Two Grid Iteration With A Conjugate Gradient Smoother Applied To A Groundwater Flow Model

. The well known two grid method is used to solve the large, sparse, linear system resulting from a finite element method discretisation of \Gammar:(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 effective. 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 effective than the standard two grid method. 1. Introduction. In this paper we consider the use of the two grid method, with various smoothers, for solving systems of linear equations arising from a finite element discretisation of the 2 dimensional elliptic partial differential equation: \Gamma r:(krp) = 0 (1.1) with appropriate boundary conditions. A stan..