Research Topic
Matrix-free finite element methods and GPU-portable geometric multigrid solvers for global mantle convection simulation.
Supervisors
Professor Ulrich Rüde, Professor Harald Köstler (NHR@FAU)
Thesis Abstract
Towards Kilometre-Scale Global Mantle Convection: Matrix-Free Finite Elements and Multigrid on Heterogeneous Exascale Systems
My work targets 10¹³ degrees of freedom in global mantle circulation, a milestone equivalent to 1km uniform grid spacing. This resolves thin thermal boundary layers and plume conduits at Earth-like convective vigour, enabling direct comparison with seismic tomography. To this end, I co founded TERRA-NG, designing wedge-element Stokes operators and GPU-portable geometric multigrid solvers with adaptive Galerkin coarsening, implemented in Kokkos across NVIDIA, AMD and Intel hardware. I further explore neural operators as fast surrogates for geophysical forward models.
Publications
- Fabian Böhm et al. “Code Generation and Performance Engineering for Matrix-Free Finite Element Methods on Hybrid Tetrahedral Grids”. In: SIAM Journal on Scientific Computing 47.1 (Jan. 2025), B131–B159. issn: 1095-7197. doi: 10.1137/24m1653756. url: dx.doi.org/10. 1137/24M1653756.
Fabian Böhm et al. Large-scale Multigrid with Adaptive Galerkin Coarsening. 2025. url: https://arxiv.org/abs/2511.13109.
Conference Presentations
ICPP 2026 in October
Awards
- Best Poster Award at FEM Symposium 2023 in Graz, Austria.