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.
