Two-Grid Analysis of Minimal Residual Smoothing
as a Multigrid Acceleration Technique

Jun Zhang
Department of Mathematics
The George Washington University
Washington, DC 20052, USA
and
Department of Computer Science and Engineering
University of Minnesota
4-192 EE/CS Building, 200 Union Street S.E.
Minneapolis, MN 55455, USA

Abstract

We analyze the two-level method accelerated by a minimal residual smoothing (MRS) technique. The two-grid analysis is sufficient for our purpose because our MRS acceleration scheme is only applied on the finest level of the multigrid method. We prove that the MRS acceleration scheme is a semi-iterative method with respect to the underlying two-level iteration and that the MRS accelerated two-level method is a polynomial acceleration of first order. We explain why MRS may not effectively accelerate standard multigrid method for solving Poisson-like problems. The iteration matrices for the MRS accelerated coarse-grid-correction operator and the MRS accelerated two-level operator are obtained. We give bounds for the residual reduction rates of the accelerated two-level method. Numerical experiments are employed to support the analytical results.

Key words and phrases: Multigrid method, minimal residual smoothing, multigrid acceleration techniques, two-grid analysis.


This article has been published in Applied Mathematics and Computation, Vol. 96 (1), 27--45 (1998).