The smoothing effect of a simultaneous directions parallel method as applied to Poisson problems

By using local Fourier analysis, a simultaneous directions parallel method, which is a particular instance of the parallel fractional step algorithm, is shown to possess smoothing effects when applied to Poisson problems. The specific smoothing factor is determined and the expected factor values are found to be consistent with those obtained. The simultaneous directions approach is an advantageous alternative to other existing smoothers in the multigrid environment. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006