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.

Contributed July 17, 1996.