Multi-Level Minimal Residual Smoothing: A Family of
General Purpose Multigrid Acceleration Techniques

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506--0046, USA

Abstract

We employ multi-level minimal residual smoothing (MRS) as a pre-optimization technique to accelerate standard multigrid convergence. The MRS method is used to improve the current multigrid iterate by smoothing its corresponding residual before the latter is projected to the coarse grid. We develop different schemes for implementing MRS technique on the finest grid and on the coarse grids, and several versions of the inexact MRS technique. Numerical experiments are conducted to show the efficiency of the multi-level and inexact MRS techniques.


Key words: Minimal residual smoothing, multigrid method, residual scaling techniques.


This paper has been accepted for publication in Journal of Computational and Applied Mathematics.