Talks

Suppose that A, B, and C are compact selfadjoint operators on a Hilbert space such that A+B+C=0. We show that the possible eigenvalues of these operators are described by certain combinatorial objects called hives. We will also see that the Horn inequalities (first described in the compact case in joint work with Li and Timotin) can also be obtained from this hive model.

In this colloquium talk, we will explore the interplay between expectations and reality in computational fluid dynamics, with a particular focus on structure-preserving properties and the development of suitable finite element methods for incompressible and compressible flows. Specifically, we will discuss the continuity requirements that arise in approximating key physical quantities such as pressure and velocity. We will examine how these requirements can be effectively realized — whether by "cutting, gluing, or weakly connecting via rubber bands" — and support our approach with computational examples to motivate and illustrate the findings.

Additionally, I will take this opportunity to share insights into my current research and outline potential future research directions.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

Model-based optimization is a central element of Process Systems Engineering and supports decision-making across different stages of process development. This talk will provide a brief overview of current work at the Institute of Process Systems Engineering, with a focus on process synthesis and model-based experimental design. The examples will address challenges in the design and evaluation of distillation processes as well as in reactor design and optimization. The underlying mathematical problems range from mixed-integer nonlinear programming to nonlinear dynamic optimization. Based on selected applications, the talk will discuss problem-specific challenges, current solution approaches, and open questions.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

Hierarchic formulations for shear-deformable beams, plates and shells are based on a clever reparametrization of the kinematic equations and possess distinct variables for transverse shear. This results in several interesting and promising properties:
1. Hierarchic formulations are intrinsically free from transverse shear locking. That is, transverse shear locking is avoided a priori, independent of the utilized discretization scheme.
2. The hierarchic structure can be exploited towards an intrinsically selective mass scaling (ISMS) scheme. ISMS enables efficient and accurate simulations in explicit dynamics.
3. Hierarchic parametrizations enable intrinsically selective loss scaling (ISLS), which helps improve efficiency when solving problems in structural mechanics using physics-informed neural networks (PINNs).

This talk will introduce the key concepts behind hierarchic formulations for beams, plates and shells. Examples illustrate the applicability to small and large rotations, statics and explicit dynamics, and various discretization schemes and solution strategies. In addition, the talk will provide a brief overview on other current research topics from the Institute for Structural Analysis at TUHH.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

The symmetric Lanczos process plays a vital role in the computation ofeigenvalues and the solution of huge sparse linear systems with a symmetric real or Hermitian matrix. The theoretical behavior differs drastically from that observed in finite precision. This has been investigated for over 50 years by many researchers. In this talk we present some new points of view
based on an augmented stability result obtained by Chris Paige.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

In 2001 bi-continuous semigroups were introduced in the PhD thesis by Kühnemund. Such semi-
groups operate on a Banach space in the presence of another norming Hausdorff locally convex
topology that is used to describe their continuity properties, so-called bi-continuity. The theory
of bi-continuous semigroups was advertised as being more applicable than the already long exist-
ing theory of strongly continuous, locally equicontinuous semigroups on Hausdorff locally convex
spaces.
In this talk, we will show that this advertisement has something in common with many other adver-
tisements, it is misleading, not only for semigroups but also for cosine families (and other operator
families). Namely, we will show that bi-continuous semigroups and cosine families are exactly the
strongly continuous, locally—even exponentially—equicontinuous semigroups and cosine families
with respect to the mixed topology under some very mild assumptions.
This talk is based on joint work with Christian Seifert

Zoomlink:
https://tuhh.zoom.us/j/85249558979?pwd=lqzsbf4fkjWnNmaeuhNwUNV9Bv64MR.1

Zoomlink:
https://tuhh.zoom.us/j/82040837302?pwd=brm8cbX5IgJyHnHqqvGuroBFT1afJr.1

Electromagnetic Compatibility (EMC) and Signal Integrity (SI) are areas of electrical engineering that are vital to the functionality of all electronic devices and systems. EMC ensures compliance with internal and external electromagnetic interference. SI ensures error-free ransmission of data over wired interconnects; for example, on printed circuit boards. To address the highly complex, cross-disciplinary design for EMC and SI, decomposition, segmentation, and subsequent hierarchical, physics-based modeling are performed. Although an active field of research, machine learning (ML) has yet to become an inherent part of modeling. Given the limited availability of generalized datasets and highly complex tasks, the adoption of ML cannot be achieved using a brute-force, universal black-box approach. Instead, the modeling
hierarchy must be considered to introduce ML efficiently. Through analysis of EMC in electric vehicle powertrains and SI in high-speed interconnects we derive a general hierarchical modeling structure. Coupled with a review of ML methods and applications, we demonstrate how ML can be integrated into the established modeling workflow, demonstrated with hierarchical Gaussian process regression, neural networks, and a novel interface for circuit comprehension with large language models.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09