A note on multigrid for the three-dimensional Poisson equation in cylindrical coordinates

摘要

Following Young and Dauwalder (1965), Iyengar and Manohar (1988) derived high-order difference methods for the solution of the three-dimensional Poisson equation and heat equation in polar cylindrical coordinates. In this note, we implement and compare S- and V-cycles in the multigrid context for the fourth-order method derived by Iyengar and Manohar (1988), for the solution of the three-dimensional Poisson equation. Defect correction is also studied. Suitable restrictions and prolongations for the three-dimensional problems are given. It is seen that the S-cycle is more efficient than the V-cycle and defect correction is more economical than the direct implementation of the fourth-order method.