A comparison of element agglomeration algorithms for unstructured geometric multigrid

Abstract

This paper compares the performance of seven different element agglomeration algorithms on unstructured triangular/tetrahedral meshes when used as part of a geometric multigrid. Five of these algorithms come from the literature on AMGe multigrid and mesh partitioning methods. The resulting multigrid schemes are tested matrix-free on two problems in 2D and 3D taken from radiation transport applications; one of which is in the diffusion limit. In two dimensions all coarsening algorithms result in multigrid methods which perform similarly, but in three dimensions aggressive element agglomeration performed by METIS produces the shortest runtimes and multigrid setup times.

Agglomeration-Based Geometric Multigrid Solvers for Compact Discontinuous Galerkin Discretizations on Unstructured Meshes

“…However, the technique has been used successfully for finite volume methods [11,4,18], where it is easier to update the element-averages after coarsening. This is also true for high-order discontinuous Galerkin methods, since they are straight-forward to implement on meshes of arbitrarily shaped elements [7,6].…”