The Poisson equation on the unit disk: a multigrid solver using polar coordinates

摘要

A multigrid solver for the Poisson equation on the unit disk is presented. It is shown that the problems due to the use of polar coordinates, namely the singularity at the origin and the anisotropy of the operator, constitute no obstacle to an efficient realization of a multigrid program. Our numerical results attest to the efficiency of the solver, also in comparison with well-known packages.