Preconditioning with a Decoupled Rowwise Ordering on the CM-5

Decoupled rowwise ordering is an ordering scheme for 2-dimensional grids, which is tailored for preconditioning 5-point diierence equations arising from discretizations of partial diierential equations. This paper describes the ordering scheme and implementations of a conjugate gradient solver and SSOR preconditioners which use the decoupled rowwise and the red black ordering schemes on the CM-5 parallel supercomputer. The rowwise decoupled preconditioner leads to faster convergence than the red black preconditioner, and it reduces the solution time by a factor of 1:5 to 2:5 over a nonpreconditioned solver on a variety of test problems.