A Cost-Effective Multigrid Projection Operator

(to appear in Journal of Computational and Applied Mathematics.)

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

zhang@math.gwu.edu    http://gwis2.circ.gwu.edu/~yaohan

      February 1, 1996, revised April 20, 1996

                      Abstract

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.