Shape Optimization for Industrial Problems: A PhD at the Fraunhofer ITWM

Hi, my name is Sebastian Blauth and I am working as a PhD student at the Fraunhofer Institute for Industrial Mathematics (ITWM) in cooperation with the TU Kaiserslautern. The great thing about this collaboration is that I get to see two different perspectives on applied mathematics. First, the theoretical point of view which comes mostly from the side of the university, and second, the angle from the industry that I get to see through the Fraunhofer Institute. This is also reflected in the fact that I have two supervisors: one professor from the university and one employee from the institute.

My research deals with microreactors, which are very small chemical reactors with typical dimensions of less than a millimeter. Due to their high surface to volume ratio, they have very good thermal and chemical properties which makes them attractive for all kinds of applications. In particular, the kind of reactor I consider has the following layout. In its first component an exothermic chemical reaction takes place. The second part of it is a metal block which conducts the generated heat away to its final section, a cooling system. There, the heat is absorbed by a cooling liquid and the whole reactor is cooled that way.

The goal of my work is to optimize the quality of such a reactor by changing its shape. Of course the physics of the problem also have to be considered: this leads to constraints in the form of partial differential equations. Therefore, the optimization task is a so-called PDE constrained shape optimization problem. Such problems are in some sense similar to PDE constrained optimal control problems, but here the control variable is actually given by the domain of the PDE, which introduces additional difficulties.

As the topic I am working on also concerns industrial applications and is not purely academic, it is also important to have sufficient resources for the simulation and optimization of problems. Luckily, the Fraunhofer ITWM is exactly the right spot for such demands as problems from industry are daily business here: the institute has its own computer cluster which allows employees and PhD students to compute large numerical studies.

In my opinion, a very great aspect of my work is that I am completely involved from the very beginning. Therefore, I get insight into all major parts of applied mathematics: when I began working on my PhD in October last year, I started with the modeling and numerical simulation of the problem, and now I am working on the optimization problems using the models I derived earlier.

Altogether, I really appreciate working on my PhD in this cooperation between academia and industry as well as the great, supportive environment and the nice colleagues and supervisors.

If you would like to know more about my work, feel free to contact me: my mail address is sebastian.blauth@itwm.fraunhofer.de.