Acceleration and Stabilization Properties of Minimal Residual Smoothing Technique in Multigrid

Jun Zhang
Department of Computer Science and Engineering
University of Minnesota
Minneapolis, MN 55455, USA

Abstract

We analyze the standard multigrid method accelerated by a minimal residual smoothing (MRS) technique. We show that MRS can accelerate the convergence of the slow residual components, thus accelerates the overall multigrid convergence. We prove that, under certain hypotheses, MRS stabilizes the divergence of certain slow residual components and thus stabilizes the divergent multigrid iteration. The analysis is customarily conducted on the two-level method.


Key words: two-level method, conjugate gradient-type methods, convergence acceleration.

1991 AMS subject classifications: 65F10, 65N06.


This paper has been accepted for publication in Applied Mathematics and Computation.