My name is Philipp and I finished my Master of Science in Mathematics, in Heidelberg, in 2016. I am interested in numerical methods for PDEs - mostly FEM.
The Master's thesis was about using Newton's method to solve variational eigenvalue problems. These problems are interesting for quantum chemists and physicists, as they can use eigenvalues and eigenvectors to approximate the behaviour of the Hamiltonian. That basically works in the same way as you can find an orthonormal basis of eigenvectors to a real, symmetric matrix $A$. The mapping $x↦Ax$, can now be described using a decomposition of $x$ in that basis. Using only a few vectors, e.g. the ones corresponding to the $m$ largest eigenvalues, will give you an approximation. The hope of using Newton's method was to derive a fast and robust solver for these problems. The method was in fact quite fast, but it was absolutely not robust.
You can find my thesis here. It includes an abstract written in English on page iii.
After I finished the Master's degree I wanted to experience how numerical methods are used in the industry. Currently I work in a team that simulates the behavior of electrical motors. Here I develop a Python-framework that interacts with the FEM-Solver Ansys Maxwell, and that includes several analytical models to do simulations quickly.
Additionally, I work on two bigger projects. One project is about the modelling of parameters in the differential equations that describe the behavior of the electrical engine. The other project is about the simulation of the vibration that is generated by the engine.
As it is usual in the industry, I am the only mathematician in the company. Therefore, I do a lot of small projects that includes modelling, finding algorithms and giving advise.
One of the things I miss most about my time at university is teaching. During my time in Heidelberg I was employed as research assistent for the following lectures:
- WS 2013: Numerical Linear Algebra
- SS 2013: Numerics of Partial Differential Equations
- WS 2012: Numerics of Ordinary Differential Equations
- SS 2012: Introduction into Numerics
- WS 2011: Introduction into Numerics
- WS 2010: Analysis I
When I started with the Master's program, I got the opportunity to be a lecture assistant to the following lectures:
- 2014/2015 Linear Algebra I and II
- 2016 Numerical Analysis of Ordinary Differential Equations
That job included the creation of exercises and exams, a lot of organisation and (the best part) substitution giving the lecture.