ingo.eble/de
[5] S.M. Rump, INTLAB - INTerval LABoratory, in Developments in Reliable Computing
(ed. by Tibor Csendes), Kluwer Academic Publishers, 77-104, 1999.
INTLAB: http://www.ti3.tu-harburg.de/intlab/

Vortrag (PDF, 100KB)

11.02.21 15:00 Online Domänentransfer von Gesichtsbildern aus Passdokumenten mit Generative Adversarial Networks [Projektarbeitsvortrag]
Dominic Hinz
25.01.21 15:00 Zoom The Korteweg-de Vries equation on graphs
Christian Seifert
12.01.21 09:00 Online (Zoom). Zugangsdaten in der Einladung. "New Algorithms for Block-Structured Integer Programming: Theory and Practice" (Bachelorarbeit)
Vanessa Oetjen, E-10 / E-11 (Prof. Mnich)


Meeting ID: 875 3553 8628
Passcode: 750232
11.01.21 15:00 Zoom Stabilization of Control Systems in Banach Spaces
Dennis Gallaun
04.01.21 15:00 Zoom Something with ... wait for it ... networks and robots*
Sonja Otten

Production processes are usually investigated using models and methods from queueing theory (queue = line where people wait for goods or services). Control of warehouses and their optimization rely on models and methods from inventory theory. Both theories are fields of Operations Research, but they comprise quite different methodologies and techniques. In classical Operations Research these theories are considered as disjoint research areas. Today's emergence of complex supply chains (=production-inventory networks) calls for integrated production-inventory models, which are focus of my research. We have developed Markov process models for several production-inventory systems and derived the steady state distribution of the global system. For most of the production-inventory systems the obtained steady state is of product form. This enables us to analyse the long term average costs with the aim to find the optimal inventory size.
In my talk, I focus on a basic production-inventory model and present the essentials of the other models. Furthermore, I show the connection to the industrial project “Robotic Mobile fulfillment system”.

*title by Karsten Kruse
07.12.20 15:00 Zoom Vector-valued holomorphic functions in several variables
Karsten Kruse
30.11.20 15:00 Zoom r-cross t-intersecting families via necessary intersection points
Yannick Mogge
23.11.20 15:00 Zoom About myself, my master thesis and current/future research
Judith Angel

An overview about the master thesis will be given, treating numerical methods for solving a PDE-constrained optimization problem. Afterwards, an outlook on advanced numerical methods for PDEs and modelling of tsunamis will be presented.
16.11.20 16:15 Online (Zoom Link folgt) "Geodesics with few colour changes in the hypercube" (Bachelorarbeit)
Branko Schaub
16.11.20 15:00 Zoom From Stein's Method to Stochastic Geometry
Matthias Schulte

Stein's method is a powerful technique to establish convergence in distribution of a sequence of random variables to a standard Gaussian random variable. After an introduction to this approach, its application to several problems from stochastic geometry is discussed.
13.10.20 16:00 Zoom Overview on Axon and Myelin Segmentation of Microscopy Data Using Convolutional Neural Networks [Forschungsprojektarbeit]
Ruhullah Najafi
23.09.20 10:00 Zoom Verbesserung eines Segmentieralgorithmus für flache Fingerabdrücke auf Basis einer vergleichenden Analyse [Bachelorarbeit]
Thomas Plotz
11.09.20 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 / Online-Stream Rationale Aktivierungsfunktionen in neuronalen Netzen (Bachelorarbeitsvortrag)
Fabian Bahr
10.09.20 15:30 (Zoom Link wird am 09.09. per E-Mail angekündigt) Bildsegmentierung durch Deep Learning mit U-Net und dem Mumford-Shah-Funktional [Bachelorarbeit]
Jannik Jacobsen
26.08.20 16:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074/75 Fast Strategies for Waiter-Client and Client-Waiter Games [Bachelorarbeit]
Sophie Externbrink, E-10
24.08.20 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 / Online-Stream Neuronale Netze basierend auf Radiale-Basis-Funktionen (Bachelorarbeitsvortrag)
Marcel Franz
10.08.20 15:30 Zoom On the Axioms of Quantum Mechanics
Dennis Schmeckpeper

This will be an introductory talk on how the fundamental assumptions of quantum mechanics are modeled and how this relies on the spectral theory of unbounded self-adjoint operators on separable Hilbert spaces.
03.08.20 15:30 Zoom $\mathcal{H}_2 \otimes \mathcal{L}_\infty$-Optimal Model Order Reduction
Rebekka Beddig

I will introduce myself and present the topic of my master thesis.

In my thesis, I derived a method for model order reduction of parametric linear time-invariant systems. With this method we can compute parametric reduced-order models that are optimal with respect to the $\mathcal{H}_2 \otimes \mathcal{L}_\infty$-error. The method combines interpolatory methods with numerical optimization. We furthermore discuss the computation of the $\mathcal{H}_2 \otimes \mathcal{L}_\infty$-error and have a look at some numerical results.
27.07.20 15:00 Zoom Time-parallel flow estimation
Sebastian Götschel

Deformable image registration is a key technology in medical imaging; there the goal is to compute a meaningful spatial correspondence between two or more images of the same scene. One approach is to use an optimal control formulation to compute a stationary velocity field that parameterize the deformation map. The same methods can be used to estimate the motion of contrast agents from 3d ultrasound images.

This is work-in-progress; in the talk I’ll introduce the application problem and discuss computational techniques for its solution, with a focus on using parallelization in time to reduce the time-to-solution. It should be accessible for a broad audience.
23.07.20 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 PDE-Constrained Optimization of Parabolic Problems [Masterarbeit]
Judith Angel
21.07.20 16:00 Zoom Vortrag (Zoom Link wird am 21.07. per E-Mail angekündigt) Geometric Deep Learning in Medical Image Segmentation and Comparisons with UNET (Masterarbeit)
Björn Przybyla
20.07.20 15:30 Zoom Noncommutative geometry, K-theory and other interesting stuff
Julian Großmann

An overview talk about interesting topics in mathematical physics I used over the last years. It should be accessible for a broader audience.
13.07.20 15:30 Zoom Evolution Equations
Christian Seifert

This will be an overview talk on Evolution Equations (and a bit on Evolutionary Equations).
06.07.20 15:30 Zoom Uniqueness of solutions to the Caffarelli-Silvestre Problem
Jan Meichsner

We consider the Caffarelli-Silvestre problem in a Banach space $X$ which is finding a solution $u$ to the problem
u''(t) + \frac{1-2\alpha}{t} u'(t) = Au(t), \quad u(0)=x
where $\alpha \in (0,1)$ is a given parameter and $A \in \mathcal{S}_{\omega}$ is a sectorial operator. Goal of the presentation will be to sketch of a proof that a solution got to be unique (we will not deal with existence but this is a much easier anyway).
The proof is simpler and independent of what can be found in

J. Meichsner and C. Seifert. On the Harmonic Extension Aproach to Fractional Powers in Banach Spaces. arxiv preprint https://arxiv.org/abs/1905.06779
29.06.20 15:00 Zoom A new approach to the QR decomposition of hierarchical matrices
Vincent Griem

All existing QR decompositions for hierarchical matrices suffer from numerical drawbacks that limit their use in many applications. In this talk, I will present a new method based on the recursive WY-based QR decomposition by Elmroth and Gustavson. It is an extension of an already existing method for a subclass of hierarchical methods developed by Kressner and Susnjara.

I will try to keep things as simple as possible and give a short introduction to hierarchical matrices as well. Previous knowledge of hierarchical matrices is not necessary to understand the basic ideas and main obstacles of the new algorithm. Although this talk is similar to my last one in November I will try to focus on some aspects we have only touched upon and present some new results as well.
22.06.20 15:30 Zoom Analysis of the discretization error in the RBF-FD method
Willi Leinen

Partial differential equations can be solved numerically by the radial basis function-generated finite difference (RBF-FD) method, which can be viewed as a generalization of the finite difference method to unstructured point sets.
A so-called stencil is computed for each interior node and radial basis functions are used for the computation of the stencil weights. The discretization error depends on the type of the point set (i.e. on the number of interior and boundary nodes and their distribution), the stencil size, the RBF type and the shape parameter of the RBF.
In this talk, I present an introduction of the RBF-FD method and a numerical analysis of the influence of the various parameters on the discretization error. I focus on Poisson's equation and on the convection-diffusion equation in three-dimensions.
15.06.20 15:30 Zoom Approximate null-controllability of heat-like equations in $L_1(\mathbb{R}^d)$
Dennis Gallaun
25.05.20 15:30 Zoom On periodic Finite Sections
Riko Ukena, E-10

I will introduce myself and talk about my master thesis.

The topic of my thesis was "On periodic finite sections", which are an approximation method based on the regular finite section method. The methods are used to approximate (the inverses of) infite matrices by finite matrices.
18.05.20 15:30 Zoom Many-Body Localization: A Spectral Theoretic Investigation of Spin Chains
Katharina Klioba, E-10

Since most of you couldn't attend my master thesis defense due to the university closure, I would like to use this talk to present you some results of my master thesis "Many-body localization: A spectral theoretic investigation of spin chains". Spin chains are a class of quantum-mechanical models well-suited to study many-body localization (MBL) phenomena due to their one-dimensional structure. After a brief introduction to one-particle (Anderson) localization and spectral properties of infinite-dimensional operators, we will see possible definitions and manifestations of MBL. The proofs of MBL for two specific spin chains will be sketched, illustrating how one-particle and many-body techniques can be combined. Furthermore, I would like to use this talk to properly present myself in case you wondered who that person in the guest office was.
11.05.20 15:30 Zoom $\mathcal{H}$-Matrix Approximation of Finite Element Problems
Jonas Grams

Since I am new to the institute, I want to use this talk to introduce myself to you, and talk a little bit about my master thesis.

For the thesis I studied the approximability of the inverse of finite element matrices, i.e. matrices which are gained from the discretization of elliptic PDE's with the finite element method, by hierarchical matrices. So, after introducing myself, i will give an overview about the construction of the approximation and the error analysis.
06.05.20 10:00 Online Development of Solid-State LIDAR Configuration Tool and Optimization of SPAD Detection Performance [Master thesis]
Puja Dutta, student of Microelectronics and Microsystems Engineering

supervision by Prof. Ernst Brinkmeyer (retired 2013, hence not hosted by him)

no maths topic
05.05.20 10:00 Videokonferenz Numerical Treatment of Hyperbolic Equations [Bachelorarbeit]
Triani Nur Zahra
04.05.20 15:30 Online On the observability of non-autonomous systems
Fabian Gabel

Vortrag (PDF, 219KB)

27.04.20 15:30 Online Lattice Index of Coupled Cell Networks
Haibo Ruan

For a regular coupled cell network, we define an index of integer tuples for its associated lattice of synchrony subspaces, and use this index for identifying equivalent synchrony subspaces to be merged to each other. Based on this equivalence, the initial lattice of synchrony subspaces can be reduced to a lattice of synchrony subspaces which corresponds to a simple eigenvalue case discussed in previous work. The result is a reduced lattice of synchrony subspaces, which affords a well-defined non-negative integer index that can be used for bifurcation analysis in regular coupled cell networks.
22.04.20 11:00 per Videokonferenz Error analysis of radial basis functions finite difference discretization (Bachelorarbeit)
Paul Jürß
20.04.20 15:30 Online SISDC for NWP, geometric constraints in Rossby wave interactions and a little about me
Joscha Fregin

After only two weeks of being able to get to know you in person, I will use this talk to introduce myself and talk about present and past work. My presentation will be divided into three parts. After shortly introducing myself (1), I'll cover the following topics related to my masters thesis (2) and my PhD research (3).

2. Amplitude dynamics of resonant Rossby wave triads in Nambu form:
Non-linear interactions play a fundamental role in the redistribution of energy amongst Rossby waves. For weakly interacting waves, geometric constraints govern the dynamics of forced and unforced resonant Rossby wave triads. These constraints allow to cast the dynamical equations in Nambu formulation.

3. How Semi-Implicit Spectral Deferred Correction (SISDC) can improve Numerical Weather Prediction (NWP) models and climate projections:
The multitude of time scales associated with atmospheric waves (e.g. Rossby-, gravity-, sound-waves) poses difficulties in modeling the full governing equations. The CFL condition usually requires the adaption of the time step to the fastest waves to prevent instabilities. However, the fastest waves (i.e. sound waves) in general transport a negligible amount of energy and therefore have minimal impact on the dynamics. By treating the fastest waves implicitly, instabilities can be prevented despite a CFL-number > 1. Using SISDC to integrate the linearized Boussinesq equations has proven to be valuable alternative to implicit-explicit Runge-Kutta and diagonally implicit Runge-Kutta methods. Applying SISDC to the full compressible governing equations may improve cost and accuracy of state of the art NWP models.
16.04.20 11:00 Video-Online Multiscale Hierarchical Convolutional Neural Networks - Implementations and Applications (Projekarbeit)
Ernst Nathanael Winter
07.04.20 10:00 per Videokonferenz (Zugangsdaten kommen per Email) Graphen- und spektraltheoretische Interpretation des Bilateralen Filters [Bachelorarbeit TM]
Lars Stietz
06.04.20 15:30 Zoom Introduction to different functional calculi with applications
Jan Meichsner, TUHH, Institut für Mathematik, Lehrstuhl für angewandte Analysis, TUHH, Institut für Mathematik (E-10), Am Schwarzenberg-Campus 3, Gebäude E, 21073 Hamburg

The presentations aims to give a rather short non-technical introduction in the general concept of a functional calculus including several examples and applications.

The presentation will (mostlikely) make use of the tool 'Zoom'. The audience will not have to do much but simply follow a link the speaker provides everybody with who asks in advance (jan.meichsner@tuhh.de). Members of the institute will get the link via the common email list.
24.03.20 14:00 per Videokonferenz Verbesserung der Ansteuerung von Time-of-Flight Tiefenbildsensoren [Bachelorarbeit TM, Kooperation mit der Basler AG]
Johannes Bostelmann
24.03.20 11:00 per Videokonferenz Über periodisierte "finite sections" [Masterarbeit TM]
Riko Ukena
18.03.20 13:45 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Many-Body Localization: A Spectral Theoretic Investigation of Spin Chains [Masterarbeit]
Katharina Klioba
28.02.20 10:00 TUHH, M 0.571 Entwicklung, Modellierung und Simulation eines neuartigen, kostengunstigen und zuverlässigen Wellenenergiewandlers [Bachelorarbeit TM, gemeinsam mit Institut M-13]
Leonard Paul Schulz
27.02.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 A short presentation about myself
Don Julio Urizarna Carasa

Quite often, we wonder about the people around us but we are too shy to actually ask. On Thursday 27.02.2020, the Institute für Mathematik has organised a presentation about the one that is – up to the current date and not for very long – its latest “outstanding” acquisition.

During the presentation, you will finally be able to respond to the following questions:

- Why is he so fascinating?

- What was his last piece of work?

- What has he done during his first month?

These and any other question will be discussed during the meeting and who knows, maybe one day, in your closest cinema.
20.02.20 13:15 Raum H - SBC5 - H0.03 Novel Space-Time Finite Element Discretizations*
Prof. Dr. Marek Behr, Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University

Moving-boundary flow simulations are an important design and analysis tool in many areas, including civil and biomedical engineering, as well as production engineering. Interface-capturing offers flexibility for complex free-surface motion, while interface-tracking is very attractive due to its mass conservation properties at low resolution. We focus on these alternatives in the context of flow simulations based on stabilized finite element discretizations of Navier-Stokes equations, including space-time formulations that allow extra flexibility concerning grid design at the interface.

Space-time approaches offer some not-yet-fully-exploited advantages; among them, the potential to allow some degree of unstructured space-time meshing. A method for generating simplex space-time meshes has been developed, allowing arbitrary temporal refinement in selected portions of space-time slabs. The method increases the flexibility of space-time discretizations, even in the absence of dedicated space-time mesh generation tools. The resulting tetrahedral and pentatope meshes are being used in the context of cavity filling flow simulations, such as those necessary to design injection molding processes.
19.02.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Comparison of Unsupervised Dimensionality Reduction Techniques (Bachelorarbeit)
Lior Polak
11.02.20 14:00 Am Schwarzenberg-Campus 5 (H), Raum H0.02 Solving nonlinear non-autonomous equations
Hendrik Vogt, Fachbereich 3 - Mathematik, Universität Bremen, Postfach 330 440, Bibliothekstraße 5, 28359 Bremen

We show the existence of solutions of nonlinear non-autonomous Cauchy problems
\partial_t u(t,x) - \nabla_x \cdot (a(t,x)\nabla_xu(t,x))= f(t,x,u(t,x),\nabla u(t,x)),
\qquad u(0,\cdot)=u_0
for a bounded open set $\Omega\subseteq \mathbb R^n$.
The coefficient matrix $a$ is supposed to be symmetric, uniformly elliptic,
Lipschitz continuous w.r.t.\ $t\in(0,\tau)$ and measurable w.r.t.\ $x\in\Omega$;
the nonlinearity $f$ is required to satisfy a linear growth condition.
We show that, given $u_0\in H_0^1(\Omega)$, there exists $u\in L_2(0,\tau;H_0^1(\Omega))
\cap H^1(0,\tau;L_2(\Omega))$ solving the problem mentioned above.

The proof relies on Schaefer's fixed point theorem. In the
course of the proof one uses maximal regularity properties of solutions of
inhomogeneous linear problems and compact embeddings of vector-valued Sobolev spaces.

The result partly generalises [ArCh10].

The talk is based on joint work with Wolfgang Arendt and Jürgen Voigt.

[ArCh10] W. Arendt, R. Chill: Global existence for quasilinear
diffusion equations in isotropic nondivergence form. Ann. Sc. Norm. Super. Pisa
Cl. Sci. (5) IX, 523-539 (2010).
10.02.20 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Das Verhalten von IDR-Verfahren unter Einfluss von Rundungsfehlern (Bachelorarbeit)
Henning Schwarz
30.01.20 14:00 Raum H - SBC5 - H0.04 Fractional derivatives and integrals as application of different functional calculi
Jan Meichsner, Institut für Mathematik (E-10), Lehrstuhl Angewandte Analysis

The question of possible generalisations of the operation of differentiation towards fractional powers can be traced back to a letter from L'Hospital to Leibniz in 1695 ([1]).
Since this time, mathematicians developed plenty of different approaches to fractional differentiation and integration generalising different aspects of the known theory.
The possibly most prominent examples are the fractional derivatives (and integrals) of Riemann-Liouville and Weyl ([4]).
Both can also be understood as instances of the sectorial functional calculus of sectorial operators as it was introduced in [2] and further promoted in [3].
Nonetheless, a direct use of the abstract techniques from operator theory seems to be rare in applications.
Therefore, the talk aims for introducing the audience in the basic principles of functional calculus and how to use it to recover the above mentioned instances of fractional derivatives.


[1] B. Ross. The Development of Fractional Calculus 1695--1900. $\mathit{\text{Historia Math., 4(1):}}$ 75--89, 1977.

[2] A. McIntosh. Operators which have an $H_{\infty}$ functional calculus. $\mathit{\text{Miniconference on operator theory and partial differential equations:}}$ 210--231, 1986.

[3] M. Haase. $\mathit{\text{The Functional Calculus for Sectorial Operators,}}$ volume 169 of $\mathit{\text{Operator Theory: Advances and Applications.}}$ Birkhäuser Basel, 2006.

[4] K. S. Miller and B. Ross. $\mathit{\text{An Introduction to the Fractional Calculus and Fractional Differential Equations.}}$ John Wiley & Sons, 1993.
23.01.20 14:45 Eißendorfer Straße 40 (N), Raum 0007 Einblicke in die Modellierung des Materialverhaltens von Elastomerwerkstoffen
Nils Hendrik Kröger, Deutsches Institut für Kautschuktechnologie e.V., Hannover, Eupener Straße 33, 30519 Hannover, Deutschland

Im Maschinen- und Automobilbau werden für mechanisch extrem beanspruchte, temperatur- und chemikalienbeständige Bauteile Elastomerwerkstoffe benötigt. Typische Beispiele sind Reifen, Zahn- und Keilriemen, Motor- und Aggregatelager, Luftfedern und Fahrwerkbuchsen sowie statisch und dynamisch beanspruchte Dichtungen. Die Anforderungen bezüglich Zuverlässigkeit und Leistungsdichte sind speziell in Verbindung mit den hochsensiblen, sicherheitsrelevanten Funktionen der Bauteile besonders hoch.
Insbesondere im Rahmen der Digitalisierung in der Produktion gewinnen Simulationsmodelle verstärkt an Bedeutung. Viele Verarbeitungsschritte in der Herstellung von Elastomerbauteilen beginnend mit dem Mischen, dem Walzen und der Extrusion oder des Spritzgießens, über die Vulkanisation beeinflussen die endgültigen mechanischen Eigenschaften. Im Laufe ihres Einsatzlebens verändern sich diese Eigenschaften auf Grund von thermo-oxidativer Alterung, so dass auch Lebensdauervorhersagen zur einer Herausforderung werden. Die zuverlässige Erstellung von „Digitalen Zwillingen“ für Elastomerbauteile bedarf so einer Beschreibung vieler auch untereinander gekoppelter Effekte.
Dieser Vortrag bietet Einblicke in verschiedene Modellierungsansätze einzelner Abschnitte des Leben von Elastomeren. Hauptfokus ist hierbei die Beschreibung der mechanischen Eigenschaften unter Berücksichtigung der Vernetzung und Alterung.

