Water flow generated by pillar in sinusoidal motion (from PhD research Yous van Halder) 

Scientific Computing (SC) enables the simulation of phenomena, processes and systems that cannot be studied by real experiments for technical, financial, safety or ethical reasons. SC also allows for automatic design and optimization, through inverse computations. Many disciplines in science and engineering have their own computational branches now. With continuing growth in speed, memory and cost-effectiveness of computers and similar improvements in numerical mathematics, the future benefits of SC are enormous.

Within CASA’s SC group, we propose, analyze, develop and implement new numerical mathematics methods, particularly structure-preserving discretization methods for partial differential equations and numerical linear algebra methods for linear systems of equations. We carry over these methods to Computational Science and Engineering (CSE), for application to particularly fluid-structure-interaction and energy-conversion problems.

Air vortices generated by impulsively started wind-turbine model blade (from PhD research René Beltman) 

Neural network developed for tokamak-plasma simulation (from MSc research Philipp Horn)
Traditionally, CSE is model-driven; based on mathematical models of first principles (physical laws for instance). Because of the immense growth in the availability of data, CSE is becoming data-driven as well, with an important role in this for neural networks. Within CASA’s SC group, neural-network technology in CSE is also studied. One of our research goals is to further develop neural networks in the context of CSE, combining data- and model-driven approaches, hand-in-hand with the development of more theory for a rational and trustworthy use of data and neural networks within CSE.

more publications…

  1. Horn P, Saz Ulibarrena V, Koren B, Portegies Zwart S. A generalized framework of neural networks for Hamiltonian systems. Journal of Computational Physics. 2025 Jan 15;521:113536. doi: 10.1016/j.jcp.2024.113536
  2. Koren B. A Journey in Scientific Computing. Eindhoven: Technische Universiteit Eindhoven, 2025. 32 p.
  3. Cai Y, Wei J, Hou Q, Fan H, Tijsseling AS. A Lagrangian particle model for one-dimensional transient pipe flow with moving boundary. Engineering Applications of Computational Fluid Mechanics. 2025;19(1):2452360. doi: 10.1080/19942060.2025.2452360
  4. Ferrandi G, Hochstenbach ME, Rosário Oliveira M. A subspace method for large-scale trace ratio problems. Computational Statistics and Data Analysis. 2025 May;205:108108. doi: 10.1016/j.csda.2024.108108
  5. Gidisu PY, Hochstenbach ME. Block discrete empirical interpolation methods. Journal of Computational and Applied Mathematics. 2025 Jan 15;454:116186. doi: 10.1016/j.cam.2024.116186
  6. Baumeier B, Çaylak O, Mercuri C, Peletier M, Prokert G, Scharpach W. Local existence and uniqueness of solutions to the time-dependent Kohn–Sham equations coupled with classical nuclear dynamics. Journal of Mathematical Analysis and Applications. 2025 Jan 15;541(2):128688. doi: 10.1016/j.jmaa.2024.128688
  7. Cai Y, Wei J, Hou Q, Tijsseling AS, Duan H. Numerical simulation of three-dimensional two-phase pipe flows with GPU-accelerated Riemann-based smoothed particle hydrodynamics. Engineering Applications of Computational Fluid Mechanics. 2025;19(1):2448225. doi: 10.1080/19942060.2024.2448225
  8. Gidisu PY, Hochstenbach ME. A DEIM-CUR factorization with iterative SVDs. Journal of Computational Mathematics and Data Science. 2024 Sept;12:100095. doi: 10.1016/j.jcmds.2024.100095
  9. Ferrandi G, Hochstenbach ME. A homogeneous Rayleigh quotient with applications in gradient methods. Journal of Computational and Applied Mathematics. 2024 Feb;437:115440. doi: 10.1016/j.cam.2023.115440
  10. Saz Ulibarrena V, Horn P, Portegies Zwart S, Sellentin E, Koren B, Cai MX. A hybrid approach for solving the gravitational N-body problem with Artificial Neural Networks. Journal of Computational Physics. 2024 Jan 1;496:112596. doi: 10.1016/j.jcp.2023.112596