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Date Time Venue Talk
12/13/18 02:00 pm Am Schwarzenberg-Campus 3 (E), Room 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.
12/06/18 02:00 pm Am Schwarzenberg-Campus 3 (E), Room 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.
11/02/18 11:30 am Am Schwarzenberg-Campus 3 (E), Room 3.074 Analyzing MRI Data using Geometric Deep Learning (Bachelor Thesis)
Daniel Klisch
11/01/18 02:15 pm Am Schwarzenberg-Campus 3 (E), Room 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].

References:

[1] Implementation and Performance Analyses of a Highly Efficient Algorithm for Pressure-Velocity Coupling. Master Thesis Computational Engineering, Darmstadt, 2015,
http://fabian-gabel.de/masterthesis_ce/raw/master/masterthesis.pdf.

[2] On the L^p Theory of the Stokes Operator in Lipschitz Domains. Master Thesis Mathematics, Darmstadt, 2018,
http://fabian-gabel.de/masterthesis_math/raw/master/masterthesis.pdf.
10/18/18 01:45 pm Am Schwarzenberg-Campus 3 (E), Room 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.
10/11/18 03:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Konstruktion aufspannender Strukturen in Walker-Breaker-Spielen
Jonas Eckhoff

BA-Vortrag
10/11/18 02:00 pm 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.
09/26/18 01:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Verschiedene Ansätze zur Bildzerlegung
Malte Seemann
09/26/18 11:00 am Am Schwarzenberg-Campus 3 (E), Room 3.074 Eindimensionale Quasikristalle, endliche Abschnitte und Invertierbarkeit [Bachelorarbeit]
Luis Weber
09/26/18 10:00 am Am Schwarzenberg-Campus 3 (E), Room 3.074 Quasiperiodische Schrödingeroperatoren und Konditionszahlen [Bachelorarbeit]
Jonas Sattler

* Talk within the Colloquium on Applied Mathematics