Vorträge

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.

LITERATUR
[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.

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.

Zoomlink:
https://tuhh.zoom.us/j/84729171896?pwd=ODArbForaUxMM3Q3VTJsNG1kaVNYQT09

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.

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.

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.

Zoomlink:
https://tuhh.zoom.us/j/84729171896?pwd=ODArbForaUxMM3Q3VTJsNG1kaVNYQT09

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.

Zoomlink:
https://tuhh.zoom.us/j/84729171896?pwd=ODArbForaUxMM3Q3VTJsNG1kaVNYQT09