The Multigrid Iteration Applied to the Collocation Method

We describe an application of the multigrid iteration to the collocation approximation for elliptic equations using a bicubic Hermite basis. A block relaxation and a projection operator specific to the collocation approximation were required to obtain convergence. We illustrate the method with the two-point boundary problem: Results are also given for an elliptic problem in two dimensions. Comments on computational efficiency are given along with operational counts. Results for a block SOR algorithm are also given. Comparison with a multigrid finite difference method indicates that the collocation method is less efficient.