Minisymposia 2019

The importance of the availability of efficient drugs for public health can hardly be overestimated, while the process of introducing new drugs takes easily at least half a decade before industrial production can start. Modeling and simulation provide a powerful  paradigm for modern drug development. The most essential part for understanding how the drug acts and how it is to be administered to human beings, is the pharmacological analysis of the target genes it influences via binding to receptors at both the intercellular and the  intracellular level.This is traditionally done with multi-compartmental models which can be seen as an attempt to simplify the very complex dynamics of drug transport in such a heterogeneous structure as the human body. With increased computing power and informatics-related fields like HPC, it starts to become more attractive to extend these simple ODE-based multi-compartmental models to PDE-based finite element models by adding spatial resolution. In this minisymposium we are interested in mathematical and computational analysis of modern models for drug distribution and action. The emphasis is on issues like formulation of appropriate reaction-diffusion equations, based on drug homogenity assumptions in the individual compartments, which translate in coupling of PDE and ODE, and on their analysis and numerical simulation.Depending on the coupling and the structure of the equations the analysis techniques to show the well-posedness of the modeled system of equations may require additional effort. In highly heterogeneous structures homogenization techniques can provide a better model with a less complicated numerical access. In addition, the shadow limit (the infinite diffusion coefficient-limit) allows to consider a reduced system in this context. We are also interested in modern discretization techniques tailored to the specific parts in the coupled systems and on numerical aspects of the solution of the discretized problem including coupled and decoupled aproaches, preconditioning, parallelization and scalability.

Organizers: Jurjen Duintjer Tebbens (Uni Prag), Elfriede Friedmann (Uni Heidelberg)

Topology optimization is applied successfully in many technical areas. By using mathematical topology optimization methods, new structural concepts are generated. The established methods are efficient in the field of structural design, taking linear structural properties, deterministic variables and linear static loading conditions into account. E.g. with the use of the homogenization method the mean compliance is minimized considering a mass constraint. Other objectives and constraints like local stresses and displacements can be used as well. Because of utilizing existing analytical sensitivities these method are fast. As the results are generated fast and the optimization problem is easy to formulate, the acceptance of the method in practice is high. But it is still a research task to include more complex constraints which cannot easily be included in the mathematical optimization process. E.g. the consideration of the manufacturing process like casting and stamping and related constraints or the consideration of more complex nonlinear mechanical behavior i.e. of crash in the case of the structural optimization of vehicles or vehicle components used for transport systems. Furthermore the design varriables and parameters are mainly considered deterministic, the consideration of stochastic variables is not established.
In this Mini-symposium the leading scientists in the area of structural optimization will present latest results in topology optimization with specific emphasis on complex constraints or design variables. The scope starts with new theoretical methods up to successful complex application examples.
After the successful world congress WCSMO-12 with more than 500 participants in Braunschweig in 2017 (http://www.wcsmo12.org/), the Mini-Symposium should strengthen the scientific community working on Structural Optimization in Europe.

Organizers: Thomas Vietor (TU Braunschweig), Axel Schumacher (BU Wuppertal), Sierk Fiebig (Volkswagen, Braunschweig)

Computer-based simulations are nowadays taken for granted in applied mathematics as well as in mechanical engineering. Curiously, this kind of scientific experiment is often handled quite differently than experiments in other fields of sciences, which leads to the obscure situation that computer-based experiments, as the technically easiest repeatable type of experiments, are least regulated, documented or available. Hence, the associated claimed scientific results often remain unverifiable. As a side effect of this circumstance, generations of graduate students are re-implementing the wheel over and over again, without any knowledge transfer or evolutionary refinement. Due to the current lack of mandatory requirements for (the publication of) computer-based experiments, many simple, yet effective, measures for improvement are often ignored in the busy day-to-day life of researchers. To ensure long-term scientificity and sustainability in scientific computing, research software engineering or computational science and engineering, some formalization of computer-based experiments is direly in order. In this minisymposium we present definitions, best practices and examples for replicable, reproducible and reusable computer-based experiments.

Organizers: Jörg Fehr (Uni Stuttgart), Christian Himpe (MPG Magdeburg)

Rotor dynamics is one of the classical branches of Applied Mechanics and at the same time one of active demand by industry. Advances, such as lightweight construction, downsizing and function integration, in rotating machinery challenge computer aided engineering. This minisymposium pays special attention to fluid structure interaction, either inside or outside the rotor. The former occurs in various types of  bearings and seals and is particularly relevant for high-speed rotors and the latter occurs in fully or partially filled rotors. As another branch of coupled problems this minisymposium investigates thermo- and electromechanical couplings and their effects on rotor dynamics. It also examines vibrational control of rotors that adds further domains to the rotor model. The considered approaches to master these complexities are either model order reduction, co-simulation or full monolithical simulations.

The aim of this minisymposium is to bring together leading scientists in the fields of applied mathematics, mechanics and further engineering in order to advance semi-analytical and numerical methods in coupled multiphysical problems with a particular focus on rotordynamics.

Organizers: Wolfgang Seemann (KIT Karlsruhe), Aydin Boyaci & Dominik Kern (TU Chemnitz)

The question of stability has been at the heart of the control of any process ever since in the last decades. Among various stability concepts, input-to-state stability (ISS), going back to E. Sontag, has a special role. ISS unified the paradigms of Lyapunov and input-output stability relative to disturbances, proposed powerful methods for analysis of large-scale networks of nonlinear systems as well as fostered the development of new techniques for designing nonlinear stabilizing controllers: ISS feedback redesign, ISS small-gain theorems, robust backstepping etc. This success made ISS central for the robust control of nonlinear ordinary differential equations. However, modern applications of control theory to chemical reactors, traffic networks, multi-body systems (e.g. robotic arms, flexible elements in aircraft),  fluid-structure interactions etc., require methods for robust stabilization of coupled systems, described by distributed parameter systems, most importantly, by partial differential equations (PDEs). A profound understanding of ISS for PDEs would give us an ultimate tool to tackle these problems. Recently, intensive efforts have been made towards this goal. Remarkably, ISS for distributed parameter systems is currently attracting interest from both the control engineering as well as the mathematical systems theory community. The employed methods range from PDE theory over operator theory to nonlinear control theory (Lyapunov theory, small-gain approach, PDE backstepping). Although several foundational results in ISS theory of distributed parameter systems have been established in the last years, there is a number of challenging open problems ranging from applied questions, as ISS analysis of real-world systems, and ISS boundary control of PDEs to open problems in the operator-theoretic framework. The diverse and emerging nature of the topic suggests to intensify the scientific exchange of specialists in these deeply interrelated fields. With this Minisymposium, we aim to bring together young researchers that have a strong experience in ISS for PDEs and those from related fields in order to discuss recent advances. By this, we would like to push forward the solution of some important open questions as well as to connect ISS to other current developments in control theory (such as port-Hamiltonian systems).

Organizers: Andrii Mironchenko (Uni Passau), Felix Schweninger (Uni Hamburg)