Local mode analysis of multicolor and composite relaxation schemes

We develop local mode analysis of multicolor (or more generally multicoupling) numerical processes and provide practical procedures for computing their symbols and predicting their convergence and smoothing properties, in the context of multigrid methods. We apply our analysis, including simple numerical examples, to multicolor point relaxation, especially in the context of the novel composite relaxation [20.]; [13.]) for products of discrete operators, such as the biharmonic.