Language of the talk is going to be either German or English depending on the audience preferences.
\mathbf{\text{Edit: There seems to be a problem with Nils' train. The start of the talk will be delayed by 30minutes. }}
16.01.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Greedy methods in kernel based approximation
Kristof Albrecht

Positive Kernels provide methods to solve multivariate interpolation problems, but standard kernel methods usually lead to ill-conditioned linear systems. Therefore, a suitable choice of interpolation centers and basis functions reqiures particular care.

In this talk, i will give an introduction to kernel based approximation and discuss greedy point selection strategies, which will improve the stability of the interpolation method.
09.01.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 A tractable approach for 1-bit compressed sensing on manifolds
Sara Krause-Solberg, Institut für Mathematik (E-10), Lehrstuhl Angewandte Analysis

Compressed Sensing deals with reconstructing some unknown vector from few linear measurements in high dimension by additionally assuming sparsity, i.e. many entries are zero. Recent results guaranteed recovery even when just signs of the measurements are available (one-bit CS). A natural generalization of classical CS replaces sparse vectors by vectors lying on manifolds having low intrinsic dimension. In this talk I introduce the one-bit problem and proposes a tractable strategy to solve one-bit CS problems for data lying on manifolds. This is based on joint work with Johannes Maly and Mark Iwen.
19.12.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Parallel-in-Time PDE-constrained Optimization*
Dr. Sebastian Götschel, Zuse Institut Berlin (ZIB)

Large-scale optimization problems governed by partial differential equations (PDEs) occur in a multitude of applications, for example in inverse problems for non-destructive testing of materials and structures, or in individualized medicine. Algorithms for the numerical solution of such PDE-constrained optimization problems are computationally extremely demanding, as they require multiple PDE solves during the iterative optimization process. This is especially challenging for transient problems, where methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the associated optimality system. The evaluation of the reduced gradient then requires one solve of the state equation forward in time, and one backward-in-time solve of the adjoint equation. In order to tackle real-life applications, it is not only essential to devise efficient discretization schemes, but also to use advanced techniques to exploit computer architectures and decrease the time-to-solution, which otherwise is prohibitively long.

One approach is to utilize the increasing number of CPU cores available in current computers. In addition to more common spatial parallelization, time-parallel methods are receiving increasing interest in the last years. There, iterative multilevel schemes such as PFASST (Parallel Full Approximation Scheme in Space and Time) are currently state of the art and achieve significant parallel efficiency. In this talk, we investigate approaches to use PFASST for the solution of parabolic optimal control problems. Besides enabling time parallelism, the iterative nature of the temporal integrators within PFASST provides additional flexibility for reducing the cost of solving nonlinear equations, re-using previous solutions in the optimization loop, and adapting the accuracy of state and adjoint solves to the optimization progress. We discuss benefits and difficulties, and present numerical examples.

This is joint work with Michael Minion (Lawrence Berkeley National Lab).
16.12.19 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Präkonditionierer für lineare Systeme aus RBF-FD diskretisierten partiellen Differentialgleichungen (Bachelorarbeit)
Henrik Wyschka
12.12.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Molecular-Continuum Flow Simulation with MaMiCo: Where HPC and Data Analytics Meet
Prof. Dr. Philipp Neumann, Helmut-Schmidt-Universität

Molecular-continuum methods, as referred to in my talk, employ a domain decomposition and compute fluid flow either by means of molecular dynamics (MD) or computational fluid dynamics (CFD) in the sub-domains. This enables multiscale investigations of nano- and microflows beyond the limits of validity of classical CFD.

In my talk, I will focus on latest developments in the macro-micro-coupling tool (MaMiCo). MaMiCo enables the coupling of arbitrary CFD and MD solvers, hiding the entire coupling algorithmics from the actual single-scale solvers. After a brief discussion of the limits of the MD method, I will focus on various aspects of the molecular-continuum coupling and its realization in MaMiCo, including parallelization, multi-instance sampling for MD (that is ensemble averaging) and filtering methods that extract smooth responses from the fluctuating MD description to enhance consistency on the side of the continuum solver. I will further present preliminary results from a study which aims to generate open boundary force models for MD using machine learning.
05.12.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 A new approach to the QR decomposition of hierarchical matrices
Vincent Griem

All existing QR decompositions for hierarchical matrices suffer from numerical drawbacks that limit their use in many applications. In this talk, I will present a new method based on the recursive WY-based QR decomposition by Elmroth and Gustavson. It is an extension of an already existing method for a subclass of hierarchical methods developed by Kressner and Susnjara.

I will try to keep things as simple as possible and give a short introduction to hierarchical matrices as well. Previous knowledge of hierarchical matrices is not necessary to understand the basic ideas and main obstacles of the new algorithm.
26.11.19 17:00 Am Schwarzenberg-Campus 5 (H), Raum H0.10 Two-scale convergence for evolutionary equations
Marcus Moppi Waurick, Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, Scotland, Room number: LT1007

In the talk, we shall develop a general framework for the treatment of both deterministic and stochastic homogenisation problems for evolutionary equations. The versatility of the methods allow the unified treatment of static, dynamic as well as mixed type problems.
21.11.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Parallel-in-time integration with PFASST: from prototyping to applications
Robert Speck, Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Wilhelm-Johnen-Straße, 52428 Jülich

The efficient use of modern supercomputers has become one of the key challenges in computational science. New mathematical concepts are needed to fully exploit massively parallel architectures. For the numerical solution of time-dependent processes, time-parallel methods have opened new ways to overcome scaling limits. With the "parallel full approximation scheme in space and time" (PFASST), multiple time-steps can be integrated simultaneously. Based on spectral deferred corrections (SDC) methods and nonlinear multigrid ideas, PFASST uses a space-time hierarchy with various coarsening strategies to maximize parallel efficiency. In numerous studies, this approach has been used on up to 448K cores and coupled to space-parallel solvers with finite differences, spectral methods or even articles for discretization in space. Yet, since the integration of SDC or PFASST into an existing application code is not straightforward and the potential gain is typically uncertain, we will present in this talk our Python prototyping framework pySDC. It allows to rapidly test new ideas and to implement first toy problems more easily. We will also discuss the transition from pySDC to application-specific implementations and show recent use cases.
18.11.19 14:15 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Das verbesserte Produkt Hierarchischer Matrizen durch Verwendung von erweiterten Summen-Ausdrücken (Masterarbeit)
Max Gandyra
14.11.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Where are my ions? A new algorithms to track fast ions in the magnetic field of a fusion reactor
Daniel Ruprecht, TUHH, Institut für Mathematik, Lehrstuhl für Computational Mathematics, Am Schwarzenberg-Campus 3, Gebäude E, 21073 Hamburg

The plasma in a fusion reactor is heated by neutral beam injection: injecting high energy neutrons which quickly ionize and swirl around in the reactor's magnetic fiel. Modelling this process requires solving the Lorentz equations numerically over long times (up to a second) with very small time steps (order of nanoseconds), which means very many time steps and thus long simulation times (from days up to a week). The talk will introduce GMRES-Boris-SDC (GBSDC), a new time stepping algorithm that can reduce computational cost compared to the currently used Boris method. The method is a potpourri of various numerical techniques, including the GMRES linear solver, spectral deferred corrections, the velocity Verlet scheme and the Boris trick. I will describe the algorithm and show examples of its performance for benchmarks with varying degree of realism.

This is joint work with Dr Krasymyr Tretiak, School of Mathematics, University of Leeds.
12.11.19 15:15 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Project presentations of Canadian interns
Josiah Vandewetering and Braeden Syrnyk

During their work-term at TUHH the two Canadian students worked on projects relating to current research in the institute.
As their term comes to an end they will present their ongoing work in short talks.
05.11.19 16:30 Am Schwarzenberg-Campus 3 (E), Raum 3.091 Kempe Chains and Rooted Minors
Samuel Mohr, Technische Universität Ilmenau
24.10.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Observability Estimates in Banach Spaces and Applications
Dennis Gallaun

In this talk we study sufficient conditions for obserability of systems in Banach spaces. In an abstract Banach space setting we show that an uncertainty relation together with a dissipation estimate implies an observability estimate with explicit dependence on the model parameters. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider elliptic operators on Lp spaces. Combined with the well-known relation between observability and controllability we derive sufficient conditions for null-controllability and bounds on the control cost.
The talk is based on joint work with Christian Seifert and Martin Tautenhahn.
17.10.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Extension of vector-valued functions and weak-strong principles
Karsten Kruse

We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space $E$ over the field $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$, which have weak extensions in a space $\mathcal{F}(\Omega,\mathbb{K})$ of scalar-valued functions on a set $\Omega$, to functions in a vector-valued counterpart $\mathcal{F}(\Omega,E)$ of $\mathcal{F}(\Omega,\mathbb{K})$. The main tool is the representation of vector-valued functions as linear continuous operators.
25.09.19 10:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Stabilität gewöhnlicher Differentialgleichungen (Bachelorarbeit)
Patrizia Hermann
23.09.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Erkennung und Vorhersage von Meinungsbildern anhand neuronaler Netze (Bachelorarbeit)
Nesrine Zarrouki
09.09.19 15:00 Raum H0.03 Application of Hierarchical Matrices to Scattered Data Interpolation [Promotionsvortrag]
Michael Wende
30.08.19 15:00 Raum H 0.07 Inexact Iterative Projection Methods for Linear and Nonlinear Eigenvalue Problems
Nicolai Rehbein
15.08.19 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Bildbasierte Verarbeitung von Pulverbett- und Schmelzbadaufnahmen der additiven Fertigung von Ti-6Al-4V [Masterarbeit]
Julia Schawaller, Studiengang TM, jetzt Airbus
11.07.19 16:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Factorization and Symmetrization of stabilized Gaussian RBFs*
Sabine Le Borne, Technische Universität Hamburg, Institut für Mathematik, Lehrstuhl Numerische Mathematik, Am Schwarzenberg-Campus 3, Gebäude E, 21073 Hamburg
09.07.19 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Segmentierung von Fischröntgenbildern mittels Machine Learning [Masterarbeit]
Stefan Dübel
04.07.19 16:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Analysis of the discretization error in the RBF-FD method
Willi Leinen
27.06.19 16:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Inexakte iterative Projektionsverfahren für lineare und nichtlineare Eigenwertprobleme
Nicolai Rehbein, Institut für Mathematik, TUHH

Ich präsentiere einen allgemeinen Ansatz für das Jacobi-Davidson-Verfahren basierend auf einem beliebigen iterativen Verfahren zum Lösen eines linearen oder nichtlinearen Eigenwertproblems. Die Auswirkung eines inexakten Lösens der Korrekturgleichung wird betrachtet und hieraus kann lineare Konvergenz für drei Fälle von verschiedene Vorbedingungen bewiesen werden.
21.06.19 13:45 Am Schwarzenberg-Campus 3 (D), Raum D1.021 Recent Applications of Deep Learning, Wavelet Theory and Persistent Homology
Mijail Guillemard

We give an overview or recent developments on Deep Learning, its relations to wavelet
theory and applications to image analysis with interactions with persistent homology.
06.06.19 16:00 D1.021 On differential-algebraic equations in infinite dimensions
Sascha Trostorff, CAU Kiel, Arbeitsbereich Analysis, Ludewig-Meyn-Straße 4, 24098 Kiel

We consider differential-algebraic equations on (possibly) infinite dimensional Hilbert spaces, that is, we consider equations of the form
(Eu)'+Au & =0\quad(\text{on }\mathbb{R}_{\geq0}),\\
u(0) & =u_{0},
where $E,A$ are linear operators on a Hilbert space $H$ and $E$ is bounded and allowed to have a non-trivial kernel. These equations cannot have a unique solution for each $u_{0}\in H$ (just look at the case $E=0$). Thus, finding the ``right'' space of initial values arises as a natural question. Imposing growth conditions on the operator pencil
we determine the maximal space of admissible initial values. First, we treat the case of bounded $A$ and then generalise the results to the case of unbounded $A$. In particular, we discuss whether we can find a $C_{0}$-semigroup yielding the mild solutions of the above problem.
24.05.19 13:45 D1.021 Schneiden, Kleben, Glattbügeln - Spektraltheorie für Heimwerker
Marko Lindner, TUHH, Institut fuer Mathematik, Lehrstuhl fuer angewandte Analysis

Es geht um eine Fortführung des Vortrages von Anfang Februar:

Kann man Pseudoeigenvektoren der unendlichen Matrix $A$ bzw. ihrer endlichen Ausschnitte $A_n$ aus den jeweils anderen gewinnen? Wir hatten u.a. gesehen, dass die sogenannte untere Norm von $A_n$ für große $n$ mit der von $A$ in Verbindung steht. (Entsprechende Aussagen übertragen sich auf die Resolvente.)

Diesmal soll das Ganze in Abhängigkeit von $n$ quantifiziert werden.

Vortrag (PDF, 159KB)

21.05.19 17:30 Am Schwarzenberg-Campus 3 (E), Raum 3.091 A coset enumeration approach to CSP refutation (Masterarbeit)
Joshua Stock
17.05.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Radiale Basisfunktionen – ein Crashkurs
Jens-Peter M. Zemke, Institut für Mathematik, Lehrstuhl für numerische Mathematik

Radiale Basisfunktionen (RBF) dienen der Interpolation und Approximation mehrdimensionaler verteilter Daten. In diesem Vortrag werden RBF motiviert, die positive Definitheit und damit eindeutige Lösbarkeit der Interpolationsaufgabe einiger RBF hergeleitet, sowie Erweiterungen, wie bedingt definite RBF und flache RBF, vorgestellt. Der Fokus liegt hierbei auf den Beweistechniken und den Ideen hinter RBF.
10.05.19 13:45 D1.021 A Model for the Description of Fluid Flow
Fabian Gabel

Based on 6 + 2 assumptions, we will derive a model (a system of PDEs) with the purpose to describe the movement of a fluid. Ideally, at the end of the talk, we will have arrived at the incompressible Navier-Stokes equations.
03.05.19 13:45 H0.09 Mathematical basics of general relativity II
Jan Meichsner, TUHH, Institut fuer Mathematik, Lehrstuhl fuer angewandte Analysis

Part II of the presentation on general relativity. In this part we will talk about the basic equations and how physical quantities are described in terms of mathematical objects.
26.04.19 13:45 H0.07 Mathematical basics of general relativity I
Jan Meichsner, TUHH, Institut fuer Mathematik, Lehrstuhl fuer angewandte Analysis

I am not an expert on the field but during my studies I spent some time on understanding the mathematical basics of the general theory of relativity. I would present them in two parts. In the first part on the 26th of April I would concentrate on basics of differential geometry which are needed to describe the mathematics of the theory. In a second part on the 3rd of May I would explain how the before introduced structures are used to create a mathematical model of general relativity.
25.04.19 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Kernschätzung bei Aggregationsproblemen mit radialen Basisfunktionen (Masterarbeit, TM)
Torben Jentzsch
24.04.19 16:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 A Riesz Decomposition Theorem for Schrödinger Operators on Graphs
Florian Fischer, Universität Potsdam, Institut für Mathematik

In the classical potential theory on the Euclidean space and in the potential theory of transient Markov chains a unique decomposition of superharmonic functions into a harmonic and a potential part is well-known. In this talk the basic concepts and ideas to gain such a decomposition for Schrödinger operators on graphs will be shown. The talk will show results of my master's thesis supervised by Matthias Keller.
12.04.19 13:45 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Monotonie von Spektren für metrische Graphen
Christian Seifert

Wie verändert sich das Spektrum des Laplace-Operators (oder allgemeiner von Schrödinger-Operatoren) auf metrischen Graphen unter Variation der Graphenparameter? Einige Antworten auf die Frage gibt es im Vortrag.
26.03.19 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Morphologische Operationen in der Bildverarbeitung [Bachelorarbeit]
Jasper Reese, TM-Student
22.03.19 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Solitonen der KdV-Gleichung in Netzwerken [Bachelorarbeit]
Mitja Roeder
22.03.19 09:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Neuronale Netze und die Aktivierung von Neuronen [Bachelorarbeit]
Cornelia Hofsäß
28.02.19 15:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Bicentric Polygons
Yannick Mogge

I will give a short summary of my master thesis as well as a quick introduction of myself.
07.02.19 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Accessibility Assistance for the Interactive Navigation of Texts [Masterarbeit]
Imad Hamoumi
06.02.19 13:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Endliche Ausschnitte und Resolventen
Marko Lindner

Was wird aus (Pseudo-)Eigenwerten und -vektoren beim Abschneiden einer unendlichen Matrix? (Sie bleiben welche.)
Gibt es auch Aussagen in die umgekehrte Richtung?
Wie gut lassen sich diese Aussagen quantifizieren?

Vortrag (PDF, 1.0MB)

28.01.19 13:15 H0.08 Extrapolation spaces and Desch-Schappacher perturbations of bi-continuous semigroups*
Christian Budde, Bergische Universität Wuppertal, Arbeitsgruppe Funktionalanalysis

We construct extrapolation spaces for non-densely defined (weak) Hille--Yosida operators. In particular, we discuss extrapolation of bi-continuous semigroups. As an application we present a Desch--Schappacher type perturbation result for this kind of semigroups. This talk is based on joint work with B. Farkas.
24.01.19 13:30 D1.024 On eventual regularity properties of operator valued functions*
Marco Peruzzetto, Christian-Albrechts-Universität zu Kiel, Arbeitsbereich Analysis

For two Banach spaces $X,Y$ let $u:\mathbb{R}_{\geq 0}\rightarrow \mathcal{L}(X;Y)$ be an operator valued function and $\mathtt{P}$ a regularity property. Assume that each orbit $t\mapsto u(t)x$ has the regularity property $\mathtt{P}$ on some interval $(t_x,\infty)$ in general depending on $x\in X$. In this paper we prove a Baire-type theorem, which allows to remove the dependency of $x$ in certain situations. Afterwards, we provide some applications which are of interest in semigroup theory. In particular, we generalize and explain the result obtained by Bárta in his article ``\emph{Two notes on eventually differentiable families of operators}'' (Comment. Math. Univ. Carolin. 51,1 (2010), 19-24).
17.01.19 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 RBF Approximation with hierarchical matrices
Vincent Griem

In this presentation we will talk about the application of hierarchical matrices to solve the least squares problem arising in the RBF Approximation of scattered data.

We will shortly introduce hierarchical matrices as well as some central aspects of the RBF approach to scattered data. The main part will be about different ideas regarding the QR decomposition of hierarchical matrices.
18.12.18 15:00 H0.05 Predicting Stock Prices Based on Press Release Sentiment: A Comparison of Naïve Bayes Classifiers and Support Vector Machines [Masterarbeitsvortrag]
Max Lübbering
18.12.18 11:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Knochendetektion in Röntgenbildern mittels Deep Learning [Forschungsprojektarbeit]
Stefan Dübel
13.12.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Solving PDEs by the RBF-FD approach
Willi Leinen

I will present an introduction of the RBF-FD method and properties of the arising linear systems.
06.12.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies
Dirk Peschka, Weierstraß-Institut, Berlin

In this talk we present results of a comparative study, where we analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices, i.e., the van Roosbroeck system.

The relation between the quasi-Fermi levels and the densities of electrons and holes is given by the equation of state. Three common challenges, that can corrupt the precision of numerical solutions of the van Roosbroeck system, will be discussed: boundary layers of the quasi-Fermi potentials at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.
06.12.18 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Hot spots of quantum graphs
Jonathan Rohleder, Matematiska institutionen, Stockholms universitet

The Hot Spots Conjecture of J. Rauch asserts that the hottest and coldest points of an insulated body should move towards its boundary for large times, if the insulation is perfect. Via the semigroup associated with the Neumann Laplacian this reduces to proving that maximum and minimum of the eigenfunction(s) associated with the smallest positive eigenvalue are located on the boundary. This conjecture is not true in full generality but is currently open, for example, for convex domains.

In this talk we will examine the corresponding question on metric graphs: for the Laplacian on a finite metric graph with standard (continuity and Kirchhoff) vertex conditions we consider the possible distribution of maxima and minima of eigenfunctions associated with the smallest nonzero eigenvalue. Among other things, we give examples to show that the usual notion of “boundary” of a metric graph, namely the set of vertices of degree one, has limited relevance for determining the “hottest” and “coldest” parts of a graph.

This is joint work with James Kennedy (Lisbon).
29.11.18 14:00 D1.024 Approximation techniques for passive mechanical control systems*
Ines Dorschky, Fachbereich Mathematik, Universität Hamburg

In this talk we study approximation techniques for input-output systems, which appear in the modeling process of mechanical systems. So, the focus will be on linear dynamical systems with a second derivative term.
These system can become very large in practice and therefore, expensive to be used for simulations and controller design.
Since this frequently happens to all control systems coming from real-live application, model order reduction became a major field in control theory over the last decades.
Here however, beside approximating the input-output behavior of the original system, the special structure should be preserved in the reduced-order model.
So far, reduction techniques designed for the linearized model fail in this aspect. On the other hand, there is a wide variety of methods that directly treat the second order control system. However, up to this point none of those methods deliver reasonable error-bounds for the approximation.
In this talk an approximation method is presented for the special class of passive mechanical systems. Roughly speaking passivity for control systems means that the system itself cannot produce energy. For this class the special canonical structure, given by so called Jordan triples for matrix polynomials, can be exploited.
In the end an error bound in the gap metric will be derived. The gap metric is used as a measure for the distance of two linear systems. It is defined via the distance of the closed subspaces of stable trajectories corresponding to zero initial conditions of the systems. Hence, the gap metric error-bound ensures the quality of the approximation of the state/signal system.
27.11.18 16:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Fast winning strategies in biased Maker{Breaker graph games
Mirjana Mikalacki, University of Novi Sad, Faculty of Sciences, Department of Mathematics and Informatics

We study two standard biased (1 : b) Maker-Breaker positional games
| the Perfect Matching game and the Hamilton Cycle game, played on
the edge set of the complete graph on n vertices, Kn. Given Breaker's bias
b, possibly depending on n, our goal is to determine the minimal number
of moves in which Maker can win in each of these two graph games.

