Coarsening by compatible relaxation

A proper coarse variable set for algebraic multigrid (AMG) solvers can be constructed using compatible relaxation (CR). For a given coarse set, CR is a modified relaxation scheme that keeps the values of the coarse variables intact. Its convergence factor is a predictor of the potential AMG efficiency, similarly to the smoothing factor in geometric multigrid. A practical, CR-based coarse set construction algorithm is presented. Numerical results for model problems are demonstrated. Copyright (C) 2004 John Wiley Sons, Ltd.