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Name: Paula HILBERT
Current position: PhD student (University Assistant) at ASC
Research group: NumPDEs (Prof. Dirk PRAETORIUS)
Starting date: March 2025
Dissertation topic: “Optimal Preconditioning and Iterative Algebraic Solvers for FEM on Locally Refined Meshes”

For the efficient approximation of partial differential equations, iterative solvers play a central role. In practice, one does not compute the exact finite element solution but rather solves the corresponding (nonlinear or linear) system of equations using an iterative method that is deliberately terminated “at the right time.” In my dissertation, I focus on the development and analysis of such methods. I decided to pursue a PhD in mathematics because I have been fascinated, since the beginning of my studies, by the opportunity to immerse myself deeply in a mathematical topic for several years—without the distraction of excessive responsibilities.

I was already able to write my master’s thesis on a related topic within my current research group. Since I greatly enjoyed both the subject itself and the teamwork and supportive social environment, it quickly became clear to me that I wanted to continue here for my doctoral studies. While my master’s thesis primarily dealt with the analysis of existing linear solvers, my PhD now allows me to address the questions that intrigue me most: Why do solvers look the way they do? Can they be designed differently—or even better? And can existing ideas be extended to more general classes of problems? I find it particularly appealing that this research also gives me room for creativity.

At the moment, my biggest challenge is the uncertainty about whether my own results are of interest to others. This makes it all the more valuable to have the opportunity to present my findings within the group, receive encouraging feedback, and benefit from constructive criticism. It constantly reminds me how important not only a suitable research topic but also a supportive work environment is.

As for the future, I honestly don’t know yet what it will bring. I look forward to a wide range of career possibilities—whether in academia, business, or industry—after completing my PhD. I am confident, as I am receiving an excellent education at ASC and know that I can continue to rely on support throughout my professional journey.

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