This is joint work with Miloš Stojakovic.
22.11.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Chernoff approximation of operator semigroups
Yana Kinderknecht, Universität des Saarlandes, Fb. Mathematik

In this talk we outline classical connections between such mathematical objects as operator semigroups, evolution equations and Markov processes. Further, we present a method to approximate operator semigroups with the help of the Chernoff theorem. Many \emph{Chernoff approximations} lead to representations of solutions of (corresponding) evolution equations in the form of limits of $n$-fold iterated integrals of elementary functions when $n$ tends to infinity. Such representations are called \emph{Feynman formulae}. They can be used for direct computations, modelling of the related dynamics, simulation of underlying stochastic processes.
In some cases, Chernoff approximations can be understood as a version of the operator splitting method (known in the numerics of PDEs); some Feynman formulae provide Euler--Maruyama schemes for SDEs. Moreover, the limits in Feynman formulae sometimes coincide with path integrals with respect to probability measures (\emph{Feynman-Kac formulae}) or with respect to Feynman type pseudomeasures (\emph{Feynman path integrals}). It is planned to discuss different Chernoff approximations for semigroups corresponding to some Markov processes (e.g., subordinate Feller diffusions on star graphs and Riemannian manifolds) and for Schr\''{o}dinger groups.
Furthermore, the constructed Chernoff approximations for operator semigroups can be used to approximate solutions of some time-fractional evolution equations describing anomalous diffusion (solutions of such equations do not posess the semigroup property).
21.11.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Domino towers (Including: How to count stuff using generating functions)
Alexander Haupt

The original problem of counting domino towers was first studied by G. Viennot in 1985, see also D. Zeilberger (The Amazing 3^n Theorem). We analyse a generalisation of domino towers that was proposed by T. M. Brown (J. Integer Seq. 20.3 (2017), Art. 17.3.1), which we call S-omino towers. After establishing an equation that the generating function must satisfy and applying the Lagrange Inversion Formula, we find a closed formula for the number of towers.

The talk should hopefully also be accessible to people not used to this kind of mathematics.
15.11.18 14:00 D1.024 Observability for Systems in Banach spaces - Part II*
Christian Seifert

This talk is divided into two parts. The first part will be given on Thursday 08.11.18 by Dennis Gallaun.
In this talk we study sufficient conditions for obserability of systems in Banach spaces. In an abstract Banach space setting we show that an uncertainty relation together with a dissipation estimate implies an obserbability estimate with explicite dependence on the model parameters. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider elliptic operators on Lp(Rd) and on Lp(Td) for 1 < p < ∞. Combined with the well-known relation between observability and controllability we derive sufficient conditions for null-controllability and bounds on the control cost.
08.11.18 13:30 D1.024 Observability for Systems in Banach spaces - Part I*
Dennis Gallaun

This talk is divided into two parts. The second part will be given on Thursday 15.11.18 by Christian Seifert.
In this talk we study sufficient conditions for obserability of systems in Banach spaces. In an abstract Banach space setting we show that an uncertainty relation together with a dissipation estimate implies an obserbability estimate with explicite dependence on the model parameters. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider elliptic operators on Lp(Rd) and on Lp(Td) for 1 < p < ∞. Combined with the well-known relation between observability and controllability we derive sufficient conditions for null-controllability and bounds on the control cost.
02.11.18 11:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Analyzing MRI Data using Geometric Deep Learning (Bachelor Thesis)
Daniel Klisch
01.11.18 14:15 Am Schwarzenberg-Campus 3 (E), Raum 3.074 On a Numerical Solution Algorithm for the Navier-Stokes Equations and the Stokes Resolvent Problem in L^p
Fabian Gabel

My talk will consist of three short, independent parts, the first one being a quick introduction of myself. In the second and the third part, I will give an ''easy-to-digest'' survey of my graduate theses [1,2].


[1] Implementation and Performance Analyses of a Highly Efficient Algorithm for Pressure-Velocity Coupling. Master Thesis Computational Engineering, Darmstadt, 2015

[2] On the L^p Theory of the Stokes Operator in Lipschitz Domains. Master Thesis Mathematics, Darmstadt, 2018

Vortrag (PDF, 2.1MB)

18.10.18 13:45 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Series representations in spaces of vector-valued functions*
Karsten Kruse

It is a classical result that every $\mathbb{C}$-valued holomorphic function has a local power series representation.
This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space $E$ over
$\mathbb{C}$. Motivated by this example we try to answer the following question. Let $E$ be a locally convex Hausdorff space
over a field $\mathbb{K}$, $\mathcal{FV}(\Omega)$ be a locally convex Hausdorff space of $\mathbb{K}$-valued functions on a set $\Omega$ and $\mathcal{FV}(\Omega,E)$ be an $E$-valued counterpart of $\mathcal{FV}(\Omega)$
(where the term $E$-valued counterpart needs clarification itself).
For which spaces is it possible to lift series representations of elements of $\mathcal{FV}(\Omega)$ to elements of $\mathcal{FV}(\Omega,E)$?
We derive sufficient conditions for the answer to be affirmative which are applicable for many classical spaces of functions
$\mathcal{FV}(\Omega)$ having a Schauder basis.
11.10.18 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Konstruktion aufspannender Strukturen in Walker-Breaker-Spielen
Jonas Eckhoff

11.10.18 14:00 D1.024 Existence and Uniqueness of the Harmonic Extension Approach to Fractional Powers of Linear Operators*
Jan Meichsner, Institut fuer Mathematik, Lehrstuhl angewandte Analysis, TUHH

This talk will be an extended version of the talk I gave on the SOTA 2018 in Poland.
I will discuss existence and uniqueness of the so-called Harmonic extension approach to fractional powers of linear operators.
26.09.18 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Verschiedene Ansätze zur Bildzerlegung
Malte Seemann
26.09.18 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Eindimensionale Quasikristalle, endliche Abschnitte und Invertierbarkeit [Bachelorarbeit]
Luis Weber
26.09.18 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Quasiperiodische Schrödingeroperatoren und Konditionszahlen [Bachelorarbeit]
Jonas Sattler
25.09.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 On the Game of Lazy Cops and Robbers on Graphs (Master-Vortrag)
Fabian Hamann
25.09.18 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Ein Randwertproblem für die Maxwell-Gleichungen auf Mannigfaltigkeiten (Bachelorvortrag)
Dennis Schmeckpeper
13.09.18 10:00 Raum 3.008 in Gebäude L / DE17 Eine körpergebundene integrale Methode zur Simulation von strömungsinduziertem Schall nach Ffowcs-Williams-Hawkings (Bachelor-Vortrag)
Konrad Scheffler
06.09.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Utilizing Geometry of Smoothness-Increasing-Accuracy-Conserving (SIAC) filters for reduced errors
Prof. Dr. Jennifer Ryan, Mathematics, University of East Anglia

Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods are designed to increase the smoothness and improve the convergence rate of the DG solution form p+1 to 2p+1 through post-processing. However, introducing these filters can be challenging for multi-dimensional data since a tensor product filter grows in support size as the field dimension increases [(3p+2)*h]^d, where p + the polynomial order and d is the dimension. This becomes computationally prohibitive as the dimension increases. An alternative approach is to utilize a one-dimensional univariate filter. In this talk we introduce the Line SIAC filter and explore how the orientation, structure and filter size affect the order of accuracy and global errors. We show how line filtering preserves the properties of traditional tensor product filtering, including smoothness and improvement in the convergence rate, given an appropriate rotation. Furthermore, numerical experiments are included, exhibiting how these filters achieve the same accuracy at significantly lower computational costs.
09.08.18 15:45 H0.09 A glimpse on interpolation theory and interpolation with mixed boundary conditions*
Sebastian Bechtel, Arbeitsgruppe Analysis, TU Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt

First, we give a short introduction to abstraction interpolation theory and
relate it to the well-known interpolation results from Riesz--Thorin and
Marcinkiewicz. Then we apply the abstract methods to concrete spaces
incorporating (mixed) boundary conditions and give an overview on arising
challenges and ways to resolve them.
25.07.18 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Iterative Löser für RBF Kollokation zur Lösung von partiellen Differentialgleichungen (Bachelorarbeit)
Felix Kieckhäfer, Mathematik
19.07.18 15:45 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Quantitative unique continuation principles and application to control theory for the heat equation
Martin Tautenhahn, TU Chemnitz, Fakultät für Mathematik

This talk is divided into two. In the first part we discuss a so-called scale-free and quantitative unique continuation principle for spectral projectors of Schr\''odinger operators.
Let $\Omega = \Lambda_L = (-L,L)^d$ or $\Omega = \mathbb{R}^d$, and $H = -\Delta + V$ be a Schr\''odinger operator on $L^2 (\Omega)$ with a bounded potential $V$. If $\Omega = \Lambda_L$ we impose Dirichlet, Neumann, or periodic boundary conditions. The unique continuation principle states that for any $E \geq 0$, and any $\phi \in \operatorname{Ran} \chi_{(-\infty , E]} (H)$ we have
\begin{equation} \label{quc}
\lVert \phi \rVert_{L^2 (\Omega)}^2 \leq C_{\rm sfuc} \lVert \chi_{S_\delta \cap \Omega} \phi \rVert_{L^2 (\Omega)}^2,
where $S_\delta \subset \mathbb{R}^d$ is a union of equidistributed $\delta$-balls, and $C_{\rm sfuc} = C_{\rm sfuc} (d , E ,\allowbreak \delta , \lVert V \rVert)$ some explicitly given constant.
In the second part of the talk we will discuss an applications thereof to control theory. On the time interval $[0,T]$ we consider the controlled heat equation
\begin{equation} \label{eq:parabolic}
\partial_t u + H u = f\chi_{S_\delta \cap \Omega} ,
where $u,f \in L^2([0,T] \times \Omega)$, and $u (0,\cdot) \in L^2 (\Omega)$.
Note that the control function $f$ acts on the set $S_\delta$ only. Our aim is to study null-controllability in time $T > 0$, i.e.\ there is a control function $f$ such that $u(T,\cdot) = 0$. We provide explicit estimates on the costs of the form $\lVert f \rVert_{L^2([0,T]\times \Omega )} \leq C \lVert u_0 \rVert_{L^2 (\Omega)}$.
17.07.18 11:00 H - SBC5 / H0.06 Maximum number of clique-free edge coloring in graphs
Hiep Han, Universidad de Santiago de Chile
17.07.18 10:00 H - SBC5 / H0.06 Gallai's Conjecture for regular graphs and planar graphs
Andrea Jimenez, Universidad de Valparaíso
12.07.18 15:45 tba Sparse Frequency Estimation*
Benedikt Diederichs, Fachbereich Mathematik, Universität Hamburg

Prony's problem - estimating the frequencies of an exponential sum - and its higher dimensional
analogs have attracted a lot of attention in recent years. A somewhat neglected question is whether
this problem is well-posed. In this talk, some results in this direction will be presented.
We start by giving a brief introduction to stability in compressed sensing. Compressed sensing is
concerned with solving nite dimensional linear systems under a priori sparsity assumptions. Stability
follows from the so-called restricted isometric property (RIP) of the system matrix.
We then discuss sparse frequency estimation. Due to the continuous nature, proving an analogue of
the RIP is more dicult. To this end, we briey introduce specic functions, which are well localized
in the spatial and frequency domain. Then we deduce stability results as well as a posteriori error
This talk is based on joint work with Armin Iske.
04.07.18 13:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Image segmentation methods and an application to brain images.
Christoph Nicolai
28.06.18 15:45 Am Schwarzenberg-Campus (D), Raum D1.021 A minimax principle in spectral gaps*
Albrecht Seelmann, Fakultät für Mathematik - Technische Universität Dortmund

In [Doc. Math. 4 (1999),275--283], Griesemer, Lewis, and Siedentop devised an abstract minimax principle for eigenvalues in spectral gaps of perturbed self-adjoint operators. We show that this minimax principle can be adapted to the particular situation of bounded additive perturbations with hypotheses that are easier to check in this case. The latter is demonstrated in the framework of the Davis-Kahan sin(2\Theta) theorem.

This talked is based on joint work with I. Nakic, M. Täufer, M. Tautenhahn, and I. Veselic.
27.06.18 13:00 Am Schwarzenberg-Campus 1 (A), Raum A 0.14 Tiling edge-coloured complete graphs with few pieces
Jan Corsten, London School of Economics, Department of Mathematics
21.06.18 15:30 Am Schwarzenberg-Campus 5 (H), Raum H0.05 Poisson local eigenvalue statistics for continuum random Schrödinger operators
Adrian Dietlein, LMU München, Mathematisches Institut

I'll start with a short recap of the lattice Anderson
model, with a focus on Minami's estimate and its applications. In
particular it implies Poissonian local eigenvalue statistics, which
is believed to be a characteristic feature of spectrally localized
quantum mechanical systems. In the second part of the talk I'll
present our main technical result, a level-spacing estimate for
continuum random Schrödinger operators, and argue why it implies
Poissonian local eigenvalue statistics. If time permits I'll comment
on the proof's methods.
The talk is based on joint work with Alexander Elgart.
07.06.18 15:45 tba Silvestre-Caffarelli approach to Fractional Powers of Linear Operators*
Jan Meichsner

We are going to discuss (again) the approach of describing fractional powers of linear operators on
Banach spaces as it was performed by Silvestre and Caffarelli when they were studying the fractional
Laplacian. Even though useful it is still an open problem whether this is possible for all sectorial
operators and, if so, whether it is unique.
The presented content is work in progress.
28.05.18 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Predicting Companies Mentioned in News Articles, a Comparison of Two Approaches: Latent Dirichlet Allocation with k-Nearest Neighbor versus Bag of Words with k-Nearest Neighbor [Projektarbeit]
Max Lübbering
17.05.18 16:30 TUHH, Gebäude A, Raum A0.19 On the stability of Prony's method*
Stefan Kunis, Institut für Mathematik, Uni Osnabrück
16.05.18 09:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Kantenerhaltendes Entrauschen mittels bilateraler Filter [Bachelorarbeit]
Leon Haag, Studiengang TM
14.05.18 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 A Comparison of Distance Metrics in Collaborative Recommender Systems [Projektarbeit]
Imad Hamoumi
02.05.18 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Random Walks On Graphs [Bachelorarbeit]
Scott Huntington, Studiengang CS
26.04.18 15:45 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Polynomial chaos: applications in electrical engineering and bounds
Eduard Frick

The study of electromagnetic fields in 2D circuits often leads to resonances. We use a polynomial chaos expansion (due to uncertain circuit parameters), which is analytically and numerically troublesome near the resonance frequencies. As a toy model for the convergence of the polynomial chaos expansion, we look at the parallel RLC circuit with uncertain capacitance and give $L^2$ error bounds depending on the degree of the expansion, the random distribution, the distance to resonance and the so-called quality factor of the circuit (which is a measure for the damping).
25.04.18 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Nicht-parametrische Methoden der Bildregistrierung [Masterarbeit]
Max Ansorge, TM-Student
24.04.18 16:15 Geomatikum (Bundesstraße 55), Raum 1240 Strukturierte Pseudospektren in der Systemtheorie
Dennis Gallaun, Institut für Mathematik

Im Rahmen des Lothar-Collatz-Seminars spreche ich am Geomatikum (Uni Hamburg) über strukturierte Pseudospektren in der Systemtheorie.

Abstract: https://www.c3s.uni-hamburg.de/en/news-events/seminar-c3s/gallaun.pdf
22.03.18 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Lanczos' Algorithm in Finite Precision and Quantum Mechanics
Jens-Peter M. Zemke
21.03.18 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Algebraische Präkonditionierer für Interpolationsaufgaben mit radialen Basisfunktionen
Michael Wende

Interpolationsaufgaben mit radialen Basisfunktionen fuehren auf vollbesetzte Sattelpunktprobleme, deren iterative Loesung eine Praekonditionierung erfordert. Die Systemmatrizen koennen als H-Matrizen approximiert und fuer die Konstruktion algebraischer Praekonditionierer verwendet werden. Als Praekonditionierer verwenden wir die Nullraummethode sowie ein Gebietszerlegungsverfahren. Mittels der Nullraummethode kann die Loesung des indefiniten Systems im Wesentlichen auf die Loesung eines positiv definiten Systems geringfügig kleinerer Groesse zurueckgefuehrt werden. Die positiv definiten Systeme koennen mit einer approximativen Cholesky-Zerlegung in der Arithmetik hierarchischer Matrizen praekonditioniert werden. Kleinere Probleme werden auf diese Art zufriedenstellend geloest, aber fuer groessere Punktzahlen nimmt die Effektivität der Cholesky-Praekonditionierung ab.
Im Gebietszerlegungsverfahren wird die Kombination aus Nullraummethode und Cholesky-Praekondiitonierung nur in jedem Teilgebiet angewendet und das globale System mit einer aeusseren GMRes-Iteration geloest. Ein weiterer Vorteil der Gebietszerlegung liegt in der Parallelisierbarkeit der Konstruktion des Praekonditionierers.
19.03.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Physikalisch motivierte Untersuchungen der Kondition von Scharfetter-Gummel Matrizen [Bachelorarbeit]
Judith Angel
19.03.18 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Polynomielles Chaos: Abschätzungen und Anwendungen in der Elektrotechnik [Bachelorarbeit]
Katharina Klioba, Studiengang TM
09.03.18 11:00 Am Schwarzenberg-Campus 4 (D), Raum 1.021 Spectral asymptotics of Robin Laplacians on polygonal domains
Magda Khalile, Université Paris-Sud

Let \Omgea\subseteq\R^2 be a curvilinear polygon and Q_\Omega^\gamma be the Laplacian in L_2(\Omega) with the Robin boundary condition \partial_\nu \psi = \gamma \psi, where \partial_\nu is the outer normal derivative and \gamma>0. We are interested in the behavior of the eigenvalues of Q_\Omega^\gamma as \gamma becomes large. We prove that there exists N_\Omega \in\N such that the asymptotics of the N_\Omega first eigenvalues of Q_\Omega^\gamma is determined at the leading order by those of model operators associated with the vertices: the Robin Laplacians acting on the tangent sectors associated with \partial\Omega. In the particular case of a polygon with straight edges the N_\Omega first eigenpairs are exponentially close to those of the model operators. Moreover, if the polygon admits only non-resonant or concave corners, we prove that, for any fixed j\in\N, the N_\Omega+j eigenvalue E_{N_\Omega+j}(Q_\Omega^\gamma) behaves as E_{N_\Omega+j}(Q_\Omega^\gamma) = -\gamma^2+\mu_j^D+o(1) as \gamma\to\infty, where \mu_j^D stands for the jth eigenvalue of the operator D_1\oplus\ldots\oplus D_M and Dn denotes the one-dimensional Laplacian on (0,l_n), where l_n is the length of the nth side of \Omega, with the Dirichlet boundary condition. Finally, we prove a Weyl asymptotics for the eigenvalue
counting function of Q_\Omega^\gamma for a threshold depending on \gamma, and show that the leading term is the same as for smooth domains.
01.02.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Multivariate Populationsbilanz-Systeme
Robin Ahrens, E-10

Populations-Bilanzen und ihre Simulation spielen in vielen Prozessen der Chemie, Pharmazie und Biotechnolgie eine zunehmend wichtige Rolle. Partikel werden dabei anhand bestimmter Eigenschaften wie Masse oder Volumen gezählt. Ein wichtiger Teil dieser Simulationen ist die Aggregation.
In diesem Vortrag wird dieser Vorgang in multivariaten Problemen behandelt, eine Diskretisierung und ein effizienter Algorithmus vorgestellt.
25.01.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Korrektur der chromatischen Aberration von Objektiven [Bachelorarbeit]
Christopher Göthel, Studiengang TM

Kooperation mit der Basler AG
11.01.18 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Image Outliers Detection and GUI Automation [Projektarbeit]
Intsar Saeed
21.12.17 14:00 Am Schwarzenberg-Campus 4 (D), Raum 1.023 Lineare Relationen und Randtripel
Dr. Christian Kühn, TUHH, Am Schwarzenberg-Campus 3

Teil 2 des Vortrags über lineare Relationen und Randtripel.
20.12.17 14:00 Am Schwarzenberg-Campus 5 (H), Raum H0.06 Packing nearly optimal Ramsey R(3,t) graphs
Prof. Lutz Warnke, Georgia Institute of Technology

Auf Homepage hochgeladen.

Vortrag (PDF, 4.3MB)

14.12.17 14:30 Am Schwarzenberg-Campus 4 (D), Raum 1.021 Lineare Relationen und Randtripel
Christian Kühn

Ist S ein symmetrischer Operator in einem Hilbertraum, so stellt sich oft die Frage, welche selbstadjungierten Erweiterungen der Operator S hat und ob sich Aussagen über die Spektren (beispielsweise über die Eigenwerte) dieser Erweiterungen machen lassen. Ein mathematisches Konzept, welches hierbei hilfreich sein kann, ist das Konzept der Randtripel. Dabei stellt es sich als hilfreich heraus, nicht nur Operatoren sondern auch lineare Relationen (''mehrwertige Operatoren'') zu betrachten.

Der Vortrag soll einen einführenden Charakter haben. Es werden also die grundlegenden Definitionen und Sätze angegeben und anhand von einfachen Beispielen illustriert.
23.11.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Strukturierte Pseudospektren in der Systemtheorie
Dennis Gallaun

In diesem Vortrag stelle ich mich und meine Masterarbeit kurz vor.

