About this role
PhD Position Numerical Analysis (Delft, NL, 2628 CD) Delft University of Technology (TU Delft) Intern Posted on Sep 28, 2026 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 found...