A p-cycle analysis of multigrid method

Abstract

We suggest a new strategy for multigrid iterations based on our analysis for p-cycle multigrid method. First, we improve a recent result on multigrid V-cycle analysis given by Bramble and Pasciak to p-cycle multigrid method. We show that the convergence rate improves slowly with p, eventually bounded by a constant which is in agreement with many previous experiments. Based on the this observation, we use p-cycle only in the first few multigrid iterations, which is more effective than the standard p-cycle.