Im Rahmen meiner Masterarbeit habe ich mich mit strukturierten Pseudospektren und deren Bezug zur Systemtheorie beschäftigt.
Strukturierte Pseudospektren sind ein wichtiges graphisches Werkzeug in der Stabilitätstheorie endlich-dimensionaler linearer Systeme mit ungenauen Parametern. In diesem Vortrag beschäftigen wir uns mit der Verallgemeinerung strukturierter Pseudospektren auf unendlich-dimensionale Systeme und gehen auf den Bezug zur Stabilität stark stetiger Halbgruppen ein.
16.11.17 14:00 D - SBC4, D1.021 A bound on the averaged spectral shift function and a lower bound on the density of states for random Schrödinger operators on R^d
Martin Gebert, King's College London

We prove a locally uniform lower bound on the density of states of continuum random Schrödinger operators in the localised regime. The main technical ingredient is a new bound on the expectation of the spectral shift function for random Schrödinger operators in the localised regime, corresponding to a change from Dirichlet to Neumann boundary conditions along the boundary of a finite volume. The bound scales with the surface area. (Joint with Adrian Dietlein, Abel Klein, Peter Hislop, Peter Müller)
09.11.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Gewichtete positiv definite Kernel / Simulation des Kühlvorgangs eines Fluid-gefüllten Behälters mit OpenFOAM
Vincent Griem Willi Leinen

Wir beiden stellen uns und unsere Masterarbeiten jeweils kurz vor.

Im ersten Vortrag (von Vincent Griem) geht es um gewichtete positiv definite Kernel und
ihre Anwendung in der Interpolation. Nach einer kleinen Einführung in
die Interpolation durch positiv definite Funktionen wird die
Erweiterung durch zusätzliche Gewichtsfunktionen vorgestellt und der Einfluss und mögliche
Nutzen dieses Vorgehens untersucht. Es wird insbesondere eine
Verbindung zum diagonalen Skalieren zur Verbesserung der Kondition
einer Matrix hergestellt. Abschließend folgen noch einige numerische

Im zweiten Vortrag (von Willi Leinen) geht es um die Simulation des Kühlvorgangs eines
Fluid-gefüllten Behälters mit OpenFOAM. Dabei werden einerseits
die mathematischen Grundlagen der Simulation, wie z.B. die
Finite-Volumen-Methode sowie die PDEs zur Modellierung von Wärmeleitung
und Strömung, vorgestellt. Andererseits wird auf die Software OpenFOAM,
mit deren Hilfe die Simulation durchgeführt wurde, eingegangen. Als
Anwendungsbeispiel wird die Kühlung einer Weinflasche im Gefrierschrank
untersucht. Zum Abschluss werden die numerischen Ergebnisse
der Simulation vorgestellt.
12.10.17 13:15 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Acceration of Path Computations for Electrical Harnesses in Aircrafts [Bachelorarbeit]
Julia Schawaller
26.09.17 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Approximation einer Randintegralgleichung [Bachelorarbeit]
Riko Ukena, Studiengang TM
26.09.17 09:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Strukturierte Pseudospektren in der Systemtheorie [Masterarbeit]
Dennis Gallaun, Studiengang TM (erster ''eigener'' Absolvent), bald WiMi @ E-10

Strukturierte Pseudospektren sind ein wichtiges graphisches Werkzeug in der Stabilitätstheorie endlich-dimensionaler linearer Systeme mit ungenauen Parametern. In diesem Vortrag beschäftigen wir uns mit der Verallgemeinerung strukturierter Pseudospektren auf unendlich-dimensionale Systeme und gehen auf den Bezug zur Stabilität stark stetiger Halbgruppen ein.
22.09.17 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Verhalten und Anwendbarkeit von künstlichen neuronalen Netzen für kleine Datenmengen [Projekarbeit]
Marcel Bengs, Student Theoretische Maschinebau
30.08.17 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Simulation der Wärmeleitungsgleichung in zufälligen Medien [Bachelorarbeit]
Björn Przybyla
25.08.17 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Application of Convolutional Neural Networks for Pitch Detection [Masterarbeit]
Carl Henning Cabos
13.07.17 14:15 Am Schwarzenberg-Campus 1 (A), Raum A0.10 Allowing non-symmetric gauge bodies helps simplifying the theory of radii functionals
Dr. René Brandenberg, Zentrum Mathematik, Technische Universität München

We all know that sometimes problems get easier by generalizing them. In this talk we want to present several recent results on radii functionals of convex bodies. This results were possible allowing non-symmetric gauge bodies, where in the past only
symmetric ones were studied (via general Minkowski spaces).
21.06.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Construction of Traces of Dirichlet forms
Ali BenAmor, Department of Mathematics, Faculty of Sciences of Gabes, University of Gabes, Tunisia
15.06.17 14:45 Raum H - SBC5 H0.03 (noch unbestaetigt) Bi-stetige Halbgruppen*
Jan Meichsner, Institut fuer Mathematik, Lehrstuhl angewandte Analysis, TUHH

In dem Vortrag wird es um bi-stetige Halbgruppen gehen. Das Konzept geht auf die Dissertation
'Bi–Continuous Semigroups on Spaces with Two Topologies: Theory and Applications' von
F. Kühnemund aus dem Jahre 2001 zurueck. Betrachtet werden Halbgruppen auf einem
Banachraum, welche nicht stark-stetig sind. Das wird behoben, indem man sich eine groebere
Topologie betrachtet.
Da ich Anfaenger auf dem Feld bin, wird der Vortrag eine Einfuehrung enthalten und die Nuetzlichkeit
des Konzepts an einigen Beispielen illustriert.
11.05.17 15:45 Am Schwarzenberg-Campus (H), Raum H0.04 Oszillationstheorie für Jacobi-Operatoren mit unendlich-dimensionalen Fasern
Julian Großmann

Die Sturm’sche Oszillationstheorie stammt von Charles-François Sturm um 1830, und bezieht sich meistens auf sogenannte Sturm-Liouville-Probleme, d.h. Eigenwertprobleme für gewisse Differentialgleichungen. Im Vortrag wird das diskrete Analogon davon betrachtet und in Verbindung mit dem spektralen Fluss in von-Neumann-Algebren gebracht.
03.05.17 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Verbesserung der Bildqualität bei Diffusionsgewichtetem MRT mit Hilfe von Inpainting [Masterarbeit]
Joshua Engels
27.04.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Schrödinger operators and singular infinite rank perturbations
Christian Kühn

In dem Vortrag werde ich ein abstraktes Konzept vorstellen, um selbstadjungierte Operatoren mit singulären Störungen zu untersuchen und dieses anschließend auf Schrödingeroperatoren mit Delta-Interaktionen anwenden.
21.04.17 09:00 H 0.06 Approximation of Spectra and Pseudospectra on a Hilbert Space [Promotionsvortrag]
Torge Schmidt
03.04.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Using neural networks to classify paths in two-dimensional environments [Bachelorarbeit]
Kieron Kretschmar, TM-Student
31.03.17 14:00 H0.03 Efficient and Accurate Evaluation of Aggregation Integrals in Population Balance Equations (Promotionsvortrag)
Lusine Shahmuradyan
27.03.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Numerische Simulation eines Modells einer Heißwasserhydrolyse (Bachelorarbeit)
Thorben Abel
28.02.17 10:00 H 0.08 Minimierung des kleinsten Eigenwerts für Laplace-Operatoren auf metrischen Graphen [Bachelorarbeit]
Yannick Jean Paul Lucien Saive, TM-Student
15.02.17 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Präkonditionierer basierend auf filternden Matrix-Zerlegungen (Bachelorvortrag)
Rasmus Wormstädt
06.02.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Solving PDEs Numerically: RBF Collocation and Finite Volume Methods for Semiconductor Problems
Dr. Patricio Farrell, Weierstrass Institut, Berlin

Partial differential equations model a wide range of physical phenomena.
Unfortunately, most of them cannot be solved directly, making it necessary
to develop efficient and robust numerical solution methods. In this talk,
we focus on two different ones: Radial basis functions (RBFs) and finite volume
methods (FVM). The former allow to solve differential equations without the
cumbersome generation of a grid. Moreover, RBFs can be used to improve flawed grids.
The latter are particularly useful in the context of semiconductor device simulation.
They yield robust numerical solutions even in the presence of boundary layers. The presented
finite volume scheme additionally satisfies a discrete maximum principle, just like the
continuous semiconductor equations (the van Roosbroeck system).
26.01.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 The need for linear system solvers in dispersive wave modeling*
Jörn Behrens, UHH

Tsunami modeling is - to first (and very accurate) approximation - performed with the help of shallow water theory and equations. This is still the method of choice for many applications, including forecasting, hazard assessment and inundation modeling. However, for long propagation distances as well as highly nonuniform topographies dispersive effects become important. While truly dispersive model equations are fully three-dimensional and therefore expensive with respect to computational requirements, a common approach to dispersive modeling comprises a non-hydrostatic correction of shallow water equations. In order to derive this correction term, a linear system of equations needs to be solved in each time step - even when the time-stepping scheme is explicit.

In the presentation we will introduce the basic modeling concepts for tsunami simulation, will show the derivation of non-hydrostatic correction terms and motivate further research on solvers for linear systems of equations.
19.01.17 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Convergence of positive operator semigroups
Moritz Gerlach, Universität Potsdam

We give new conditions for strong convergence of positive operator
semigroups as time tends to infinity. This is achieved by a new approach
that combines the splitting theorem by Jacobs, de Leeuw and Glicksberg
with a purely algebraic result about positive group representations.
Thus, we obtain convergence theorems not only for one-parameter
semigroups but also for a much larger class of semigroup representations
without any continuity or regularity assumption in time.
In particular, this generalizes results from the literature that, under
technical assumptions, a bounded positive strongly continuous semigroup
that contains or dominates a kernel operator converges strongly as time
tends to infinity. One can also derive a generalization of a famous
theorem by Doob for operator semigroups on the space of measures.
15.12.16 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Optimierung von Pasteurisierungsprozessen
Lea Versbach

Ich werde in einem ca. 45 minütigen Vortrag meine Masterarbeit, die ich im Juni 2016 an der Uni Lund verteidigt habe, vorstellen.
Die Arbeit mit dem Titel ''Evaluation of a Gradient Free and a Gradient Based Optimization Algorithm for Industrial Beverage Pasteurisation Described by Different Modeling Variants'' entstand in Zusammenarbeit mit der Firma Krones AG in Kopenhagen.
Ziel ist die Optimierung thermaler Behandlung von Getränken und flüssigen Dosenkonserven. Dazu wurden Pasteurisierungsprozesse mathematisch formuliert, simuliert und die Optimierung mit Python durchgeführt.
13.12.16 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 The essential spectrum of Toeplitz operators on the unit disk
Raffael Hagger, Leibniz Universität Hannover

Consider the usual function space L^2(D) on the unit disk D and
the (closed) subspace of holomorphic functions A^2(D). An important class of bounded
linear operators arises by restricting multiplication operators M_f on L^2(D) to A^2(D). More
precisely, if P denotes the orthogonal projection onto A^2(D), one considers operators of
the form PM_f in A^2(D), so-called Toeplitz operators. In this talk we are going to study the
essential spectrum of these Toeplitz operators. It is a classical result that if the defining
symbol f is continuous up to the boundary, the essential spectrum can be obtained by
evaluating f at the boundary. As it turns out, this statement can be generalized to more
general symbols by using techniques that were developed to solve a similar problem on
the sequence space \ell^2(\Z).
12.12.16 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Nuklearität und Tensorprodukte*
Karsten Kruse

Im Vortrag wird es darum gehen, wie man eine vektorwertige Gleichung löst, wenn man die entsprechende Gleichung schon einmal skalarwertig gelöst hat. Typische Beispiele hierfür sind elliptische Differentialgleichungen. Hierbei geht es dann weniger darum, den Differentialoperator selbst zu untersuchen, sondern die Eigenschaften der Räume, auf denen er lebt.
24.11.16 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Fractional Powers of Linear Operators*
Jan Meichsner

Im wesentlichen ein 60 bis 90 minütiger Arbeitsstandbericht. Es werden grundlagen der Theorie fraktionaler Operatoren erläutert und danach auf die Problematik der Einführung durch harmonische Erweiterung eingegangen.
15.11.16 16:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Endliche Abschnitte des Fibonacci-Hamilton-Operators [Bachelorarbeit]
Hagen Söding, Studiengang TM
10.11.16 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Krylovraum-Verfahren für Sequenzen linearer Gleichungssysteme (Masterarbeitsvortrag)
Robin C. Ahrens
02.11.16 13:30 TUHH, Gebäude A, Raum A0.19 Vier konkrete Anwendungen von Toeplitzoperatoren*
Albrecht Böttcher, TU Chemnitz

Vier konkrete Anwendungen von Toeplitzoperatoren

Es werden vier konkrete und sehr unterschiedliche Anwendungen von Toeplitzoperatoren vorgestellt. Diese sind (1) ein Problem aus der optimalen ell-eins-Kontrolle, (2) Spektralfaktorisierung von Polynomen vom Grad 20000, (3) Berechnung des Volumens der Fundamentalgebiete gewisser hochdimensionaler Gitter, und (4) Bestimmung der Grenzmenge der Nullstellen von Polynomen vom Fibonacci-Typ in der Hausdorffmetrik. Der Vortrag erlaubt es, viermal abzuschalten und ebenso oft wieder einzusteigen.


Four concrete applications of Toeplitz operators

I present four concrete and very different applications of Toeplitz operators. These applications are (1) a problem in optimal ell-one control, (2) spectral factorization of polynomials of degree 20000, (3) computation of the volume of the fundamental domains of some high-dimensional lattices, and (4) the determination of the Hausdorff limit of the zero set of polynomials of the Fibonacci type. The talk allows you to switch off four times and to re-enter the same number of times.
27.10.16 09:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Verschiedene Methoden der Bildrestauration [Bachelorarbeit]
Franziska Sommer, Studiengang TM
17.10.16 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Variationsmethoden in der Bildregistrierung [Bachelorarbeit]
Björn Ludwig, Studiengang TM
13.10.16 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Mehrgitterverfahren zur Lösung der Helmholtzgleichung (Bachelorarbeit)
Clemens Oszkinat
12.10.16 12:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Iterative Lösung von dünnbesetzten Systemen aus Interpolationsaufgaben mit radialen Basisfunktionen (Bachelorarbeit)
Torben Jentzsch
12.10.16 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Präkonditionierung von indefiniten Problemen in Optimierungsaufgaben im Katastrophenmanagement (Bachelorarbeit)
Jannick Meyer
22.09.16 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Laplace-Transformation für Hyperfunktionen [Bachelorarbeit]
Lars Poppe, Studiengang TM
12.09.16 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Das Ising-Modell: Asymptotik von Toeplitzdeterminanten [Bachelorarbeit]
Louisa Granzow, Studiengang TM
07.09.16 16:30 Am Schwarzenberg-Campus 1 (A), Raum 0.019 3-Farben Ramsey-Zahl für pfadähnliche Graphen (Abschlussvortrag Bachelorarbeit)
Charlotte Knierim, Studiengang CS
25.08.16 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 The effect of the choice of time discretization on the accuracy of the computed population density function (Bachelorvortrag)
Selma Warnecke
21.07.16 11:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Unvollständige LR-Zerlegung der Matrix-Inversen (Bachelorvortrag)
Marten Hollm
20.07.16 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Efficient and Accurate Evaluation of Aggregation Integrals in Population Balance Equations
Lusine Shahmuradyan

The behaviour of particulate flow is mathematically modelled by population balance equations. The various terms of the equation model phenomena including particle transport, nucleation, growth, and aggregation. Their efficient numerical simulation requires sophisticated techniques, and various approaches proposed in the literature vary not only in computational complexity but also in the accuracy of the computed solutions. We will focus on the numerical treatment of aggregation integrals, the terms that model the aggregation process and which oftentimes dominate the overall simulation time. Within such a process, particles are characterized by a property coordinate x, e.g. the particle mass, the particle area, or the chemical composition, to mention only a few, and their distribution is quantified by a density distribution function f(x,t), which describes the property distribution of the particles at a given time t.

First, we discuss the evaluation of univariate aggregation integrals, where only one of particle characteristics is considered, and we discretise the property coordinate x through equidistant grids and approximate the density distribution f(x,t) through piecewise constant functions. Then, we extend the approach to grids with nested structures and approximation the density distribution through higher order polynomials (of degree p), which allow a better approximation. This novel approach reduces the quadratic complexity of its direct computation to an almost optimal complexity of order pNlogN with the problem size N. Furthermore, we also discuss examples of bivariate problems, where also a second property of particles is considered.

The key components of the developed algorithms are a separable approximation of the aggregation kernel, a nested grid consisting of piecewise uniform portions, application of FFT to compute the aggregation (convolution) on such uniform portions and orthogonality of basis functions which in combination lead to efficient recursion formulas. We provide extensive numerical tests for different initial setups to illustrate the performance of the developed algorithms with respect to their accuracy and efficiency, leading to (heuristic) strategies for the choice of discretization parameters.
20.07.16 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Leaky conical surfaces: spectral asymptotics, isoperimetric properties, and beyond
Dr. Vladimir Lotoreichik, Nuclear Physics Institute, Czech Academy of Sciences, Rez near Prague

Vortrag (PDF, 228KB)

13.07.16 13:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 H-Matrix Approximation for Scattered Data Interpolation
Michael Wende

Scattered data interpolation refers to an interpolation problem where the data sites are distributed irregularly within some domain. An interpolant may be constructed as a linear combination of radial basis functions centered at the data sites. Finding the coefficients in this representation leads to linear equations where the system matrices are large, dense, indefinite and ill-conditioned. These matrices can be approximated using the framework of hierarchical matrices. We will compare different approximation methods and discuss how to construct algebraic preconditioners.
07.07.16 14:15 Am Schwarzenberg-Campus 3 (E), Raum 3.074 IDR und Deflation
Stefan Möller

Es werden große dünnbesetzte Sattelpunktprobleme betrachtet, wie sie z.B. in der Strömungsmechanik auftreten. Diese i.A. unsymmetrischen und indefiniten Systeme können mittels iterativer Krylovraum-Verfahren, inkl. geeigneter Präkonditionierer, gelöst werden. Insbesondere werden sogenannte induzierte Dimensions-Reduktions-Methoden (IDR), im Speziellen QMRIDR(s), verwendet, welche zusätzlich mit einem Deflationsansatz gepaart werden. Dabei werden Informationen aus früheren Durchläufen derart recycelt, sodass es möglich ist, Sequenzen von linearen Systemen effektiv zu lösen. Als Beispiel werden die diskretisierten Oseen-Gleichungen betrachtet; weitere Anwendung kann dies darüber hinaus z.B. bei inneren Punkte-Verfahren in der linearen Optimierung finden.
04.07.16 16:15 Am Schwarzenberg-Campus 3 (A), Raum A 1.19.1 Oscillation in a posteriori error estimation
Andreas Veeser, Dipartimento di Matematica, Universita degli Studi di Milano

The goal of an a posteriori error analysis for an approximate PDE
solution is to establish the equivalence of error and a posteriori
estimator. Unfortunately, this equivalence is often only up to so-
called oscillation terms.

In this talk we shall clarify the reasons for the presence of
oscillation. Moreover, we propose a new approach to a posteriori error
estimation, where oscillation can be bounded by the error and so does
not longer spoil the aforementioned equivalence.

This is joint work with Christian Kreuzer (Bochum).
27.06.16 12:00 Raum H0.04 Die Eigenwerte eines Laplace-Operators mit Robinschen Randbedingungen
Dr. Konstantin Pankrashkin, Université Paris-Sud
24.06.16 10:30 Am Schwarzenberg-Campus 3 Building A Raum A.1.19.1 Trefftz discontinuous Galerkin methods for wave problems
Dr Andrea Moiola, University of Reading

We present a space-time discontinuous Galerkin (DG) method for linear
wave propagation problems.
The special feature of the scheme is that it is a Trefftz method,
namely that trial and test functions are solution of the partial
differential equation to be discretised in each element of the
(space-time) mesh.
The DG scheme is defined for unstructured meshes whose internal faces
need not be aligned to the space-time axes.
The Trefftz approach can be used to improve and ease the
implementation of explicit schemes based on ``tent-pitched'' meshes.
We show that the scheme is well-posed, quasi-optimal and dissipative,
and prove a priori error bounds for general Trefftz discrete spaces.
A concrete discretisation can be obtained using piecewise polynomials
that satisfy the wave equation elementwise, for which we show high
orders of convergence.
If time allows, we will describe a similar Trefftz-DG method for the
Helmholtz equation, i.e. wave equation in time-harmonic regime, for
which non-polynomial basis functions are used and quite a complete
theory has been established.
26.05.16 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Iterative Gleichungslöser für Markovketten (Bachelorarbeit)
Julia-Sophie Jürgensen
13.05.16 09:45 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Numerische Konvergenzanalyse für FEM auf nicht-konvexen polygonalen Gebieten
Ali Azarinejat

26.04.16 16:15 Am Schwarzenberg-Campus 3, Gebäude A, Raum A.0.01 und A.3.31 Solving the Vlasov equation in low-rank tensor format*
Dr. Katharina Kormann, Technische Universität München, Zentrum Mathematik - M16, Boltzmannstraße 3, 85747 Garching, Germany

The evolution of a plasma in external and self-consistent fields is modelled by the Vlasov equation for the distribution function in six dimensional phase space. Due to the high dimensionality and the development of small structures the numerical solution is very challenging. Grid-based methods
for the Vlasov equation have been shown to give accurate results but their use has mostly been limited to simulations in two or four dimensional phase space due to extensive memory requirements in higher dimensions. Compression of the solution via high-order singular value decomposition can help in reducing the storage requirements and the hierarchical Tucker format provides efficient basic linear algebra routines for low-rank representations of tensors.

