We solve Poisson's equation using new multigrid algorithms that converge rapidly. The feature of the 2D and 3D algorithms are the use of diagonally oriented grids in the multigrid hierarchy for a much richer and effective communication between the levels of the multigrid. Numerical investigations into solving Poisson's equation in the unit square and unit cube show simple versions of the proposed algorithms are up to twice as fast as correspondingly simple multigrid iterations on a standard hierarchy of grids. Similar improvements are found for a basic advection-diffusion equations.
