ON RED-BLACK SOR SMOOTHING IN MULTIGRID

Optimal relaxation parameters are obtained for red-black Gauss-Seidel relaxation in multigrid solvers of a family of elliptic equations. The resulting relaxation schemes are found to retain very high efficiency over an appreciable range of coefficients of the elliptic differentia l operator, yielding simple, inexpensive, and fully parallelizable smo others in many situations where less cost-effective block- and alterna ting-direction schemes are commonly used.