Conditional semicoarsening multigrid algorithm for the Poisson equation on anisotropic grids

A conditional semicoarsening multigrid algorithm is developed for the Poisson equation on stretched grids. The smoothing behaviour of the pointwise smoother, as predicted by local Fourier analysis, is used to determine how to coarsen the grid. This process ensures that the smoothed error can be adequately resolved on the coarse grid, which results in an efficient multigrid algorithm that is simple to implement. The use of a pointwise smoother increases the degree of parallelism of the algorithm. sulting algorithm is tested on several different grid types, some with very high degrees of stretching. The computational cost is found to scale almost linearly with the number of grid points, and parallel efficiencies of over 90% are achieved even for very coarse grids.