Compatible coarsening in the multigraph algorithm

We present some heuristics incorporating the philosophy of compatible relaxation into an existing algebraic multigrid method, the so-called multigraph solver of Bank and Smith [1]. In particular, approximate left and right eigenvectors of the iteration matrix for the smoother are used in computing both the sparsity pattern and the numerical values of the transfer matrices that correspond to restriction and prolongation. Some numerical examples illustrate the effectiveness of the procedure.