Application of the Multigrid Method to Poisson's Equation in Boundary-Fitted Coordinates

Results are presented showing an order of magnitude reduction in computer time when applying the multigrid methods to the solution of the Poisson equation in boundary-fitted coordinates. It is believed that little or no work on the application of the multigrid method to equations in boundary-fitted coordinates has been reported previously. The multigrid technique is a general strategy for obtaining solutions to partial differential equations by cycling between coarser and finer levels of discretization. The method is based on the elimination of error components whose wavelengths on a given grid are comparable to the point spacing in the grid. By cycling between coarse and fine grids, both high-frequency and low-frequency components of the error are reduced in an efficient way. The multigrid method is highly efficient in that most of the computation occurs in coarser grids rather than the finest grid upon which the solution is sought.