A Cost-Effective Multigrid Projection Operator

Jun Zhang
Department of Mathematics
The George Washington University
Washington, DC 20052, USA


A novel heuristic residual analysis is proposed to derive a computationally cost-effective residual projection operator in multigrid with the five-point Red-Black Gauss-Seidel relaxation for solving the two dimensional Poisson equation. This optimal residual injection operator is as cheap as the trivial injection operator, but is more efficient than the costly full-weighting operator and achieves near-optimal convergence rate.

1991 Mathematical Subject Classification: 65F10, 65N06, 65N22, 65N55.

Key words and phrases: Multigrid method, residual projection, Poisson equation, Red-Black Gauss-Seidel.

This paper has been published in Journal of Applied and Computational Mathematics, Vol. 76, 325--333 (1996).