Multi-level minimal residual smoothing: A family of general purpose multigrid acceleration techniques

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.