Additive and multiplicative multi-grid -- a comparison (Q1265395)

The authors do a careful analysis of the efficiency of various multigrid methods when they are combined with local mesh refinement. They also consider the need for robust smoothers for singular perturbation problems. For the one-dimensional Poisson equation on an interval they show that one ought to use a multiplicative version of multigrid rather than additive multigrid, and that one should smooth more than once on each grid. Several two-dimensional numerical examples are given which exhibit similar behavior.