In this talk, I will present a semi-Lagrangian scheme for the solution of the Vlasov equation represented as a low-parametric tensor. Interpolation formulas for the low-parametric tensor format as well as efficient implementations will be discussed. Numerical simulations for the Vlasov-Poisson equation are shown for the Landau damping test case in two, four, and six dimensional phase space as well as simulations with a constant magnetic field. Depending on the test case, the memory
requirements reduce by a factor $10^2$-$10^3$ in four and a factor $10^5$-$10^6$ in six dimensions compared to the full-grid method.
30.03.16 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Optimale Steuerung einer Laufkatze (Bachelorarbeit)
Max Ansorge
28.01.16 15:30 Am Schwarzenberg-Campus 1 (A), A1.20 Auxiliary Space Methods for Variational Problems in H{curl)*
Ralf Hiptmair, ETH Zürich

Auxiliary space preconditioning targets elliptic boundary value problems discetized by means of finite elements. The idea is to use a related discrete boundary value problem, for which efficient solvers are available, as a preconditioner. The connection between both problems is established by means of a suitable prolongation operator.

We apply this strategy to variational problems for the bilinear form $(\alpha(x)\cdot,\cdot)_0+(\beta(x)curl\cdot,curl\cdot)_0$ ($\alpha,\beta$ uniformly positive coefficient functions) posed on the function space $H(curl)$ (or $H_0(curl)$).
These are commonly encountered in magneto-quasistatic models for electromagnetic phenomena (eddy current models). Finite element Galerkin discretization usually relies on Nedelec's $H(curl)$-conforming edge elements, but discontinuous Galerkin (DG) methods are a viable option, too. In any case, one faces large sparse linear systems of equations, for which efficient preconditioners are badly needed. Three settings will be discussed:

I) When edge elements are used on a single unstructured mesh, coarser meshes needed for the application of geometric multigrid solvers may not be available. They may be easy to construct, however, for a semi-structured mesh, suggesting the use of an auxiliary edge element space on that mesh.
II) In the same setting as (I), algebraic multigrid methods (AMG) could look promising. Alas, AMG schemes for edge finite element discretizations that match the performance of those for $H^{1}$-conforming finite elements are not available. To harness standard nodal AMG schemes one may use an auxiliary space of continuous piecewise polynomial vectorfields.
III) Using a DG discretization on a standard triangulation, which may be required in the context of magneto-hydrodynamics, an edge element space may serve as auxiliary space.

For all these cases we present theoretical results about the performance of the preconditioner with focus on $h$-independence and robustness with respect to jumps of the coefficients. The main ideas needed to verify the abstract assumptions of the theory of auxiliary space preconditioning will be outlined.
25.01.16 11:00 SBC 1, Gebäude A, Raum A3.35.1 Interpolationsbasierte Reduzierte-Basis-Modellierung von Lösungskurven mit Umkehrpunkten (Promotionsvortrag)
Hagen Eichel
13.11.15 09:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Optimierung von NC-Daten anhand von NURBS-Originaldaten (Masterarbeit)
Sven Schwermer
05.11.15 15:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Hierarchical matrix preconditioners for linear systems in multivariate interpolation with radial basis functions (Masterarbeit)
Inga Drewel
30.10.15 11:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 PCE Erweiterung der Randintegralmethode für 2D Platinen (Bachelorarbeit)
Mostafa Nawabi
30.10.15 10:30 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Darstellung von Regelflächen als NURBS (Bachelorarbeit)
Atchcharan Skandarupan
30.09.15 09:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Zum Spektrum des Fibonacci Hamilton Operators [Bachelorarbeit]
Dennis Gallaun, Studiengang TM

Die Untersuchung des Elektronen- und Quantentransports von Quasikristallen führt auf das Spektrum des Fibonacci Hamilton Operators. Auch mathematisch ist das Spektrum interessant: Es ist eine Cantor-Menge mit Lebesgue-Maß Null.
Mit Hilfe eines Algorithmus zur Bestimmung der Faktoren des Fibonacci-Wortes lässt sich das Spektrum, mit einer in dieser Arbeit vorgestellten Methode, approximieren.
28.09.15 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Theorie und Anwendung symmetrisierender Präkonditionierer für elliptische PDEs (Bachelorarbeit)
Moritz Boehme

Einige iterative Lösungsverfahren für lineare Gleichungssysteme sind auf die Anwendung auf symmetrisch (positiv definite) Systeme beschränkt. Wir werden theoretische Ansätze aus der Literatur diskutieren, wie nicht-symmetrische Gleichungssysteme symmetrisiert werden können, Möglichkeiten der Realisierung ausarbeiten und diese auf ihre Rechenzeit testen. Motiviert durch diese Ansätze und deren Resultate werden wir im Rahmen dieser Arbeit eine Modifizierung bzw. Kombination der Ansätze vornehmen und vergleichende Tests durchführen.
18.09.15 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Rational Arnoldi methods*
Prof. Lothar Reichel, Department of Mathematical Sciences, Kent State University, Ohio, USA

The standard Arnoldi method is one of the most popular schemes for reducing a large matrix A to a small one. The method requires the evaluation of matrix-vector products with A. Rational Arnoldi methods reduce the matrix A by both evaluating matrix-vector products and solving linear systems of equations with A. Rational Arnoldi methods are attractive to use when A has a structure that allows efficient solution linear systems of equations with A. They are commonly applied to the computation of an invariant subspace of A and to the approximation of matrix functions. We discuss implementations of rational Arnoldi methods and compares their properties.
03.09.15 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Interpolationsbasierte Reduzierte-Basis-Modellierung von Lösungskurven mit Umkehrpunkten*
Hagen Eichel, Eröffnung des Promotionsverfahrens

Bei der numerischen Simulation physikalischer Prozesse treten häufig große parameterabhängige nichtlineare Gleichungssysteme auf. Zur Verringerung des Rechenaufwands werden oft Reduzierte-Basis-Methoden verwendet, die sich in lokale und globale Methoden unterscheiden lassen, wobei letztere Umkehrpunkte bezüglich des Parameters gewöhnlich nicht zulassen. In dieser Arbeit wird ein globaler, interpolationsbasierter Ansatz für Probleme mit Umkehrpunkten entwickelt und es werden die Vorteile und Grenzen dieser Methode aufgezeigt.
19.08.15 13:00 Am Schwarzenberg-Campus 3, Raum 3.074 Variationsmethoden in der Bildverarbeitung: Die Huber-Funktion im Regularisierungsterm [Bachelorarbeit]
Christoph Nicolai, Studiengang TM

Viele Variationsmethoden in der mathematischen Bildverarbeitung nutzen die 1-Norm des Gradienten, die sogenannte Totalvariation, als Regularisierungsterm. Diese Totalvariation hat die Eigenschaft, Kanten im Bild zuzulassen und zu erhalten. Sie kann aber auch zur Entstehung von unerwünschten Kanten beitragen, dem sogenannten Staircasing-Effekt. Diese Arbeit soll die Huber-Funktion, eine Kombination zweier Normen, als mögliche Alternative vorstellen.
17.08.15 12:30 Am Schwarzenberg-Campus 3, Raum 3.074 tba
Hendrik Vogt, Universität Bremen
24.06.15 14:30 Am Schwarzenberg-Campus 3, Raum 3.074 Erstellen einer Nurbs-Toolbox
Hogir Akan

08.06.15 13:00 Am Schwarzenberg-Campus 3, Raum 3.074 Form-Methoden zur Lösung von partiellen Differentialgleichungen
Karsten Poddig

12.05.15 13:00 Am Schwarzenberg-Campus 3, Raum 3.074 QD- und LR-Algorithmen für rangstrukturierte Eigenwertaufgaben (Masterarbeitsvortrag)
Michael Wende
08.05.15 10:00 Schwarzenbergstrasse 95E, Raum 3.074 On functional calculus estimates for Tadmor-Ritt operators
Felix Schwenninger, Twente

A linear operator $T$ on a Banach space is called Tadmor-Ritt if its spectrum is contained in the closed unit disc and the resolvent satisfies $C(T)=\sup_{|z|>1} \|(z-1)R(z,T)\|<\infty$. Such operators can be seen as discrete analog for sectorial operators.
We prove corresponding $H^{\infty}$-functional calculus estimates, which generalize and improve results by Vitse. Moreover, they are in conformity with the best so-far known power-bound for Tadmor-Ritt operators in terms of the constant $C(T)$.
We furthermore show the effect of having discrete square function estimates on the derived estimates.
22.04.15 15:00 Raum 0.14 in Gebäude A, Am Schwarzenberg Campus 1 Universality results in G(n,p)
Peter Allen, London School of Economics, UK

We say a graph $G$ is universal for a set of graphs $\mathcal{H}$ if for each $H\in\mathcal{H}$ we have $H\subset G$. There are several results stating that the random graph $G(n,p)$ is universal for various classes of graphs $\mathcal{H}$, for appropriate functions $p=p(n)$. In order for $p$ not to be very close to one, we need the graphs in $\mathcal{H}$ to be quite sparse. There are then (at least) three natural graph classes one could consider: trees, graphs with bounded degree, and graphs with bounded degeneracy. I will outline the current state of knowledge (mainly due to other people) and sketch one or two proofs
17.04.15 10:30 Schwarzenbergstrasse 95E, Raum 3.074 SQP-Methoden zur Strukturoptimierung von Fachwerken
Eike Schröder

09.04.15 16:00 Schwarzenbergstrasse 95E, Raum 3.074 On the spectrum of certain random operators: A link to Julia sets
Raffael Hagger

After the introduction of random matrices to nuclear physics by Eugene Wigner in 1955, random quantum systems have grown in popularity. Wigner's idea was to consider families of Hamiltonians that underlie a certain probability distribution to describe overly complicated systems. Of particular interest are, of course, the spectra of these Hamiltonians. In this talk we consider random, in general non-self-adjoint, tridiagonal operators on the Hilbert space of square-summable sequences. To model randomness, we use an approach by Davies that eliminates all probabilistic arguments.

Despite the rising interest, not much is known about the spectra of non-self-adjoint random operators. The Feinberg-Zee random hopping matrix reveals this in a beautiful manner. The boundary of its spectrum appears to be fractal, but a proof has not been found yet. While we can not give a proof either, we present a reason why this is very plausible. Certain tridiagonal operators share remarkable symmetries that allow us to enlarge known subsets of the spectrum by sizeable amounts. In some cases like the Feinberg-Zee random hopping matrix, this implies that the spectrum contains an infinite sequence of Julia sets.
19.03.15 15:00 Schwarzenbergstrasse 95E, Raum 3.074 Orthogonalization with a non-standard inner product and approximate inverse preconditioning*
Miro Rozložník, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic

One of the most important and frequently used preconditioning techniques for solving symmetric positive definite systems is based on computing the approximate inverse factorizations. It is also a well-known fact that such factors can be computed column-wise by the orthogonalization process applied to the unit basis vectors provided that we use a non-standard inner product induced by the positive definite system matrix A. In this contribution we consider the classical Gram-Schmidt algorithm (CGS), the modified Gram-Schmidt algorithm (MGS) and also yet another variant of sequential orthogonalization, which is motivated originally by the AINV preconditioner and which uses oblique projections.

The orthogonality between computed vectors is crucial for the quality of the preconditioner constructed in the approximate inverse factorization. While for the case of the standard inner product there exists a complete rounding error analysis for all main orthogonalization schemes, the numerical properties of the schemes with a non-standard inner product are much less understood. We will formulate results on the loss of orthogonality and on the factorization error for all previously mentioned orthogonalization schemes.

This contribution is joint work with Jiří Kopal (Technical University Liberec), Miroslav Tůma and Alicja Smoktunowicz (Warsaw University of Technology).
29.01.15 16:00 Schwarzenbergstrasse 95E, Raum 3.074 Sonneveld-Methoden und ihre strukturierten Büschel (III)
Jens-Peter M. Zemke

Die von Peter Sonneveld erdachten Methoden, allen voran die neueste, IDR(s), können zur approximativen Eigenwertberechnung linearer Operatoren herangezogen werden. Im Gegensatz zu klassischen Krylovraumverfahren, welche Tridiagonal- oder Hessenbergmatrizen berechnen, berechnen Sonneveld-Methoden Büschel aus einer Band-Hessenbergmatrix und einer oberen Band-Dreiecksmatrix, von denen einige Eigenwerte bekannt sind. Basierend auf einer trivialen Beobachtung präsentieren wir Wege, die anderen Eigenwerte stabil zu berechnen.
29.01.15 12:00 Schwarzenbergstrasse 95E, Raum 3.074 Decompositions of highly connected graphs into paths of length five
PhD Guilherme Mota, Departamento de Ciência da Computação, Instituto de Matemática e Estatística - IME, USP, Brasil

We study the Decomposition Conjecture posed by Barát and Thomassen (2006), which states that for every tree T there exists a natural number k_T such that, if G is a k_T-edge-connected graph and |E(T)| divides |E(G)|, then G admits a decomposition into copies of T. This conjecture was verified for stars, some bistars, paths whose length is a power of 2, and paths of length 3. We verify the Decomposition Conjecture for paths of length 5. In this talk I will discuss the ideas behind the proof of this result.
22.01.15 16:00 Schwarzenbergstrasse 95E, Raum 3.074 Sonneveld-Methoden und ihre strukturierten Büschel (II)
Jens-Peter M. Zemke

Die von Peter Sonneveld erdachten Methoden, allen voran die neueste, IDR(s), können zur approximativen Eigenwertberechnung linearer Operatoren herangezogen werden. Im Gegensatz zu klassischen Krylovraumverfahren, welche Tridiagonal- oder Hessenbergmatrizen berechnen, berechnen Sonneveld-Methoden Büschel aus einer Band-Hessenbergmatrix und einer oberen Band-Dreiecksmatrix, von denen einige Eigenwerte bekannt sind. Basierend auf einer trivialen Beobachtung präsentieren wir Wege, die anderen Eigenwerte stabil zu berechnen.
08.01.15 12:00 Schwarzenbergstrasse 95E, Raum 3.074 The smallest-weight multiway cut problem for trees
Peter Heinig, Uni HH, FSP Diskrete Mathematik, Bundesstr. 55 (Geomatikum) 20146 Hamburg

The following is NP-hard in general:
given an edge-weighted finite graph and a set of special vertices,
compute a minimum-weight set of edges whose removal disconnects
any special vertex from any other special vertex.
Very efficient algorithms via LP-duality are known for natural subsets of graphs, though,
such as finite trees. Basic theoretical duality-type questions remain open for infinite trees.
To prepare for future talks on the problems about infinite trees,
I will explain an efficient algorithm solving the problem for finite trees.
18.12.14 16:00 Schwarzenbergstrasse 95E, Raum 3.074 Sonneveld-Methoden und ihre strukturierten Büschel
Jens-Peter M. Zemke

Die von Peter Sonneveld erdachten Methoden, allen voran die neueste, IDR(s), können zur approximativen Eigenwertberechnung linearer Operatoren herangezogen werden. Im Gegensatz zu klassischen Krylovraumverfahren, welche Tridiagonal- oder Hessenbergmatrizen berechnen, berechnen Sonneveld-Methoden Büschel aus einer Band-Hessenbergmatrix und einer oberen Band-Dreiecksmatrix, von denen einige Eigenwerte bekannt sind. Basierend auf einer trivialen Beobachtung präsentieren wir Wege, die anderen Eigenwerte stabil zu berechnen.
05.12.14 14:00 Schwarzenbergstrasse 95E, Raum 3.074 H²-matrix methods for boundary integral equations*
Steffen Börm, Christian-Albrechts-Universität Kiel

Boundary integral equations are an important tool for analyzing elliptic partial differential equations arising, e.g., in structural mechanics or the simulation of acoustic or electromagnetic fields. Standard discretization techniques lead to large and densely populated matrices that require special algorithms.

The H²-matrix method offers efficient compression schemes for large matrices and can also perform algebraic operations like multiplication, inversion or factorization directly on the compressed matrices.

This talk gives an introduction to the basic concepts of H²-matrices and routlines two recent results: the Green hybrid compression scheme can be used to construct compressed approximations of discretized boundary element systems. Preconditioners for these systems can be constructed by applying a sequence of local low-rank updates to H²-matrices.
20.11.14 16:00 Schwarzenbergstrasse 95E, Raum 3.074 TBA
Marco Frego
13.11.14 15:30 Schwarzenbergstrasse 93, Raum A1.20 Recursive Low-Rank Truncation*
Wolfgang Hackbusch, Max-Planck-Institut für Mathematik in den Naturwissenschaften

The best approximation of a matrix by a low-rank matrix can be obtained by the singular value decomposition. For large-sized matrices this approach is too costly. Instead one may use a block decomposition. Approximating the smaller
block matrices by low-rank matrices and agglomerating them into a new, coarser
block decomposition, one obtains a recursive method. The required computation work is O(rnm) where r is the desired rank and n x m is the size of the matrix. New estimates are presented for the errors A-B and M-A,
where A is the result of the recursive truncation applied to M, while B is the best approximation.
10.11.14 16:00 Schwarzenbergstrasse 95E, Raum 3.074 Homogenization meets Operator-Theory
Marcus Waurick, TU Dresden

Homogenization theory comprises the study of heterogeneous
materials. In mathematical terms this goes along with the discussion of
differential equations with oscillatory coefficients and the behavior of the
respective solutions, when the oscillations become infinitely fast. The aim in homogenization theory is to show convergence of the solutions for infinitely fast oscillations and to find an effective equation satisfied by the limit. In a Hilbert space setting, we discuss homogenization of ordinary differential equations and give an operator-theoretic reason, when it is likely that the limit equation is of integro-differential type -- in contrast to the equation one started out with. We also discuss possible generalizations to non-autonomous and/or partial differential equations.
21.10.14 15:00 Schwarzenbergstrasse 95E, Raum 3.074 Topologie-Optimierung von Fachwerkstrukturen
Ali Azarinejat

08.10.14 16:30 Schwarzenbergstrasse 95E, Raum 3.074 Modeling and Optimization of Raw Material Blending Processes
Abschlussvortrag Mas Ayca Cangel, Mathematik, Diskrete Mathematik
22.09.14 14:00 Schwarzenbergstrasse 95E, Raum 3.074 Implementierung der Konturintegralmethode auf ebenen Bauteilen
Joshua Engels

27.08.14 10:15 Schwarzenbergstrasse 95E, Raum 3.023/24(!) Direkte und inverse Spektralprobleme am Beispiel des Laplace-Operators - Was verrät das Spektrum einer Trommel über ihre Gestalt? [Bachelorarbeitsvortrag]
Lennart Bargsten
22.08.14 10:30 Schwarzenbergstrasse 95E, Raum 3.074 Anwendung von Pseudospektren in der Regelungstechnik [Bachelorarbeitsvortrag]
Moritz Wolter
04.08.14 11:00 Schwarzenbergstrasse 95E, Raum 3.074 Directed cycle double covers and cut-obstacles
Andrea Jiménez, Instituto de Matemática e Estatística da Universidade de São Paulo, Atlanta and Sao Paulo

In this talk, we discuss our recent progress on the famous directed cycle double cover conjecture of Jaeger. We define the class of trigraphs and prove that a graph connections conjecture formulated on trigraphs implies general Jaeger's conjecture. In addition, we give supporting evidence for our conjecture. This is joint work with Martin Loebl.
04.08.14 09:00 Schwarzenbergstrasse 95E, Raum 3.074 Searching for defective subsets using queries of fixed size
Dominik Vu, University of Memphis

Given an $n$-element set which contains a known number $d$ of unknown special elements, we are allowed to use an oracle which accepts queries of size $k$ and responds positively if at least one of the elements of the queried set is in our set of unknowns. The case of a single unknown element has been studied and solved in the past by Rényi (1961), Katona (1966) and more recently by Hosszu, Tapolcai and Wiener (2013). We generalise their results in both the adaptive (on-line) and non-adaptive (parallelised) case for general d. Our approach provides new links between separability and (hyper-)graph girth, as well as new bounds for the problem.
This is joint work with F. Benevides, D. Gerbner and C. Palmer.
08.07.14 15:30 Schwarzenbergstrasse 95E, Raum 3.074 TBA
Helena Jenderek
01.07.14 15:45 Schwarzenbergstrasse 95E, Raum 3.074 Immer wieder Hurwitz Neues über unendliche, total nichtnegative Matrizen und eine alte Bemerkung B.Riemanns
Dr. Prashant Batra, Institut für Rechnertechnologie, Schwarzenbergstrasse 95E, Raum 3.074

In Zusammenhang mit der Nullstellenlage von Polynomen welche ausschließlich nichtnegative Koeffizienten aufweisen wurden von Holtz und Tyaglov (SIAM Review, 2012) speziell strukturierte, unendliche Matrizen betrachtet, deren Minoren sämtlich nicht-negativ sind genau dann, wenn das Polynom nur negative Nullstellen besitzt.

Wir werden zum einen diese aufwendige Charakterisierung der
Nullstellenlage von Polynomen deutlich vereinfachen, desweiteren den Satz von Holtz und Tyaglov auf eine Klasse ganzer Funktionen ausweiten sowie den Bezug zu bekannten Klassen total nichtnegativer Matrizen herstellen.

Als mathematische Anwendungen erhalten wir einen einfachen, unabhängigen Beweis der Charakterisierung von Holtz-Tyaglov, eine neue Verknüpungseigenschaft der betrachteten Matrizen sowie eine Charakterisierung der Nullstellenlage spezieller ganzer Funktionen.
30.06.14 15:00 Schwarzenbergstrasse 95E, Raum 3.074 Domain Decomposition for elliptic PDE eigenvalue problems*
Lars Grasedyck, RWTH Aachen

We consider the solution of a rather simple class of eigenvalue problems $Ax=\lambda{Mx}$ for symmetric positive definite matrices $A$,$M$ that stem, e.g., from the discretisation of a PDE eigenvalue problem. Thus, the problem is in principle simple, but the matrices $A$ and $M$ are large-scale and we would like to compute all relevant eigenvalues, where relevant is to be understood in the sense that all eigenvalues should be computed that can be captured by the discretisation of the continuous PDE eigenvalue problem.

