Alternating direction iterative (ADI) methods do not usually work well on parallel computers due to having to do parallel rather than serial tridiagonal solves in all but one dimension. An ADI-like iteration is developed and analyzed which does not require parallel tridiagonal solves in any direction, has at least as good of a convergence rate as ADI, and has almost no communication when a small number of iterations are used. Acceleration parameters are investigated in order to reduce the number of of iterations to a small number. Numerical experiments on a network of workstations and a parallel computer are also included.

Key words: alternating direction implicit methods, ADI, partial differential equations, iterative methods, parallel computing