  The use of multigrid and related preconditioners with the finite element
method is often limited by the difficulty of applying the algorithm effectively
to a problem, especially when the domain has a complex shape or adaptive
refinement. We introduce a simplification of a general topologically-motivated
mesh coarsening algorithm for use in creating hierarchies of meshes for
geometric unstructured multigrid methods. The connections between the
guarantees of this technique and the quality criteria necessary for multigrid
methods for non-quasi-uniform problems are noted. The implementation details,
in particular those related to coarsening, remeshing, and interpolation, are
discussed. Computational tests on pathological test cases from adaptive finite
element methods show the performance of the technique.