We propose a new method for the solution of such eigenvalue problems.
The new method combines ideas of domain decomposition, as in the automated multi-level substructuring (short AMLS) or component mode synthesis, with the concept of hierarchical matrices (short $\cal{H}$-matrices) in order to obtain a solver that scales almost linearly (linear up to logarithmic factors) in the size of the discrete space, i.e. the size $N$ of the linear system times the number of sought eigenvectors. Whereas the classical AMLS method is very effective for PDEs posed in two dimensions, it is getting very expensive in the three-dimensional case, due to the fact that the interface coupling in the domain decomposition requires dense matrix operations. We resolve this problem by use of data-sparse hierarchical matrices. In addition to the discretisation error our new approach involves a projection error due to AMLS and an arithmetic error due to $\cal{H}$-matrix approximation. We will shortly analyse the complexity in theory and practice, and consider several numerical examples that underline the performance of the solver.
24.06.14 15:30 Schwarzenbergstrasse 95E, Raum 3.074 A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations*
Leo Rebholz

We prove that in finite element settings where the divergence-free subspace of the velocity space has optimal approximation properties, the solution of Chorin/Temam projection methods for Navier-Stokes equations equipped with grad-div stabilization with parameter $\gamma$, converge to the associated coupled method solution with rate $\gamma^{-1}$ as $\gamma\rightarrow \infty$. We prove this first for backward Euler schemes, and then extend the results to BDF2 schemes, and finally to schemes with outflow boundary conditions. Several numerical experiments are given which verify the convergence rate, and show how using projection methods in this setting with large grad-div stabilization parameters can dramatically improve accuracy.
20.06.14 11:15 Firma Röders, Soltau Formwahrende Interpolation von NC-Daten [Masterarbeitsvortrag]
Michael Seeck
03.06.14 14:30 Schwarzenbergstrasse 95E, Raum 3.074 Evaluation of Coalescence Integrals in PBE on equidistant grids
Lusine Shahmuradyan
28.05.14 14:15 Schwarzenbergstrasse 95E, Raum 3.074 Where is the main diagonal of my bi-infinite matrix?
Marko Lindner

Sometimes it is convenient to have a bi-infinite enumeration of the basis elements in the domain and image spaces of an operator A - leading to a representation of A by a bi-infinite matrix.
Shifting one of these enumerations shifts the matrix and hence changes the main diagonal. So which diagonal is ''the'' main diagonal? Isreal Gohberg once diplomatically said that in a bi-infinite matrix, it is every diagonal's right to claim to be the main diagonal. However, there are concrete problems in numerics and in matrix algebra that require a concrete choice - and, as it turns out, the choices coincide: From a certain point of view, there is one distinguished diagonal that deserves being called the main diagonal (a bit more than the others). We show how to find it and we discuss examples.

This is joint work with Gilbert Strang.
13.05.14 15:30 Schwarzenbergstrasse 95E, Raum 3.074 tba
Torge Schmidt
08.05.14 14:00 Schwarzenbergstrasse 95E, Raum 3.074 Applications of Tutte's tree decomposition in the enumeration of bipartite graph families
Prof. Juanjo Rue Perna, FU Berlin

We adapt the grammar introduced by Chapuy, Fusy, Kang and Shoilekova to study bipartite graph families which are defined by their 3-connected components. More precisely, in this talk I will explain how to get the counting formulas for bipartite series-parallel graphs (and more generally of the Ising model over this family of graphs), as well as asymptotic estimates for the number of such graphs with a fixed size. This talk is based in a work in progress joint with Kerstin Weller.
06.05.14 15:30 Schwarzenbergstrasse 95E, Raum 3.074 TBA
Karsten Kruse
29.04.14 15:30 Schwarzenbergstrasse 95E, Raum 3.074 Numerical Ranges and Random Operators
Raffael Hagger
24.04.14 16:00 Schwarzenbergstrasse 95E, Raum 3.074 Preconditioners for time-dependent PDE-constrained optimization*
Martin Stoll, MPI Magdeburg
17.04.14 11:00 Schwarzenbergstrasse 95E, Raum 3.074 Störung positiver Halbgruppen, und Kernabschätzungen
Christian Seifert

... ist vielleicht nur für die Analytiker interessant.
18.02.14 15:00 Schwarzenbergstrasse 93, Gebäude A, Raum A0.14 Tight cycles and regular slices in dense hypergraphs
Dr. Peter Allen, London School of Economics, UK

We describe a general approach to the strong hypergraph regularity lemma, which we call 'regular slices', which avoids many of the usual technical complications and retains the features one would like to use in extremal hypergraph theory. This talk will avoid painful technical details in so far as that is possible and focus on an application, proving a hypergraph extension of the Erdos-Gallai theorem.

This is joint work with Julia Böttcher, Oliver Cooley and Richard Mycroft.
18.02.14 14:00 Schwarzenbergstrasse 93, Gebäude A, Raum A0.14 Sparse blow-up lemmas and maker-breaker games
Dr. Julia Böttcher, London School of Economics, UK

The blow-up lemma of Komlós, Sárközy and Szemerédi is an important tool for embedding large graphs H into dense graphs G. We recently obtained versions of this lemma for subgraphs G of sparse random and pseudo-random graphs. This has important applications in extremal graph theory on random graphs, but can also be used for the analysis of certain maker-breaker games.

In the talk I will explain our blow-up lemmas and describe their connection to maker-breaker games, after giving some necessary background.

Joint work with P. Allen, H. Hàn, Y. Kohayakawa, Y. Person.
31.01.14 14:00 Schwarzenbergstrasse 95E, Raum 3.074 tba
Anton Schiela
14.01.14 13:30 Schwarzenbergstrasse 95E, Raum 3.074 Wannier transform for Schrödinger operators with aperiodic potential
Siegfried Beckus, FSU Jena
09.01.14 14:15 Schwarzenbergstrasse 95E, Raum 3.074 Adaptive Sparse Grids and Applications: Coping with the Curse of Dimensionality
Dirk Pflüger, Stuttgart

High dimensionalities are a major roadblock for the numerical solution of problems in computational sciences. Straightforward discretizations are severely limited by the curse of dimensionality, the exponential dependency of the overall computational effort on the number of dimensions. It is therefore typically not feasible to treat more than four dimensions. In this talk, I will give a short introduction to Sparse Grids, which provide a versatile way to overcome the curse of dimensionality to a large extent, and show some of their applications. A special focus will be on spatially adaptive refinement, which adapts to the peculiarities of the problem at hand, and on adapted basis functions. Both are crucial whenever only few grid points can be spent, or where real-world problems do not meet the underlying smoothness requirements. The hierarchical basis formulation of the direct Sparse Grid approach conveniently provides a reasonable criterion for spatially adaptive refinement practically for free. This can serve as a starting point to develop suitable and problem-adapted modifications.
19.12.13 14:15 Schwarzenbergstrasse 95E, Raum 3.074 Diskrete Mathematik an der TUHH
Anusch Taraz

In this talk we survey the research activities and interests of the discrete maths group at TUHH.
We will discuss various topics such as colourings of embeddable graphs and hypergraphs, computational convexity, minimum bisection problems, and random graphs.
12.12.13 14:15 Schwarzenbergstrasse 95E, Raum 3.074 Fast Convolution
Lusine Shahmuradyan
28.11.13 14:15 Schwarzenbergstrasse 95E, Raum 3.074 IDR Verfahren
Stefan Möller
26.11.13 13:45 Schwarzenbergstrasse 95A, Raum A1.16 On Additivity and Fixing Numbers of Matrices: Uniqueness in Discrete Tomography
Dr. Barbara Langfeld, Christian-Albrechts-Universitat zu Kiel

This talk gives an overview of some classical and recent uniqueness results in Discrete Tomography. In the first part we will review the concept of J-additivity and apply it to settle a problem of Kuba on 3-dimensional lattice sets and a conjecture of Brunetti and Daurat on planar lattice convex sets. The second part of the talk deals with the computational complexity of finding a smallest set of lattice positions of a given lattice set whose disclosure yields uniqueness w.r.t. some given X-rays. It turns out that this problem is already NP-hard in the plane and for the two standard directions.

This is joint work with Peter Gritzmann and Markus Wiegelmann.
21.11.13 15:30 Schwarzenbergstrasse 95E, Raum 3.074 Methoden zur Verbesserung der Interpolation von NC-Daten auf Basis der kubischen Splineinterpolation
Tobias Hecht
31.10.13 14:15 Schwarzenbergstrasse 95E, Raum 3.074 Studie zur Kompensation von Radialen Spindelverlagerungen bei Werkzeugmaschinen
Saman Fröhlich
18.10.13 10:30 Schwarzenbergstrasse 95A, Raum A1.20 Preconditioners for two-sided eigenvalue problems and applications to model order reduction
Melina Freitag, Bath, UK
17.10.13 14:15 Schwarzenbergstrasse 95E, Raum 3.074 On the Role of the Helmholtz Decomposition in Mixed Methods for Incompressible Flows and a New Variational Crime*
Alexander Linke, WIAS Berlin

According to the Helmholtz decomposition, the irrotational parts of the momentum balance equations of the incompressible Navier-Stokes equations are balanced by the pressure gradient. Unfortunately, nearly all mixed methods for incompressible flows violate this fundamental property, resulting in the well-known numerical instability of poor mass conservation. The origin of this problem is the lack of L2-orthogonality between discretely divergence-free velocities and irrotational vector fields. Therefore, a new variational crime for the nonconforming Crouzeix-Raviart element is proposed, where divergence-free, lowest-order Raviart-Thomas velocity reconstructions reestablish L2-orthogonality. This approach allows to construct a cheap flow discretization for general 2d and 3d simplex meshes that possesses the same advantageous robustness properties like divergence-free flow solvers. In the Stokes case, optimal a-priori error estimates for the velocity gradients and the pressure are derived. Moreover, the discrete velocity is independent of the continuous pressure. Several detailed linear and nonlinear numerical examples illustrate the theoretical findings.
08.08.13 14:00 Schwarzenbergstrasse 95E, Raum 3.074 A Well-balanced bicharacteristic-based scheme for two-layer shallow water flows including wet/dry fronts
Michael Dudzinski
31.07.13 10:00 Schwarzenbergstrasse 95E, Raum 1.050 Asymmetrische Galerkinverfahren in der Signalverarbeitung (Bachelorarbeitsvortrag)
Djamschid Safi
04.07.13 14:00 Schwarzenbergstraße 95H, Raum H0.03 Numerical Treatment of Tensors*
Wolfgang Hackbusch, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig

The numerical treatment of tensors and the use of tensors for various numerical problem has rapidly increased in the last time. It is now applied to many fields in analysis (treatment of pdes, representation of multivariate functions, etc.). The key for an efficient numerical treatment is a suitable format. We discuss the various formats, their properties, and operations with tensors.

Literature: W. H.: Tensor spaces and numerical tensor calculus. Springer 2012
02.07.13 14:15 Big lecture hall at the Biocenter Grindel and Zoological Museum, Martin-Luther-King-Platz 3, 20146 H Compact course: An introduction to H-matrices, Part II
Prof. Dr. Dr. h.c. Wolfgang Hackbusch
02.07.13 10:15 Big lecture hall at the Biocenter Grindel and Zoological Museum, Martin-Luther-King-Platz 3, 20146 H Compact course: An introduction to H-matrices, Part I
Prof. Dr. Dr. h.c. Wolfgang Hackbusch
27.06.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Basisreduktionsmethoden für lineare und nichtlineare Systeme
Hagen Eichel
20.06.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Von zufälligen dynamischen Systemen zu präkonditionierten iterativen Lösern
Helena Jenderek
13.06.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Inexakte Projektionsverfahren zur Lösung linearer und nichtlinearer Eigenwertaufgaben
Nicolai Rehbein
06.06.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Ohne
Annika Eichler
30.05.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Zufällige Operatoren und Spektraltheorie
Raffael Hagger
29.05.13 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Geometrie und Spektraltheorie von Graphen und Dirichletformen
Daniel Lenz
29.05.13 13:30 Schwarzenbergstrasse 95E, Raum 1.050 H-Matrizen für Finite-Differenzen Matrizen*
Dominik Enseleit, UHH, UHH

Die Technik der Hierarchischen Matrizen H-Matrizen) ermöglicht die Berechnung einer approximativen H-Inversen oder H-LU-Zerlegung in fast linearer Komplexität und kann auf diese Weise zur effizienten Lösung linearer Gleichungssysteme eingesetzt werden. Vor der Verwendung der H-Matrix-Technik ist zu untersuchen, ob eine H-Matrix Approximation der Inversen bzw. der Faktoren der LU-Zerlegung existiert.
Resultate dieser Form konnten bereits für diverse Matrizen (z.B. Finite-Element-Matrizen) gezeigt werden, im Finite-Differenzen-Kontext sind jedoch keine Veröffentlichungen zum Einsatz der H-Matrix-Technik bekannt. Mit der Zielsetzung die Anwendbarkeit der H-Matrix-Technik für eine Finite-Differenzen-Matrix aus dem meteorologischen Transport- und Strömungsmodell METRAS zu untersuchen, wird in diesem Vortrag ein Resultat für Finite-Differenzen-Matrizen vorgestellt. Aufbauend auf dem methodischen Ansatz für Finite-Element-Matrizen wird die Existenz einer H-Matrix Approximation der Inversen von Finite-Differenzen-Matrizen gezeigt.
Die Ergebnisse können mittels numerischer Tests bestätigt werden. Bei Testproblemen, die in Anlehnung an das Gleichungssystem aus dem Modell METRAS aufgestellt werden, lässt sich im Einklang mit den theoretischen Ergebnissen jedoch eine Verschlechterung des Fehlerverlaufs in Abhängigkeit von einem Parameter feststellen. Für diese Fälle wird eine modifizierte Partitionierungsstrategie vorgestellt, deren Verwendung zu deutlich besseren Ergebnissen führt.
16.05.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Spaß mit Integraloperatoren
Torge Schmidt
25.04.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Kondensationen
Prof. Dr. Wolfgang Mackens
18.04.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Darstellung und Approximation von Tensoren im Hierarchischen Format
Stefan Kühn, MPI, Leipzig

Die effiziente Darstellung und Approximation von Tensoren gewinnt in vielen Anwendungsbereichen der Mathematik wie Quantenchemie und -physik und auch generell innerhalb der Numerik immer mehr an Bedeutung. In diesem Vortrag werden wir ein neues Format zur Darstellung von hochdimensionalen
Tensoren vorstellen - das sogenannte Hierarchische Format oder auch Hierarchische Tucker-Format - und die grundlegende Arbeitsweise einer darauf basierenden inexakten Arithmetik erläutern. Der Schwerpunkt liegt auf der Approximation von Tensoren, sowie den Vorteilen des neuen Formates im Vergleich zu Standardformaten wie dem kanonischen Format oder der
31.01.13 14:00 Schwarzenbergstrasse 95E, Raum 1.050 Variationelle Charakterisierung von Eigenwerten nichtlinearer Eigenwertaufgaben
Heinrich Voß
30.01.13 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Potentialstörungen akkretiver Operatoren und elliptische Operatoren in Divergenzform
Hendrik Vogt
22.01.13 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Titchmarsh-Weyl theory for elliptic differential operators on unbounded domains*
Jussi Behrndt, TU Graz, Österreich

In this talk we describe the spectral properties of selfadjoint Schrödinger operators on unbounded domains with
an associated Dirichlet-to-Neumann map. In particular, a
characterization of the isolated and embedded eigenvalues, the corresponding eigenspaces, as well as the continuous and absolutely continuous spectrum in terms of the limiting behaviour of the Dirichlet-to-Neumann map is obtained. Furthermore, a sufficient criterion for the absence of singular continuous spectrum is provided. The results are natural multidimensional analogues of classical facts from singular
Sturm–Liouville theory.
19.12.12 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Wissenswertes über Krylov-Raum-Verfahren
Jens-Peter M. Zemke
17.12.12 10:00 Schwarzenbergstrasse 95E, Raum 1.050 Some relations between discrete and continuous Laplacians, and averaging operators on graphs
Dr. rer. nat. Konstantin Pankrashkin
12.12.12 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Robust successive computation of eigenpairs for nonlinear eigenvalue problems*
Cedric Effenberger, École polytechnique fédérale de Lausanne EPFL, Lausanne

We consider eigenvalue problems which are nonlinear in the eigenvalue
parameter. Newton-based methods are well-established techniques for determining individual eigenpairs of such nonlinear eigenvalue problems. If a larger number of eigenpairs is sought, however, the tendency of these methods to re-converge to previously discovered eigenpairs is a hindrance. In this talk, a deflation strategy for nonlinear eigenvalue problems will be presented, which overcomes this limitation in a natural way. Furthermore, we will comment on how this deflation approach can be implemented in a Jacobi-Davidson framework with only minimal overhead.
05.12.12 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Verschiedene Transporteigenschaften
Christian Seifert
28.11.12 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Invariant pairs for nonlinear eigenvalue problems*
Prof. Dr. Daniel Kressner, École polytechnique fédérale de Lausanne EPFL, Lausanne

The concept of invariant subspaces is fundamental to linear eigenvalue problems and provides an important theoretical foundation in the design of numerical eigenvalue solvers. It turns out that there is no straightforward extension of this concept to eigenvalue problems that are nonlinear in the eigenvalue parameter. One obstacle is that eigenvectors belonging to different eigenvalues may become linearly dependent in the nonlinear case. Invariant pairs offer an elegant way to avoid this obstacle and appear to be the most natural extension of invariant subspaces. In this talk, we give an overview of the properties of invariant pairs and explain how they can be used in the design of numerical algorithms for nonlinear eigenvalue problems, as they arise for example in band diagram calculations for photonic crystals and fluid-structure interaction problems.
21.11.12 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Über kleine, große und ganz große Matrizen
Marko Lindner
31.10.12 15:00 Schwarzenbergstrasse 95E, Raum 1.050 Ein Streifzug durch allerlei
Sabine Le Borne
24.10.12 15:00 Schwarzenbergstrasse 95, Raum 1.050 Schrödinger-Operatoren mit kompakter Resolvente*
Peter Stollmann, TU Chemnitz, TU Chemnitz, Fakultät für Mathematik, 09107 Chemnitz

Ein klassischer Satz von Friedrichs besagt, dass Schrödingeroperatoren kompakte Resolvente besitzen, wenn das zugrundeliegende Potential bei Unendlich gegen Unendlich geht. In diesem Vortrag werden wir einen einfachen Beweis einer Verallgemeinerung präsentieren, basierend auf einer gemeinsamen Arbeit mit D. Lenz (Jena) und D. Wingert.
02.10.12 14:00 Schwarzenbergstrasse 95 E, Raum 3.032 Varianten der Eigenvektorberechnung mittels Algorithmen basierend auf Induzierter Dimensions-Reduktion (IDR) (Bachelorarbeitsvortrag)
Nina T. Piontek
26.09.12 16:00 Schwarzenbergstrasse 95 D, Raum D0013 Anwendung eines auf Induzierter Dimensions-Reduktion basierenden Eigenwertlösers auf ein FEM-Modell (Bachelorarbeitsvortrag)
Aulikki Wilhelmi genannt Hofmann
26.09.12 15:00 Schwarzenbergstrasse 95 D, Raum D0013 Vergleich der drei Hauptklassen von Krylov-Raum-Verfahren zur Eigenwertberechnung an ausgewählten Beispielen aus der FEM-Analyse (Bachelorarbeitsvortrag)
Sarajaddin Rahmani
05.09.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 Contributions to the Optimal Choice of Parameters in Induced Dimension Reduction algorithms (Masterarbeitsvortrag)
Olaf Rendel
22.08.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 Vergleich von Lanczos- und Sonneveld-Algorithmen zur Lösung großer dünnbesetzter linearer Gleichungssysteme über endlichen Körpern an Beispielen aus der Kryptographie (Bachelorarbeitsvortrag)
Matthias Marx
08.08.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 Zur optimalen Wahl der Parameter in präkonditioniertem Multi-Shift QMRIDR am Beispiel der Helmholtz-Gleichung (Bachelorarbeitsvortrag)
Michael Garben
22.06.12 10:00 Schwarzenbergstrasse 95, Raum 3.053 Vergleich dreier Klassen von Krylov-Raum-Verfahren an ausgewählten Beispielen aus der FEM-Analyse (Bachelorarbeitsvortrag)
Mehran Majidi
15.06.12 09:00 Schwarzenbergstrasse 95, Raum 3.053 Approximation of convergence rates of the Lanczos iteration through potential theory (Bachelorarbeitsvortrag)
Dawid Golebiewski
14.03.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 The Lanczos algorithms and their relations to formal orthogonal polynomials, Padé approximation, continued fractions, and the qd algorithm*
Martin Gutknecht, ETH Zurich; Seminar for Applied Mathematics, LEO D3 (Leonhardstrasse 27), 8092 Zurich, Switzerland

In their seminal 1952 paper on the conjugate gradient (CG) method Hestenes and Stiefel pointed out that their method, which is applicable to linear systems of equations with symmetric positive definite matrix only, is closely related to certain orthogonal polynomials, the corresponding Gauss quadrature formulas, certain continued fractions, and their convergents (or `partial sums'). The latter can be seen to be Padé approximants of a function that involves the resolvent of the matrix.

