MULTIGRID SMOOTHING FACTORS FOR RED-BLACK GAUSS-SEIDEL RELAXATION APPLIED TO A CLASS OF ELLIPTIC-OPERATORS

Analytic formulae are obtained for the smoothing factors yielded by Ga uss-Seidel relaxation in two-color ordering for a class of scalar elli ptic operators. Block and point relaxations, in conjunction with full or partial coarsening, are encompassed for operators with general (con stant, positive) coefficients in general dimensions and for an arbitra ry number of relaxation sweeps. It is found that there is no direct de pendence of the smoothing factors on the dimension, and that the effec t of the number of relaxation sweeps on the smoothing factor is usuall y independent of the operator coefficients and of the relaxation schem e. The results are compared with computed results of two-level analyse s. Smoothing strategies implied by the formulae are discussed.