PhD Position Numerical Analysis

About this position

What if a simulation did not just approximate physical laws, but obeyed them exactly? Join us to design structure-preserving fast FEM solvers for time-dependent PDEs, from fluids to electromagnetics.

Job description

The Numerical Analysis group within the Delft Institute of Applied Mathematics at TU Delft (see link) is offering a full-time PhD position in the area of efficient structure preserving finite element methods for time-dependent PDEs.

Time-dependent PDEs are ubiquitous in science and engineering, governing the behaviour of fluids, electromagnetics, and many other physical systems. Numerical discretization techniques are fundamental to obtaining (approximate) solutions of these PDEs. Better approximations are typically achieved by refining the mesh and time steps, and/or increasing the order of the methods (e.g. increasing the degree of basis functions in finite elements), leading to larger systems that are computationally more expensive to solve.

For this reason, numerical methods that can produce a more accurate solution with the same mesh, time step, and order are advantageous. One approach to constructing more accurate numerical methods is to design them such that key properties of the PDEs are exactly preserved, instead of only approximated: for example, conservation of energy, mass, and momentum; symplecticity; or preservation of the underlying de Rham complex structure. This class of numerical methods is called structure-preserving discretization, and is the main topic of this project.

Specifically, this project will focus on both the construction of structure-preserving discretizations for time-dependent PDEs and the efficient solution of the resulting systems with iterative solvers for large-scale systems and HPC. The ultimate aim is to develop solvers that have strong theoretical foundations and are practically viable for real-world applications.

The PhD will be supervised by Artur Palha in the Numerical Analysis group at TU Delft. The group is internationally recognized for its contributions to structure-preserving finite element methods, iterative methods, and parallel computing.

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.

Job Requirements

Strong Background: You hold a Master’s degree (MSc) in Applied Mathematics, Computational Science, Physics, Aerospace Engineering, or a closely related field. You have a solid foundation in numerical analysis, partial differential equations, and numerical 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.

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 in or outside academia is a plus, but not required.

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.

TU Delft (Delft University of Technology)

Working at TU Delft means contributing to solutions that really make a difference.

For over 180 years, we have been training engineers who make an impact worldwide in companies, government bodies, or as entrepreneurs. Our alumni turn knowledge into concrete solutions for the challenges of today and tomorrow.

These challenges are changing rapidly. That is why we focus on themes such as energy, climate, digitalisation, artificial intelligence (AI), and smart mobility every day. Our education and research are directly aligned with what society needs now and in the future.

At TU Delft, our people make the difference. With their knowledge and curiosity, our staff provide a high-quality education and conduct pioneering research that extends beyond the campus. You will have the opportunity to take the initiative, work with others, and grow as a professional.

Working at TU Delft means join an international community of professionals and students. Together, we create knowledge, innovations, and solutions that help move the world forward.

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