Coarsening unstructured meshes by edge contraction

A new unstructured mesh coarsening algorithm has been developed for use in conjunction with multilevel methods. The algorithm preserves geometrical and topological features of the domain, and retains a maximal independent set of interior vertices to produce good coarse mesh quality. In anisotropic meshes, vertex selection is designed to retain the structure of the anisotropic mesh while reducing cell aspect ratio. Vertices are removed incrementally by contracting edges to zero length. Each vertex is removed by contracting the edge that maximizes the minimum sine of the dihedral angles of cells a ected by the edge contraction. Rarely, a vertex slated for removal from the mesh cannot be removed; the success rate for vertex removal is typically 99.9% or more. For two-dimensional meshes, both isotropic and anisotropic, the new approach is an unquali ed success, removing all rejected vertices and producing output meshes of high quality; mesh quality degrades only when most vertices lie on the boundary. Three-dimensional isotropic meshes are also coarsened successfully, provided that there is no di culty distinguishing corners in the geometry from coarselyresolved curved surfaces; sophisticated discrete computational geometry techniques appear necessary to make that distinction. Three-dimensional anisotropic cases are still problematic because of tight constraints on legal mesh connectivity. More work is required to either improve edge contraction choices or to develop an alternative strategy for mesh coarsening for three-dimensional anisotropic meshes