PhD Position Computational Mathematics: High-Performance Solvers for 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 magnetohydrodynamic (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 4 years. The starting date is 1st of March. Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 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.

Job requirements

• 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 analyzing 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.

TU Delft (Delft University of Technology)

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context.

Faculty of Electrical Engineering, Mathematics and Computer Science

The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three scientific disciplines. Combined, they reinforce each other and are the driving force behind the technology we all use in our daily lives. Technology such as the electricity grid, which our faculty is helping to make completely sustainable and future-proof. At the same time, we are developing the chips and sensors of the future, whilst also setting the foundations for the software technologies to run on this new generation of equipment – which of course includes AI. Meanwhile we are pushing the limits of applied mathematics, for example mapping out disease processes using single cell data, and using mathematics to simulate gigantic ash plumes after a volcanic eruption. In other words: there is plenty of room at the faculty for ground-breaking research. We educate innovative engineers and have excellent labs and facilities that underline our strong international position. In total, more than 1000 employees and 4,000 students work and study in this innovative environment.

Conditions of employment

Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 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.

Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from €3059 - €3881 gross per month, from the first year to the fourth year based on a fulltime contract (38 hours), plus 8% holiday allowance and an end-of-year bonus of 8.3%.

As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

The TU Delft offers a customisable compensation package, discounts on health insurance, and a monthly work costs contribution. Flexible work schedules can be arranged.

If you need to relocate to the Netherlands for this job, TU Delft is committed to making your move as smooth as possible. The HR unit, Coming to Delft Service, offers information to help you prepare your relocation. In addition, Coming to Delft Service organises events to help you settle in the Netherlands, and expand your (social) network in Delft. A Dual Career Programme is available to support your accompanying partner with their job search in the Netherlands.

Additional information

If you would like more information about this vacancy or the selection procedure, please contact Vandana Dwarka, via v..n.s.r.dwarka@tudelft.nl.