Kohl N, Bauer D, Böhm F, Rüde U (2023)
Publication Type: Journal article
Publication year: 2023
DOI: 10.1080/17445760.2023.2266875
This paper presents efficient data structures for the implementation of matrix-free finite element methods on block-structured, hybrid tetrahedral grids. It provides a complete categorization of all geometric sub-objects that emerge from the regular refinement of the unstructured, tetrahedral coarse grid and describes efficient iteration patterns and analytical linearization functions for the mapping of coefficients to memory addresses. This foundation enables the implementation of fast, extreme-scalable, matrix-free, iterative solvers, and in particular geometric multigrid methods by design. Their application to the variable-coefficient Stokes system subject to an enriched Galerkin discretization and to the curl-curl problem discretized with Nédélec edge elements showcases the flexibility of the implementation. Finally, the solution of a curl-curl problem with (Formula presented.) (more than one hundred billion) unknowns on more than 32,000 processes with a matrix-free full multigrid solver demonstrates its extreme-scalability.
APA:
Kohl, N., Bauer, D., Böhm, F., & Rüde, U. (2023). Fundamental data structures for matrix-free finite elements on hybrid tetrahedral grids. International Journal of Parallel, Emergent and Distributed Systems. https://doi.org/10.1080/17445760.2023.2266875
MLA:
Kohl, Nils, et al. "Fundamental data structures for matrix-free finite elements on hybrid tetrahedral grids." International Journal of Parallel, Emergent and Distributed Systems (2023).
BibTeX: Download