PhD Position Computational Mathematics Solvers Indefinite Systems

Do you enjoy combining theory and computation to solve hard problems? As our colleague, you’ll advance simulation strategies for indefinite systems in plasma fusion and quantum physics.

The Numerical Analysis group within the Delft Institute of Applied Mathematics at TU Delft is offering a full-time PhD position in the area of advanced iterative solvers and preconditioning strategies for large-scale indefinite systems.

Indefinite systems are at the heart of some of the most pressing challenges in modern science and technology. They occur in magneto hydrodynamic (MHD) stability problems for plasma fusion, and in discretized nonlinear Schrödinger equations arising in quantum many-body physics, both giving rise to large indefinite systems that challenge existing solvers. The mathematical and computational hurdles of solving such systems are immense: slow or unstable convergence, lack of robustness, and scalability bottlenecks on modern parallel architectures.

As a PhD researcher, you will be at the frontier of tackling these challenges. The project will focus on mapping and understanding the convergence behavior of methods for indefinite systems, and on translating these insights into effective novel preconditioning and parallelization strategies. The ultimate aim is to deliver solvers that are both theoretically grounded and practically viable for real‑world applications.

The PhD will be supervised by Vandana Dwarka in the Numerical Analysis group at TU Delft. The group is internationally recognized for its contributions to iterative methods, numerical linear algebra, and parallel computing. The project will be carried out in close interaction with experts from the Max Planck Institute for Plasma Physics (Garching), the University of Toulouse, and IBM, ensuring strong connections to application domains.

Besides carrying out mathematical research and preparing scientific publications, you will be expected to actively participate in seminars and discussions within the department, as well as present your work at (inter) national conferences and workshops. You will also carry out minor teaching tasks (at most 15 % of your time). Teaching and communication will be in English. If desired, you can take Dutch language courses offered by the TU Delft Language Center.

The project has a duration of four years. The starting date is 1st of March.

Doctoral candidates will be offered a four‑year period of employment in principle, but in the form of two employment contracts. An initial 1.5‑year contract with an official go/no‑go progress assessment within 15 months, followed by an additional contract for the remaining 2.5 years assuming everything goes well and performance requirements are met.

• Strong Background:
  You hold a Master’s degree (MSc) in Applied Mathematics, Computational Science, Physics, or a closely related field. You have a solid foundation in numerical analysis, partial differential equations, and linear algebra.
• Theoretical and Practical Balance:
  You enjoy developing and analysing mathematical theory, but also have the skills and motivation to implement algorithms and test them in practice on large‑scale problems.
• Programming
  
  Skills:
  
  You are proficient in at least one scientific programming language (such as Python, Julia, C++, or MATLAB) and are motivated to work with parallel computing environments.
• Collaborative Communicator:
  You are able to communicate your ideas clearly and work effectively with a diverse set of researchers and stakeholders, both within mathematics and in application domains.
• Curious and Open‑Minded:
  You are eager to explore connections between mathematics, physics, and computing, and motivated to learn new techniques.
• Internship
  
  Experience:
  
  An internship or collaboration outside academia is considered a pre‑condition.
• Inclusive Outlook:
  We welcome applications from researchers who will add to the diversity of our team, in the broad and intersectional sense of the word.

Delft University of Technology is built on strong foundations. As creators of the world‑famous Dutch waterworks and pioneers in biotech, TU Delft is…