PhD Position in Topology Optimization of Large-Scale Systems with Many Local Constraints

Catholic University of Leuven Department of Computer Science


At the Department of Computer Science of KU Leuven, the Numerical Analysis and Applied Mathematics research unit NUMA works on numerical methods, algorithms and software for simulation and data analysis, with applications in many fields in science and engineering. The research in NUMA focuses, amongst others, on numerical simulation, optimization and high performance computing.


Topology Optimization (TO) is a powerful technology which allows to compute optimized designs of physical systems  in a fully automated manner, without any assumed parameterization of the geometry. From the mathematical standpoint, it consists of solving nonlinear optimization problems constrained by partial differential equations. This technology allows to improve the performance in various physical settings such as structural design, heat exchangers, or nanophotonic crystals.

In general, the optimized designs need to meet multiple industrial specifications, which take the form of equality and inequality constraints in the mathematical program modelling the optimal design problem. Of particular interest are local constraints, which are bounds prescribed on local physical quantities which need to be imposed everywhere in the design domain.  These type of constraints arise in various physical applications; for instance, it is desirable in structural design to impose a maximum admissible value for the Von Mises stress everywhere in the structure in order to prevent mechanical failure. However, they remain especially challenging to implement since they result in the need to enforce as many constraints as the number of nodes used to represent the computational domain.

The goal of this PhD thesis is to develop efficient methods able to enforce arbitrary local constraints in large-scale Topology Optimization problems. A particular focus will be given on the development of methods compatible with the use of domain decomposition methods which are commonly used for solving large-scale 3D optimization problem. The work will involve the development and the mathematical analysis of novel optimization methods, as well as their numerical implementation for computing three-dimensional optimal designs.


  • Candidates must hold a master’s degree in Mathematical Engineering, Applied Mathematics, or equivalent.
  • Candidates should have an excellent background in mathematics (notably finite elements methods  and numerical optimisation).
  • Candidates should have experience with scientific programming and the will to use  it as a daily and powerful research tool (python)
  • Excellent proficiency in English is required, as well as good communication skills, both oral and written.


  • A high-level and exciting international research environment.
  • A supportive and collaborative team in which you can develop know-how and expertise in state-of-the-art simulation methods.
  • The opportunity to build up research and innovation skills that are essential for a future career in research and development, both in an industrial and academic context
  • A competitive salary and travel funding


For more information please contact Prof. dr. Florian Feppon,  mail:

You can apply for this job no later than February 15, 2023 via the
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  • Employment percentage: Voltijds
  • Location: Leuven
  • Apply before: February 15, 2023
  • Tags: Ingenieurswetenschappen
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