# Outcomes

GRUMMP is quite successful in coarsening isotropic unstructured meshes -- nearly all vertices are removed in each case, and mesh quality is quite good. Two-dimensional anisotropic meshes are also handled well. The weakest area, by far, is anisotropic three-dimensional meshes, where the number of vertices that can not be removed climbs sharply, and mesh quality is poor (even allowing for anisotropy).

Two strategies that have some chance at success have not yet been investigated:

- Local transformation of anisotropic mesh fragments into a space where the mesh is approximately isotropic. In this scenario, edge contraction could be applied in the transformed space. The isotropic edge contraction criteria should strongly inhibit tangling of connectivity among vertices that should be in different levels of the anisotropic mesh.
- Creation of the coarse anisotropic mesh by construction. This approach would likely involve determining the coarse surface mesh topology and then projecting that topology out through the appropriate number of layers of anisotropic cells. A major challenge with this approach would be transition from anisotropic to isotropic meshing. Also, this approach is tantamount to generating the coarse mesh from scratch; the latter might give more flexibility and therefore be preferable for anisotropic meshes.