Research Topic
Reduced and mixed precision multigrid methods.
Supervisor
- Professor Ulrich Rüde (NHR@FAU)
Thesis Abstract
Parallel Multigrid Algorithms for Systems of Partial Differential Equations
The backbone of many scientific simulation codes is a numerical PDE solver. A solver that is simultaneously accurate and efficient must reduce discretization and rounding error to comparable level. Consequently, the floating-point precision must increase as the grid is refined, leading to super-linear storage cost. My research focuses on combating this super-linear growth and developing a mixed-precision linear-storage multigrid method. The key idea is leveraging the smoothness of the solution to compress its in-memory representation.
Publications
Daniel Bauer et al. “Multigrid with Linear Storage Complexity”. In: SIAM Journal on Scientific Computing (accepted) (2026). doi: 10.48550/arXiv.2511.19036
Conference Presentations
- Platform for Advanced Scientific Computing (PASC), Davos, 2023-06-26/28: "Multigrid in H(curl) on Hybrid Tetrahedral Grids " (poster)
- Chemnitz Finite Element Symposium 2023, Leibnitz, 2023-09-11/13: "Multigrid in H(curl) on Hybrid Tetrahedral Grids " (poster)
- SIAM Conference on Parallel Processing for Scientific Computing (SIAM PP), Baltimore, 2024-03-05/08: “Code Generation for Matrix-Free Finite Element Methods on Hybrid Tetrahedral Grids ”
- 22nd Copper Mountain Conference on Multigrid Methods, Copper Mountain, 2025-04-13/17: “Multigrid with Linear Storage Complexity”
- Workshop on Approximate Computing in Numerical Linear Algebra, Paris, 2025-10-07/10, “Multigrid with Linear Storage Complexity”
- 10th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), München, 2026-07-19/24, "Multigrid with Linear Storage Complexity"
Awards
- Winner of the Student Paper Competition for the 2025 Copper Mountain Conference on Multigrid Methods