Around the same time, in 1950 and 1952, Cornelius Lanczos published two related articles, of which the second one introduced a precursor of the biconjugate gradient (BCG or BiCG) method, which generalizes CG to the case of a nonsymmetric system. Here, the residual polynomials are formal orthogonal polynomials only, but the connections to continued fractions and Padé approximants persist. Moreover, there is a relation to the qd algorithm of Rutishauser (1954). The understanding of all these connections became probably the key to Rutishauser's discovery of the LR algorithm (1955, 1958), which was later enhanced by John G.F. Francis to the ubiquitous QR algorithm (1961/62).
29.02.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 Solving large nonsymmetric linear systems with IDR(s) on a geographically separated cluster of parallel computers*
Martin van Gijzen, Delft University of Technology; Faculty of Electrical Engineering, Mathematics and Computer Science, Mekelweg 4; 2628 CD Delft; The Netherlands

The IDR(s) method is a family of fast algorithms for iteratively solving large nonsymmetric linear systems. In the talk we will discuss an IDR(s) variant that is specifically tuned for parallel and grid computing. In particular in grid computing the inner product is a bottleneck operation. We will discuss three techniques that we have used to alleviate this bottleneck in IDR(s). Firstly, the efficient and stable IDR(s)-biortho method is reformulated in such a way that it has a single global synchronisation point per iteration step. Secondly, the so-called test matrix is chosen so that the work, communication, and storage involving this matrix is minimised in multi-cluster environments. Finally, a methodology is presented for a-priori estimation of the optimal value of s using only problem and machine--based parameters. We will also discuss a preconditioned version of IDR(s) that is particularly suited for grid computing. We will illustrate our results with numerical experiments on the DAS--3 Grid computer, which consists of five cluster computers located at geographically separated places in the Netherlands.

This is joint work with Tijmen Collignon.
15.02.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 An Optimization Problem Corresponding To a Nonlinear Eigenvalue Problem On a Rearrangement Class
Abbasali Mohammadi
01.02.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 Inexakte Iterationsverfahren zur Berechnung von Eigenwerten
Nicolai Rehbein
18.01.12 15:00 Schwarzenbergstrasse 95, Raum 3.053 Studienarbeitsvortrag: Tikhonov Regularization of Large Linear Problems via Lanczos Bidiagonalization
Negar Arazm
15.12.11 16:00 Schwarzenbergstrasse 95, Raum 3.053 Topology and non-Rocal geometry of wall-bounded flows
Diplomvortrag Moritz Kompenhans
23.11.11 10:00 Schwarzenbergstrasse 95, Raum 3.053 Der Wiedemann-Algorithmus und andere Krylov-Raum-Verfahren (Studienarbeitsvortrag)
Raphael Elsner
21.11.11 11:00 Schwarzenbergstrasse 95, Raum 3.053 Linearisierung von rationalen Eigenwertaufgaben
Osman Cakir
07.09.11 14:30 Schwarzenbergstrasse 95, Raum 3.053 Eigenwertberechnung mittels IDRStab (Studienarbeitsvortrag)
Anisa Rizvanolli
04.05.11 15:00 Schwarzenbergstrasse 95, Raum 3.053 Untersuchung zur Festigkeit von Schiffen mit Hilfe der iterativen Lösung linearer Systeme
Osman Cakir
06.04.11 16:15 Schwarzenbergstrasse 95, Raum 3.053 Die modale Berechnung der Strukturverformung von Schiffen im Seegang
Anne Schwenkenberg
06.04.11 15:00 Schwarzenbergstrasse 95, Raum 3.053 Adaption reduzierter Basen
Uwe Köcher
06.04.11 14:00 Schwarzenbergstrasse 95, Raum 3.053 Krylov-Unterraum-Verfahren für Operatoren (Studienarbeitsvortrag)
Abdessalem Helal
16.03.11 15:00 Schwarzenbergstrasse 95, Raum 3.053 The Lanczos Algorithm in Finite-Precision Arithmetic*
Ivo Panayotov, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, England

The Lanczos algorithm was introduced in 1950 as means of solving eigenvalue problems. Despite its apparent elegance, the algorithm was initially neglected by the scientific community because it was observed to depart from its theoretical properties due to the effects of finite-precision computer arithmetic. The algorithm regained popularity several decades later when it was shown that despite its departure from theory, it nevertheless produces highly accurate eigenvalue estimates.

In my talk, I will briefly introduce the Lanczos algorithm and will present bounds characterizing the quality of eigenvalue estimates generated by the algorithm in exact arithmetic. Then, I will describe the difficulties of producing similar bounds in finite-precision arithmetic, and will present rounding error results, including recent ones, which overcome these difficulties.
21.02.11 14:00 Schwarzenbergstrasse 95, Raum 3.053 Performance of the Preconditioned IDR(s)-based Residual Reduction Method
Prof. Seiji Fujino, Research Institute for Information Technology, Kyushu University, Fukuoka, Kyushu, Japan

We devised an IDR(s)-based SOR method and presented its effectiveness in view of efficiency and robustness by comparison with other iterative methods one year ago. In this talk, we consider the preconditioned IDR(s)-based Residual Reduction (R2) method as an extension of the IDR(s)-based SOR method in view of robust preconditioning. Moreover, we present numerical experiments that clearly show that our proposed IDR(s)-R2 method outperforms other approaches.
15.12.10 16:15 Schwarzenbergstrasse 95, Raum 3.053 Inexaktes BiCGStab (Bachelorarbeitsvortrag)
Deniz Ataç
15.12.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Matlab-Implementierung eines QR-Algorithmus mit multiplen Shifts und aggressiver frühzeitiger Deflation (Studienarbeitsvortrag)
Berivan Upçin
08.12.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Singular optimal control, Lur'e equations and even matrix pencils
Prof. Dr. Timo Reis, Institut für Numerische Simulation, Technische Universität Hamburg-Harburg

Lur'e equations are a generalization of algebraic Riccati equations and they arise in linear-quadratic optimal control with cost functional being singular in the input.
For Riccati equations, it is well-known that there is a one-to-one correspondence between set of solutions and certain Lagrangian eigenspaces of a 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.
24.11.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Demands of modal reanalysis techniques in Engineering Design
Jiacong Yin, Peking University, China

1. A brief introduction about our group in Peking University
2. Seismic design of buildings with accidental eccentricity
3. Structural design of wind turbine blades
09.11.10 14:00 Schwarzenbergstrasse 95, Raum 3.053 Spline-Ausgleich für die glatte Approximation von NC-Daten (Bachelorarbeitsvortrag)
Michael Seeck
20.10.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Entwicklung eines Algorithmus zur effektiven Lösung großer nichtlinearer Gleichungssysteme
Fabian Krome
22.09.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Eine graphische Benutzeroberfläche bei Kurvenverfolgung (Studienarbeitsvortrag)
Uwe Köcher
22.09.10 14:00 Schwarzenbergstrasse 95, Raum 3.053 Inexakte Inverse Iteration (Diplomarbeitsvortrag)
Fatih Berber
15.09.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Aspects of eigenvalue computations using Induced Dimension Reduction (Bachelorarbeitsvortrag)
Olaf Rendel
16.06.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Inducing dimension reduction for efficientlysolving large linear systems of equations
Gerard L.G. Sleijpen, Department of Mathematics, Utrecht University, Utrecht, The Netherlands

The Induced Dimension Reduction method was proposed in 1980 by Peter Sonneveld as an iterative method for solving large non-symmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared [Sonneveld '89]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized [van der Vorst '92]). All three methods are based on efficient short recurrences. An important similarity between the methods is that they use orthogonalization with respect to a fixed `shadow residual'. Of the three methods, Bi-CGSTAB has gained the most popularity, and is probably still the most widely used short recurrence method for solving non-symmetric systems.

Recently, Sonneveld and van Gijzen revived the interest for IDR. In 2008, they demonstrate that a higher dimensional shadow space, defined by an n by s matrix tR_0, can easily be incorporated into IDR, yielding a highly effective method. Convergence (in terms of steps, or, equivalently, in terms of matrix-vector multiplications) is often comparable to GRMES, but in contrast to GMRES, this ''s version'' of IDR relies on short recurrences and all steps are equally fast.

The original IDR method is closely related to Bi-CGSTAB. It is therefore natural to ask whether Bi-CGSTAB can be extended to an ''s-version'' in a way similar to IDR. To answer this question we explore the relation between IDR and Bi-CGSTAB. Our findings lead to an abstract description of the IDR method. It shows that there is a lot of freedom in implementing , leading to variants that are mathematically equivalent. The implementational variants, however, may have different stability and efficiency properties.

Bi-CGSTAB relies on degree 1 stabilization polynomials. Higher degree stabilization polynomials can also be exploited as is shown by Sleijpen and Fokkema in 1993. The resulting method BiCGstab(L) is often more stable than Bi-CGSTAB leading the much faster convergence. As shown by Sleijpen, van Gijzen 2009 and Tanio, Sugihara 2009, higher degree stabilization polynomials can also be incorporated in IDR and it can greatly improve stability of IDR with degree 1 stabilization polynomials. We argue that this is another implementational variant of IDR.

This is joint work with Martin van Gijzen, Delft University of Technology, Delft, The Netherlands
14.04.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 Inverse Iteration, Newton-Abschätzungen und Anwendung auf Rayleigh-Quotienten-Iterationen bei nichtlinearen Eigenwertproblemen
Prof. Hubert Schwetlick, TU Dresden, Institut für Numerische Mathematik

Bekanntlich liefert ein Schriitt $(u,\theta) \mapsto u_+^{InvIt}$ der Inversen Iteration für das nichtlineare Eigenwertproblem $T(\lambda)x=0$ dieselbe Richtung wie ein Schritt $(u,\theta) \mapsto (u_+^{Newt},\theta_+^{Newt})$ des Newtonverfahrens für das erweiterte System $T(\lambda)x=0,\;w^Hx=1$ mit einem geeigneten Skalierungsvektor $w$, d.h., es gilt $\mbox{span}\,\{u_+^{InvIt}\}=\mbox{span}\,\{u_+^{Newt}\}$. Es liegt daher nahe, zur Abschätzung der Verbesserung der Eigenvektorapproximation $u$ durch die Inverse Iteration Newton-Techniken zu verwenden. Es wird gezeigt, dass dies zu genauen Abschätzungen führt, wenn explizit mit dem Restglied zweiter Ordnung gearbeitet und dessen spezielle Produktstruktur berücksichtigt wird wie das von \textsc{Heinz Unger} [50] erstmalig (und ohne publizierten Beweis) für das lineare Problem $T(\lambda)=A-\lambda I$ getan worden ist.

Durch Kombination mit neuen Abschätzunegn für das nichtlineare klassische bzw. verallgemeinerte Rayleigh-Funktional läßt sich dann einfach die quadratische Konvergenz
der nichtlinearen Rayleigh-Funktional-Iteration wie auch die kubische Konvergenz der nichtlinearen Verallgemeinerung der zweiseitigen Ostrowskischen Rayleigh-Quotienten-Iteration herleiten.
17.02.10 14:00 Schwarzenbergstrasse 95, Raum 3.053 wird noch bekannt gegeben
Michael Dudzinski
03.02.10 13:00 Schwarzenbergstrasse 95, Raum 3.053 On the motion of several rigid bodies in an incompressible non-Newtonian fluid*
Prof. Sarka Necasova, Institute of Mathematics of the Academy of Sciences, Praha, Czech Republic

The motion of one or several rigid bodies in a viscous fluid occupying a bounded domain ­$\Omega in R^3$ represents an interesting theoretical problem featuring, among others, possible contacts of two or more solid objects. We consider the motion of several rigid bodies in a non-Newtonian fluid of a power-law type. Our main result establishes the existence of global-in-time solutions of the associated evolutionary system, when collisions of two or more rigid objects do not appear in a finite time unless they were present initially.
27.01.10 15:00 Schwarzenbergstrasse 95, Raum 3.053 A self-similar solution for the porous medium equation in a two-component domain*
Prof. Jan Filo, Comenius University, Bratislava, Slovak Republic

We solve a particular system of nonlinear ODEs defined on the two different components of the real line connected by the nonlinear contact condition
w^\prime =h^\prime \;,\qquad h=\psi(w)\qquad\text{at the point $\,x=0\,$}.
We show that, for a prescribed power-law nonlinearity $\psi$ and using the solution $(w,h)$, a self-similar solution to the porous medium equation in the two-component domain can be constructed.
16.12.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 Inverse iteration for purely imaginary eigenvalues with application to the detection of Hopf Bifurcations in large scale problems*
Prof. Dr. Karl Meerbergen, Katholieke Universiteit, Leuven

The detection of a Hopf bifurcation in a large scale dynamical system that depends on a physical parameter often consists of computing the right-most eigenvalues of a sequence of large sparse eigenvalue problems. Guckenheimer et. al. (SINUM, 34, (1997) pp. 1-21) proposed a method that computes a value of the parameter that corresponds to a Hopf point without actually computing right-most eigenvalues. This method utilises a certain sum of Kronecker products and involves the solution of matrices of squared dimension, which is impractical for large scale applications. However, if good starting guesses are available for the parameter and the purely imaginary eigenvalue at the Hopf point, then efficient algorithms are available. In this paper, we propose a method for obtaining such good starting guesses, based on finding purely imaginary eigenvalues of a two-parameter eigenvalue problem (possibly arising after a linearisation process). The problem is formulated as an inexact inverse iteration method that requires the solution of a sequence of Lyapunov equations with low rank right hand sides. It is this last fact that makes the method feasible for large systems. The power of our method is tested on numerical examples.
04.12.09 14:00 Schwarzenbergstrasse 95, Raum 3.053 Introduction of IDR-based Jacobi(s), Gauss-Seidel(s) and SOR(s) methods and its estimation
Prof. Seiji Fujino, Research Institute for Information Technology, Kyushu University, Fukuoka, Kyushu, Japan

The conventional SOR (Successive Over-Relaxation) method originated from the dissertation by D. Young in 1950. After that, the SOR method has been often used for the solution of problems which stem from various applications. The SOR method, however, has many issues on possibility of the solution because of no robustness of convergence of the SOR method.

Recently Sonneveld and van Gijzen brought epoch-making and renewed interest in the Induced Dimension Reduction (IDR) method in 2008. In addition, the Bi_IDR(s) method which was proposed by them is more elegant and stable than IDR(s) method. Furthermore, in 2009, IDR(s)Stab(L) and GBiCGStab(s,L) methods were independently proposed as one of the generalized version of IDR(s) method with polynomial of high degree L by Sleijpen and Tanio et al.

In my talk, we extend IDR Theorem to designing of the residual of the Jacobi, Gauss-Seidel and SOR methods, and accelerate their convergence rate and robustness. Through numerical experiments, we make clear improvement of performance of IDR-based Jacobi, Gauss-Seidel and SOR methods with parameters.
16.09.09 16:00 Schwarzenbergstrasse 95, Raum 3.053 Ein Verfahren zur Regularisierung von vollständigen Ausgleichsproblemen
Moritz Augustin
16.09.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 Die Newton Methode und Rayleigh Quotienten Interation für das Totale Least Squares Problem
Fatih Berber
09.09.09 10:00 Schwarzenbergstrasse 95, Raum 3.053 Über den Einfluss eines inexakten Matrix-Vektor-Produkts auf Fehlerschätzungen im Verfahren der konjugierten Gradienten
Martin Müller
02.09.09 16:15 Schwarzenbergstrasse 95, Raum 3.053 The generalized Riemann problem (GRP) method for compressible fluid flows*
Prof. Jiequan Li, School of Mathematics, Capital Normal University, Beijing, China

In this talk I will briefly review the generalized Riemann problem (GRP) method for compressible fluid flows. There were originally two versions of this method:
Lagrangian and Eulerian. The latter is always derived via a passage from the former. In our recent efforts, we developed a direct Eulerian GRP method using the ingredient of Riemann invariants. The main advantage is (1) to avoid the passage from the Lagrangian to Eulerian and thus easily to be extended into multidimensional cases; (2) treat sonic cases easily; and (3) conveniently combine with other techniques such as adaptive meshes.
We will also report some stability, convergence properties, and applications to shallow water equations on the sphere (earth).
Dr. Bippine Appadu, University of Mauritius, Reduit, Mauritius

In CFD, Atmospheric Sciences and Computational Aeroacoustics, many problems involve regions of discontinuity. When used to solve problems involving regions of shocks, dispersive schemes give rise to oscillations while dissipative schemes cause smearing, close to these regions of sharp gradients.

Based on the results of the 1-D shallow water problem, when solved using MCLF2, we observe that different cfl numbers yield results with different amount of dispersion and dissipation. This led us to devise a technique in order to locate the cfl number at which we can obtain results with efficient shock-capturing properties. This new technique involves the control of numerical effects of dispersion and dissipation in numerical schemes. We baptise this technique as Curbing of Dispersion by Dissipation for Efficient Shock-capturing, CDDES. The cfl number at which dissipation curbs dispersion optimally is then located. It is termed as the optimal cfl.

We extend the concept of CDDES to that of Minimised Integrated Square Difference Error,(MISDE). The latter is an improved technique over the CDDES technique since it can be used to obtain two optimal parameters which are generally the cfl number and another variable, for efficient-shock capturing. Another technique of optimisation is devised which enables better control over the grade and balance of oscillation and dissipation to optimise parameters which regulate dispersion and dissipation effects. This technique is baptised as Minimised Integrated Exponential Error for Low Dispersion and Low Dissipation, (MIEELDLD) and has advantages over the previous technique, MISDE.
10.07.09 10:00 Schwarzenbergstrasse 95, Gebäude D, Raum D1025 Discrete Empirical Interpolation for Nonlinear Model Reduction*
Prof. D. C. Sorensen, Rice University, Houston, Texas

A dimension reduction method called Discrete Empirical Interpolation (DEIM) will be presented and shown to dramatically reduce the computational complexity of the popular Proper Orthogonal Decomposition (POD) method for constructing reduced-order models for unsteady and/or parametrized nonlinear partial differential equations (PDEs). In the presence of a general nonlinearity, the standard POD-Galerkin technique reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term remains that of the original problem.

I will describe DEIM as a modification of POD that reduces the complexity as well as the dimension of general nonlinear systems of ordinary differential equations (ODEs). It is, in particular, applicable to ODEs arising from finite difference discretization of unsteady time dependent PDE and/or parametrically dependent steady state problems. Our contribution is a greatly simplified description of Empirical Interpolation in a finite dimensional setting. The method possesses an error bound on the quality of approximation. An application of DEIM to a finite difference discretization of the 1-D FitzHugh-Nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long-time integration that fully captures non-linear limit cycle behavior. We also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results.
17.06.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 New ideas on IDR(s)
Jens-Peter M. Zemke
13.05.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 On numerical simulation of flow in time-dependent domains
Prof. Miloslav Feistauer, Karls-Universität Prag, Department of Numerical Mathematics

The lecture will be concerned with the simulation of inviscid and viscous compressible flow in time dependent domains. The motion of the boundary of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the Euler and Navier-Stokes equations describing compressible flow. The system of the governing equations is discretized in space by the discontinous Galerkin method. The time discretization is based on a semi-implicit linearized time stepping scheme, which leads to the solution of a linear algebraic system on each time level. As a result we get an efficient and robust numerical process. The applicability of the developed method will be demonstrated by some computational results obtained for flow in a channel with a moving wall and past an oscillating airfoil.

These results were obtained in cooperation with Vaclav Kucera and Jaroslava Prokopova from Charles University in Prague, Faculty of Mathematics and Physics, and Jaromir Horacek from Institute of Thermomechanics of Academy of Sciences of the Czech Republic.
22.04.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 Berechnung erzwungener Schwingungen mittels modaler Superposition für unsymmetriche Systeme
Loubna Doubli
15.04.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 An Implementation for Model Order Reduction using Multilevel Substructuring
Nicolai Rehbein
25.03.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 On the Application of Gaussian Quadrature for the Finite Volume Evolution Galerkin Scheme
Andreas Hempel
25.02.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 Multilevel discontinous Galerkin method
Florian Prill
28.01.09 15:00 Schwarzenbergstrasse 95, Raum 3.053 IDR in variations*
Prof. Martin Gutknecht, Seminar for Applied Mathematics, ETH Zurich

The Induced Dimension Reduction (IDR) method is a Krylov space method for solving linear systems that was first developed by Sonneveld around 1979 and documented on three and a half pages of a 1980 proceedings paper by Wesseling and Sonneveld. Soon after IDR, Sonneveld introduced his widely applied Conjugate Gradient Squared (CGS) algorithm. Then, in 1990, van der Vorst suggested Bi-CGSTAB that he claimed to improve both those methods.

Bi-CGSTAB has become a method of choice for nonsymmetric linear systems, and it has been generalized in various ways in the hope of further improving its reliability and speed. Among these generalizations there is the ML(k)BiCGSTAB method of Yeung and Chan, which in the framework of block Lanczos methods can be understood as a variation of Bi-CGSTAB with right-hand side block size 1 and left-hand side block size k.

In 2007 Sonneveld and van Gijzen reconsidered IDR and generalized it to IDR(s), claiming that IDR is equally fast but preferable to Bi-CGSTAB, and that IDR(s) may be much faster than IDR = IDR(1). It turned out that IDR(s) is closely related to BiCGSTAB if s = 1 and to ML(s)BiCGSTAB if s > 1. In 2008, a new, particularly ingenious and elegant variant of IDR(s) has been proposed by the same authors.

