Minimal residual smoothing in multi-level iterative method

Abstract

A minimal residual smoothing (MRS) technique is employed to accelerate the convergence of the multi-level iterative method by smoothing the residuals of the original iterative sequence. The sequence with smoothed residuals is re-introduced into the multi-level iterative process. The new sequence generated by this acceleration procedure converges much faster than both the sequence generated by the original multi-level method and the sequence generated by MRS technique. The cost of this acceleration scheme is independent of the original operator and in many cases is negligible. The emphasis of this paper is on the practical implementation of MRS acceleration techniques in the multi-level method. The discussions are focused on the two-level method because the acceleration scheme is only applied on the finest level of the multi-level method. Numerical experiments using the proposed MRS acceleration scheme to accelerate both the two-level and multi-level methods are conducted to show the efficiency and the cost-effectiveness of this acceleration scheme.