What is the research topic at the Chair of Numerical Methods for High Performance Computing?
The goal of our group is to develop scalable numerical methods and algorithms for complex problems in the natural sciences. Many of the research topics come from computational chemistry and physics.
One example is the computation of states of many-particle systems in quantum mechanics. These problems are basically eigenvalue problems in an infinite-dimensional Hilbert space where an efficient discretization and the resolution of the corresponding discrete eigenvalue problem is required. On the one hand, the methods must then be implemented efficiently and on the other hand, theories are developed to measure the discretization error. Just as it is common in experiments, the calculations should also entail some kind of computable error bounds to certify the accuracy. Since effective models of many-body systems are often complex nonlinear eigenvalue problems, much work is still needed in this direction.
Another example is in the context of so-called implicit solvent models which are routinely used in computational chemistry. Through an interdisciplinary collaboration with chemists, we have been able to develop efficient numerical methods which have greatly accelerated the standard method. In this case, on the one hand, the research deals with the theoretical properties of these methods, such as scalability. On the other hand, we have recently created a modular software package that has implemented these methods in a unified way.
Why is interdisciplinarity so important at the chair?
On the one hand, as applied mathematicians, it is about having an impact on current research in applications. My experience has shown me that the transfer of knowledge is not finished with the publication of a method in mathematical literature. There are many important reasons that mathematicians do not think about, and only close collaboration, at least in my field of research, can lead to a successful transfer. What is the use of developing a new method that nobody uses? The goal is, therefore, to be open to applications and chemical or physical considerations play a role in addition to mathematical ones at the chair.
However, my experience has shown that this relationship between mathematics and application is not only one-sided, but there are several examples in my research where the application has generated new mathematical problems and also produced their solution. That is, the application can also be an inspiration for new mathematical theories. Mathematics, of course, plays to its strength of abstraction there, as it detaches the problem from the physical context.
The proximity to the SimTech Excellence Cluster here in Stuttgart naturally provides a good breeding ground for interdisciplinary activities, which I appreciate very much.
What prior knowledge do students need to enter your field of research in the context of a master's or doctoral thesis?
In my opinion, interest and passion are the most important things, which is of course only possible if you have an affinity for numerics. A Ph.D. or Master's thesis can of course have different flavors depending on whether there is a focus on theory or the practical aspects, which are also very interesting. In any case, one should have good previous knowledge in numerics. The exciting thing is often to experience both sides, i.e. to master the theory and then to see in the (own) implementation that the method actually behaves as the theory says. But often you only really understand a method once you have implemented it.
What do you enjoy about your work?
It is a pleasure to be able to practice my hobby every day. Of course, there are things that have to be done and are a little less fun, but there are really only very few things in my everyday life that I don't like to do. A great aspect of the job is the variety. The day-to-day business is very varied!
In addition, the field of activity is very international. This is now my fourth country (besides Switzerland, the USA and France) in which I work and I have already met many very exciting people. As I get older, I also find it a privilege to work with young people full of energy.
Prof. Benjamin Stamm
Chair of Numerical Mathematics for High Performance Computing (NMH)
Institute of Applied Analysis and Numerical Simulation