Agglomeration-Based Geometric Multigrid Solvers for Compact Discontinuous Galerkin Discretizations on Unstructured Meshes
Numerical Analysis
2022-04-08 v2 Numerical Analysis
Abstract
We present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is easily extendable to other discontinuous Galerkin discretizations, including the Local DG method and the Interior Penalty method. We demonstrate excellent solver performance for Poisson's equation, provided a flux formulation is used for the operator coarsening and a suitable switch function chosen for the numerical fluxes.
Cite
@article{arxiv.2012.08024,
title = {Agglomeration-Based Geometric Multigrid Solvers for Compact Discontinuous Galerkin Discretizations on Unstructured Meshes},
author = {Yulong Pan and Per-Olof Persson},
journal= {arXiv preprint arXiv:2012.08024},
year = {2022}
}