Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids

Abstract

We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication between the levels of the multigrid. Numerical experiments 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 conventional hierarchy of grids.