Geometric adaptive smoothed aggregation multigrid for discontinuous Galerkin discretisations
Numerical Analysis
2025-06-02 v2 Numerical Analysis
Abstract
We present a geometric multigrid solver based on adaptive smoothed aggregation suitable for Discontinuous Galerkin (DG) discretisations. Mesh hierarchies are formed via domain decomposition techniques, and the method is applicable to fully unstructured meshes using arbitrary element shapes. Furthermore, the method can be employed for a wide range of commonly used DG numerical fluxes for first- and second-order PDEs including the Interior Penalty and the Local Discontinuous Galerkin methods. We demonstrate excellent and mesh-independent convergence for a range of problems including the Poisson equation, and convection-diffusion for a range of P\'eclet numbers.
Cite
@article{arxiv.2504.13373,
title = {Geometric adaptive smoothed aggregation multigrid for discontinuous Galerkin discretisations},
author = {Yulong Pan and Michael Lindsey and Per-Olof Persson},
journal= {arXiv preprint arXiv:2504.13373},
year = {2025}
}