Two Grid Iteration with a Conjugate Gradient Smoother Applied to a Groundwater Flow Model

Abstract

The well known two grid method is used to solve the large, sparse, linear system resulting from a nite element method discretisation of ?r:(krp) = 0. Several possible choices of smoother are considered. When tested on a physically realistic problem it is found that the use of the conjugate gradient method is particularly eeective. A \computational modal analysis" on a model problem, discretised using biquadratic basis functions over 9 node quadrilaterals, is used to study the performance of each smoother. The use of conjugate gradients preconditioned by the two grid method is also considered, but this is shown to be less eeective than the standard two grid method.

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