On the acceleration of the preconditioned simultaneous displacement method

This paper considers the application of various accelerated techniques of the Preconditioned Simultaneous Displacement method (PSD method) [3]. The resulting methods possess rates of convergence which are improved by an order of magnitude as compared with the well known SOR method. However, it is shown that the PSD-Variable Extrapolation method (PSD-VE method) combined with a computational work reduction scheme [10] seems to offer a substantial saving in overall efficiency. The application of the analysis to the model problem involving Laplace's equation and the generalised Dirichlet problem is considered. In addition, the results of a number of various numerical experiments are also given. It is concluded that the PSD-VE method with Niethammer's approach is superior than SOR at least for the cases considered.