  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.
