Optimal Coarsening of Unstructured Meshes

A bounded aspect-ratio coarsening sequence of an unstructured mesh M 0 is a sequence of meshes M 1 ; : : : ; M k such that: M i is a bounded aspect-ratio mesh, and M i is an approximation of M i?1 that has fewer elements, where a mesh is called a bounded aspect-ratio mesh if all its elements are of bounded aspect-ratio. The sequence is node-nested if the set of the nodes of M i is a subset of that of M i?1. The problem of constructing good quality coarsening sequences is a key step for hierarchical and multi-level numerical calculations. In this paper, we give an algorithm for nding a bounded aspect-ratio, node{nested, coarsening sequence that is of optimal size: that is, the number of meshes in the sequence, as well as the number of elements in each mesh, are within a constant factor of the smallest possible.