In this talk we first try to explain the basic, seemingly quite general IDR approach, which differs completely from traditional approaches to Krylov space methods. Then we compare the basic properties of the above mentioned methods and discuss some of their connections.
17.12.08 14:30 Schwarzenbergstrasse 95, Raum 3.053 Non-Oscillatory Central Schemes -- a Powerful Black-Box-Solver for Hyperbolic PDE's
Prof. Alexander Kurganow, Tulane University, New Orleans, USA

I will first give a brief description of finite-volume, Godunov-type methods for hyperbolic systems of conservation laws. These methods consist of two types of schemes: upwind and central. My lecture will focus on the second type -- non-oscillatory central schemes.

Godunov-type schemes are projection-evolution methods. In these methods, the solution, at each time step, is interpolated by a (discontinuous) piecewise polynomial interpolant, which is then evolved to the next time level using the integral form of conservation laws. Therefore, in order to design an upwind scheme, (generalized) Riemann problems have to be (approximately) solved at each cell interface. This however may be hard or even impossible.

The main idea in the derivation of central schemes is to avoid solving Riemann problems by averaging over the wave fans generated at cell interfaces. This strategy leads to a family of universal numerical methods that can be applied as a black-box-solver to a wide variety of hyperbolic PDEs and related problems. At the same time, central schemes suffer from (relatively) high numerical viscosity, which can be reduced by incorporating of some upwinding information into the scheme derivation -- this leads to central-upwind schemes, which will be presented in the lecture.

During the talk, I will show a number of recent applications of the central schemes.
03.12.08 16:00 Schwarzenbergstrasse 95, Raum 3.053 Numerical entropy production as a regularity/error indicator
Prof. Gabriella Puppo, Dipartimento di Matematica, Politecnico di Torino,Italy

Uniqueness for weak solutions of conservation laws is based on the sign of the entropy production across discontinuos solutions. Although the entropy plays a fundamental role in the theory of hyperbolic systems, it is generally not used as a computational tool.
In this talk I describe how the numerical production of entropy induced by the discretization of the equations is a reliable indicator of the quality of the numerical solution. Thus the entropy production can be used as a regularity indicator, identifying the cells in which non linear limiters must be used to prevent the onset of spurious oscillations.
More quantitatively, when the solution is smooth, the entropy production has the same size of the local truncation error and can therefore be used as an a-posteriori error indicator to drive the construction of adaptive grids.
03.12.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Statistik nichtlinearer Vorgänge im Seegang
Alexander von Graefe
27.11.08 14:00 Schwarzenbergstrasse 95, Raum 3.053 Systeme gewöhnlicher Differentialgleichungen zur Beschreibung von Fußgängerdynamik
Mohcine Chraibi
20.11.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Numerical Solution of Conservation Laws over Non-Uniform, Adaptively Redefined Meshes
Dr. Sfakianakis Nikos, University of Heraklion, Greece

We start with a brief introduction to Conservation Laws and to their numerical solutions. Then we discuss the construction and manipulation of non-uniform meshes, using geometric properties of the numerical solution under consideration. Next, we examine properties (such as consistency, stability and order of accuracy) of numerical schemes over both uniform and non-uniform meshes. Finally, we combine a proper mesh selection mechanism with Entropy Conservative or oscillatory numerical schemes for the evolution step.
19.11.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Über Fehlerschätzungen im Verfahren der konjugierten Gradienten
Martin Müller
29.10.08 14:00 Schwarzenbergstrasse 95, Raum 3.053 Purifying-Iteration zur Verbesserung der Approximationsgüte einer Jacobimatrixnäherung in einem QN-Kontext
Tim Steinhoff
20.08.08 10:00 Schwarzenbergstrasse 95, Raum 3.053 wird noch bekannt gegeben
Nam Le
09.07.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Some strategies for improving Automated Muti-Level Sub-Structuring
Tobias Hilgert
11.06.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Diplomarbeit
Martin Mohr
04.06.08 15:30 Schwarzenbergstrasse 95, Raum 3.053 Über Eigenpaar-Approximationen mit (quasi-)minimalem Residuum
Jens-Peter M. Zemke
04.06.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Eigenwertprobleme Elektromagnetischer Felder in Unbeschränkten Gebieten
Kemal Yildiztekin
07.05.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Ein Verfahren zur Simulation von dreidimensionalen Strukturverformungen im Seegang mithilfe modaler Reduktion
Boris Dilba
07.05.08 10:00 Schwarzenbergstrasse 95, Raum 3.053 Auf Eigenlösern basierende Methoden für regularisierte totale Ausgleichsprobleme
Heinrich Voss
23.04.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Auf Eigenlösern basierende Methoden für regularisierte totale Ausgleichsprobleme
Heinrich Voss
02.04.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 On the multiscale rodlike model in polymeric fluids
Hui Zhang, School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P.R. China

We will show the new rigid rod-like model in a polymeric fluid. The constitutive relations considered are motivated by the kinetic theory. The micro equation has five spatial freedom variables, two of them are in the configuration domain and the others are in the macro flow domain. It is obtained the local existence of the solution with large initial data and global existence of the solution with small Deborah and Reynolds constants in periodic domains. For the case of no flow we will give the structure of stationary solutions to the micro equation with Maier-Saupe potential on the sphere. The stationary solutions are shown to be necessarily a set of axially symmetric functions, and a complete classification of parameters for phase transitions to these stationary solutions is obtained. It is shown that the number of stationary solutions hinges on whether the potential intensity crosses two critical values 6.731393 and 7.5. Furthermore, we present explicit formulas for all stationary solutions. It is first theoretically proven that there is a hysteresis phenomenon when the non-dimensional potential intensity among particles changes. In the weak shear flow, we show that there exist many stable dynamic states: flow-aligning, tumbling, log-rolling and kayaking, which depend on the initial concentrated orientation of liquid crystal particles. Theoretical analysis is reported the first time that the Kayaking state does not circulate around a fixed direction but the asymmetric axis will periodically change.
25.03.08 16:00 Schwarzenbergstrasse 95, Raum 3.053 Numerical Simulation of a Zero Pressure Gradient Boundary Layer
Sergio Hoyas
25.03.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Applications of the integral transforms to engineering problems
Jezabel Perez
07.03.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Stability Analysis of the Newmark Method Applied to Differential Algebraic Equations (DAEs)
Nicolai Rehbein
07.03.08 14:00 Schwarzenbergstrasse 95, Raum 3.053 Integratoren für Index-2 DAEs aus der Mechanik (Beta-blocking Techniken)
Claus Führer
05.03.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Detecting hyperbolic and extended strongly hyperbolic matrix polynomials
Heinrich Voss
27.02.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Fluid-Struktur Interaktion: Reduktionsansätze für den Hydromassenoperator
Alexander Menk
13.02.08 15:00 Schwarzenbergstrasse 95, Raum 3.053 Nichtlineare Dynamik verankerter Offshore-Strukturen
Katrin Ellermann
06.02.08 13:00 Schwarzenbergstrasse 95, Raum 3.053 Solving Trust Region Problems via a Sequence of Linear Eigenproblems
Jörg Lampe
19.12.07 16:00 Schwarzenbergstrasse 95, Raum 3.053 Varianten des Jacobi-Davidson Verfahrens für nichtlineare Eigenwertaufgaben
Alexander von Graefe
19.12.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 AMLS with Dynamic Substructuring
Tobias Hilgert
28.11.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Das Kummersche Verfahren für nichtlineare Eigenwertaufgaben
Gerhard Unger
21.11.07 16:00 Schwarzenbergstrasse 95, Raum 3.053 Possible improvement strategies for AMLS
Tobias Hilgert
21.11.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Numerical modelling of hyperbolic conservation laws with spatially varying flux functions, Part II
Marcus Kraft
14.11.07 16:00 Schwarzenbergstrasse 95, Raum 3.053 How to solve RLS and RTLS problems via a sequence of linear Eigenproblems
Jörg Lampe
14.11.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Numerical modelling of hyperbolic conservation laws with spatially varying flux functions, Part I
Arun K.R.
07.11.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Nonlinear problems in analysis of Krylov subspace methods
Zdenek Strakos
31.10.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Lösung linearer Matrixungleichungen mit Hilfe Interior-Point-Verfahren
Birgit Stender
26.10.07 13:00 Schwarzenbergstrasse 95, Raum 3.053 Anwendung direkter Verfahren der Optimalen Steuerung auf Probleme der Robotik
Kemal Yildiztekin
24.10.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Schallabstrahluhg planarer Strukturen mittels Jinc Funktion
Le Nam
17.10.07 16:00 Schwarzenbergstrasse 95, Raum 3.053 Bestimmung von Periodizitäten
Michael Dudzinski
10.10.07 16:00 Schwarzenbergstrasse 95, Raum 3.053 Convergence of aggregation/disaggregation methods in the presence of cyclicity
Ivo Marek
10.10.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 A Discrete Rankine-Hugoniot Solver for Hyperbolic Conservation Laws
S.V. Raghurama Rao
05.10.07 14:00 Schwarzenbergstrasse 95, Raum 3.053 Grundlagen des Quanten-Computing
Anna Klich
22.08.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 folgt noch
Bastian Ebeling
08.08.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Approximation der Hydromassen im Schiffbau
Alexander Menk
25.07.07 16:00 Schwarzenbergstrasse 95, Raum 3.053 Implementierung eines Algorithmus zur Parameteridentifzierung bei gewöhnlichen Differentialgleichungen mithilfe von SQP-Verfahren
Katja Wiebracht
25.07.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Modellierung der Koexistenz einer E-Coli- und Dictyostelium discoidum-Kokultur
Peter Ungemach
22.06.07 10:00 Schwarzenbergstrasse 95, Raum 3.053 Characterization of lung nodules in CT images using geometric features
Hanno Böttcher
16.05.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Core problems in linear algebraic systems
Chen Ma
02.05.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Stability and Accuracy of Derivatives with Respect to Parameters of RK-Methods
Tim Steinhoff
27.04.07 14:00 Schwarzenbergstrasse 95, Raum 3.053 Iterative methods for large-scale ill-posed problems
Lothar Reichel
04.04.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Discontinuous Galerkin Verfahren in der Aerodynamik: Höhere Ordnung,Fehlerschätzung und adaptive Gitterverfeinerung
Ralf Hartmann
14.03.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 MLS model reduction for second-order time-invariant dynamical systems
Frank Blömeling
14.02.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Vorstellung Promotionsthema
Duy Nam Le
07.02.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Global Convergent Algorithms for the RTLS-problem
Jörg Lampe
31.01.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Numerische Verfahren für Signorini-Kontaktprobleme
Markus Stammberger
24.01.07 15:00 Schwarzenbergstrasse 95, Raum 3.053 Untersuchung eines LQR-Reglers und eines Modell-Prädiktiven-Reglers für die Steuerung eines Raumfahrzeugs und eines Kampfjets
Janina Zachej
20.12.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Transient motion in modal coordinates
Boris Dilba
20.12.06 13:00 Schwarzenbergstrasse 95, Raum 3.053 Stabilisierte Bestimmung der Ableitung bei verrauschten Daten
Michael Dudzinski
13.12.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 On Generalized Schur Algorithms
Jens-Peter M. Zemke
29.11.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Computer aided detection and characterization of lung nodules in CT images using Support Vector Machines
Hanno Böttcher
29.11.06 13:00 Schwarzenbergstrasse 95, Raum 3.053 AMLS model order reduction: Projection by Krylov subspaces and second order dynamical systems
Frank Blömeling
22.11.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Navier-Stokes Equations in a Time Dependent Domain
Anka Zauskova
08.11.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Kinematical conservation laws - ray theory and applications
K.R. Arun
01.11.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Implementation eines ESDIRK Lösers mit zusätzlicher Ableitung der Lösung nach Parametern und Anfangswert mittels Techniken der automatischen Differentiation
Hanno Böttcher
25.10.06 16:00 Schwarzenbergstrasse 95, Raum 3.053 Evaluation of Krylov Automated Multi-Level Substructuring in Structural Dynamics
Tobias Hilgert
11.10.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 On a quadratic eigenproblem occurring in regularized total least squares
Heinrich Voss
16.08.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Untersuchung verschiedener Skalierungsvarianten im Nicht-Hermiteschen Lanczos-Algorithmus
Thomas Radtke
19.07.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Nonlinear eigenvalue problems in energy band calculation of semiconductor quantum dots
Marta Betcke
05.07.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Numerical modeling of some geophysical flows
Marcus Kraft
28.06.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Numerische Methoden für nichtklassische Schockwellen: Entropiesteuerung und Level-Set Methoden
Christian Rohde
24.05.06 14:00 Schwarzenbergstrasse 95, Raum 3.053 Anwendungen der automatischen Differentiation mit ADMAT/ADMIT/ADiMAT und INTLAB in MATLAB
Jan Müller
10.05.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 On the Comparison of the Finite Volume and the Discontinuous Galerkin Methods
Katja Baumbach
15.03.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Hierarchical substructuring combined with SVD-based model reduction methods
Frank Blömeling
22.02.06 14:00 Schwarzenbergstrasse 95, Raum 3.053 Eine Toolbox zur Automatischen Differentiation
Peter Ungemach
25.01.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Rank-One Updates in Restarted GMRES
Jens Zemke
11.01.06 15:00 Schwarzenbergstrasse 95, Raum 3.053 Interne Solitärwellen mit eingeschlossenem Kern: Eine numerische Untersuchung in 3D
Moriz Scharpenberg
12.10.05 15:00 Schwarzenbergstrasse 95, Raum 3.053 Modellreduktion für sehr große dünn besetzte Systeme 2 Ordnung mit dem Arnoldi-Verfahren
Jörg Lampe
07.09.05 15:00 Schwarzenbergstrasse 95, Raum 3.053 Modellreduktion mittels Substrukturierung
Frank Blömeling
24.08.05 16:00 Schwarzenbergstrasse 95, Raum 3.053 Numerische Simulation von Quantenpunkten
Heinrich Voss
24.08.05 15:00 Schwarzenbergstrasse 95, Raum 3.053 Efficient methods for finding transition states in chemical reactions: comparison of improved dimer method and partitioned rational function optimization method
Andreas Heyden
17.08.05 15:00 Schwarzenbergstrasse 95, Raum 3.053 Vom verborgenen Sinn
Peter Hildebrandt
29.06.05 15:00 Schwarzenbergstrasse 95, Raum 3.053 Vibroakustische Simulation in der Automobil-Entwicklung
Frank Ihlenburg
15.06.05 15:00 Schwarzenbergstrasse 95, Raum 3.053 Berechnung der SEA-Kopplungsverlustfaktoren in Stützen-Platten-Kopplung
Duy Nam Le
04.05.05 15:00 Schwarzenbergstrasse 95, Raum 3.053 Constrained Transport Method for the Finite Volume Evolution Galerkin Schemes with Application in Astrophysics
Katja Baumbach
27.04.05 16:00 Schwarzenbergstrasse 95, Raum 3.053 Model Reduction Methods Using Krylov Subspaces For Solving Rational Eigenvalue Problems
Frank Blömeling
15.12.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Pade-Approximation mit Anwendung bei symmetrischen rationalen Eigenwertproblemen Teil 2
Frank Blömeling
08.12.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Pade-Approximation mit Anwendung bei symmetrischen rationalen Eigenwertproblemen Teil 1
Frank Blömeling
01.12.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Modelling of non-Newtonian fluids
Jan Cerny
24.11.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Brände in Tunnelnetzwerken
Marcus Kraft
22.09.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Eine a priori Fehlerschranke für das AMLS Verfahren
Voss Heinrich
15.09.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 From elliptic PDEs to complex approximation
Timo Betcke
01.09.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Berechnung der SEA-Kopplungsverlustfaktoren mittels Vibrationsrechnungen
Duy Nam Le
14.07.04 16:00 Schwarzenbergstrasse 95, Raum 3.053 A Modal Approach for the Gyroscopic Quadratic Eigenvalue Problem
Kolja Elssel
14.07.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Finite volume method for the shallow water equations with source terms
Zdenek Vlk
21.04.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Polynomial Approximation in the Complex Plane
Timo Betcke
03.03.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Model reduction methods for solving symmetric rational eigenvalue problems
Frank Blömeling
18.02.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Partitionierung beim Automated Multilevel Substructuring Algorithmus
Kolja Elßel
04.02.04 15:00 Schwarzenbergstrasse 95, Raum 3.053s Angepasste Krylov-Raum Verfahren für normale Matrizen
Jens Zemke
21.01.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Rationale Eigenwertaufgabe
Lada Mazurenko
07.01.04 15:00 Schwarzenbergstrasse 95, Raum 3.053 Methoden der Modellreduktion zur Lösung symmetrischer rationaler Eigenwertprobleme
Frank Blömeling
17.12.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Eine Normalform für symplektische Matrizen
Sabine Knupfer
03.12.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Die Even-Odd Zerlegung des charakteristischen Polynomes einer RSPDT Matrix
Aleksandra Kostic
06.11.03 14:00 Schwarzenbergstrasse 95, Raum 3.053 Ein modaler Ansatz für das Quadratische Eigenwertproblem
Kolja Elßel
29.10.03 17:00 Schwarzenbergstrasse 95, Raum 3.053 Projektionsverfahren für gyroskopische Eigenwertprobleme
Marta Markiewicz
22.10.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Iterative Projektionsverfahren für nichtlineare Eigenwertaufgaben
Heinrich Voß
18.09.03 14:00 Schwarzenbergstrasse 95, Raum 3.053 Homotopiemethode für nichtsymmetrische nichtlineare Eigenwertaufgaben
Frank Blömeling
18.09.03 13:00 Schwarzenbergstrasse 95, Raum 3.053 Die Riccati Methode
Christian Schröder
09.07.03 17:00 Schwarzenbergstrasse 95, Raum 3.053 Betrachtung des Look-Ahead Lanczos Algorithmus zur Berechnung betragsmäßig kleiner Eigenwerte
Tim Steinhoff
09.07.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Numerische Modellierung von Systemen hyperbolischer Erhaltungsgleichungen
Maria Lukacova-Medvidova
02.07.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 FE-Modell-Korrektur anhand modaler Meßdaten
Bastian Ebeling
30.04.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Ein Beitrag zur Verfolgung von Eigenpfaden mit Anwendungen aus der Strukturdynamik
Nils Wagner
24.04.03 16:00 Schwarzenbergstrasse 95, Raum 3.053 Passivity Preserving Model Reduction via Interpolation of Spectral Zeros
Dan Sorensen
16.04.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Spectrally good approximations for eigenvalue problems on polygons
Timo Betcke
02.04.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Multilevel Erweiterungen der Komponenten Moden Synthese
Kolja Elssel
12.03.03 15:00 Schwarzenbergstrasse 95, Raum 3.053 Krylov Methods for Nonlinear Eigenvalue Problems
Elias Jarlebring
18.12.02 15:00 Schwarzenbergstrasse 95, Raum 3.053 Restarts für GMRES
Marta Markiewicz
11.12.02 15:00 Schwarzenbergstrasse 95, Raum 3.053 Von Arnoldi über das Jacobi-Davidson zum Riccati Verfahren für große Eigenwertaufgaben
Heinrich Voss
04.12.02 15:00 Schwarzenbergstrasse 95, Raum 3.053 ARPACK in Theorie und Praxis
Christian Schröder
20.11.02 15:00 Schwarzenbergstrasse 95, Raum 3.053 Methoden für nichtlineare Eigenwertaufgabe
Lada Mazurenko
13.11.02 15:00 Schwarzenbergstrasse 95, Raum 3.053 Die Komponenten Moden Synthese
Kolja Elßel
06.11.02 15:00 Schwarzenbergstrasse 95, Raum 3.053 Arnoldi-Tschebyscheff Algorithmus zum Lösen dünn besetzter Eigenwertprobleme
Frank Blömeling
21.08.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Effiziente Methoden für nichtlineare Eigenwertaufgaben
Timo Betcke
03.07.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Inverse Iteration für nichtlineare Eigenwertaufgaben
Martin Holters
26.06.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 MinMax Charakterisierung für nichtlineare Eigenwertaufgaben- Teil II
Heinrich Voss
12.06.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Strukturerhaltende Methoden zur Berechnung von Eigenwerten von großen dünnbesetzten schief-hamiltonischen/hamiltonischen Pencils Teil II
Sabine Knupfer
29.05.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Strukturerhaltende Methoden zur Berechnung von Eigenwerten von großen dünnbesetzten schief-hamiltonischen/hamiltonischen Pencils
Sabine Knupfer
08.05.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Gebietszerlegung-Multigrid-Schwarz-Verfahren und mehr
Reinhard Nabben
10.04.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 MinMax Charakterisierung für nichtlineare Eigenwertaufgaben
Heinrich Voß
20.03.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 MinMax Charakterisierung für Nichtlineare Eigenwertaufgaben
Heinrich Voß
13.03.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Anwendung der Komponenten-Moden-Synthese zur Berechnung des Dynamischen Verhaltens großer Strukturen
Timo Betcke
27.02.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Eigenwert / Eigenvektor - Relationen
Jens Zemke
13.02.02 10:00 Schwarzenbergstrasse 95, Raum 3.053 Ein Verfahren der Ordnung (1+sqrt(3))zur Bestimmung des kleinsten Eigenwertes einer Toeplitz Matrix
Aleksandra Kostic

In this article we compare the set of integer points in the homothetic copy ${n\Pi}$ of a lattice polytope ${\Pi\subseteq{{\mathbb R}}^d}$ with the set of all sums${ x_1+\ldots +xn}$ with ${x_1,\ldots,x_n\in \Pi\cap{{\mathbb Z}}^d}$ and ${n\in{{\mathbb N}}}$. We give conditions on the polytope ${\Pi}$ under which these two sets coincide and we discuss two notions of boundary for subsets of${{{\mathbb Z}}^d}$ or, more generally, subsets of a finitely generated discrete group.

* Vortrag im Rahmen des Kolloquiums für Angewandte Mathematik