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. Ferrandi G, Hochstenbach ME. A homogeneous Rayleigh quotient with applications in gradient methods. Journal of Computational and Applied Mathematics. 2024 Feb;437:115440. doi: 10.48550/arXiv.2206.13457, 10.1016/j.cam.2023.115440
  2. 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
  3. Wang ZC, Gao PX, Zhou ZD, Tijsseling AS, Qu YZ, Yan WJ et al. A numerically stable flexural dynamics model of complex multi-span fluid-conveying pipes with flexible components and its application to clamp stiffness identification. Thin-Walled Structures. 2024 Feb;195:111488. doi: 10.1016/j.tws.2023.111488
  4. Xia L. Enhancing Optimization Efficiency in Training Neural Networks with Rounding Bias and Adaptive Methods. Eindhoven: Eindhoven University of Technology, 2024. 188 p.
  5. den Boef P, Maubach J, Schilders W, van de Wouw N. Large-Scale H2 Optimization for Thermo-Mechanical Reliability of Electronics. In van Beurden M, Budko NV, Ciuprina G, Schilders W, Bansal H, Barbulescu R, editors, Scientific Computing in Electrical Engineering: SCEE 2022, Amsterdam, The Netherlands, July 2022. Cham: Springer. 2024. p. 144-151. (Mathematics in Industry). doi: 10.1007/978-3-031-54517-7_16
  6. Fan H, Hou Q, Tijsseling AS, Sun X, Lian J. Mass shedding rate of an isolated high-speed slug propagating in a pipeline. Engineering Applications of Computational Fluid Mechanics. 2024 Jan 24;18(1):2303372. doi: 10.1080/19942060.2024.2303372
  7. Hochstenbach ME, Košir T, Plestenjak B. Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models. Numerical Linear Algebra with Applications. 2024 Mar;31(2):e2540. Epub 2023 Nov 9. doi: 10.1002/nla.2540
  8. Xia L, Massei S, Hochstenbach ME, Koren B. On Stochastic Roundoff Errors in Gradient Descent with Low-Precision Computation. Journal of Optimization Theory and Applications. 2024 Feb;200(2):634-668. Epub 2023 Dec 20. doi: 10.1007/s10957-023-02345-7
  9. Ferrandi G. Rayleigh Quotients in Gradient Methods and Linear Dimensionality Reduction. Eindhoven: Eindhoven University of Technology, 2024. 194 p.
  10. Sun Z, Hou Q, Tijsseling AS, Lian J, Wei J. Smoothed particle hydrodynamics with diffusive flux for advection–diffusion equation with discontinuities. Computers and Mathematics with Applications. 2024 Apr 15;160:70-85. doi: 10.1016/j.camwa.2024.02.012