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 differential operator, yielding simple, inexpensive, and fully parallelizable smoothers in many situations where less cost-effective block- and alternating-direction schemes are commonly used.