A Cost-Effective Multigrid Projection Operator

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. 1 Introduction The multigrid method has been shown to be very effective in solving linear systems arising from discretized PDE boundary-value problems [2, 3]. It offers convergence rates independent of the size of the problems. Individual multigrid operators, including relaxation (smoother), projection (restriction) and interpolation (prolongation) operators, should be optimally combined to..