A High Accuracy Multigrid Method for the Three-Dimensional Poisson Equation

Based on the Taylor expansion,a fourth-order and a sixth-order compact difference scheme for the three-dimensional (3-D) Poisson equation are presented.A multigrid method and multigrid accelerating technique are employed to overcome the difficulties (larger cost and lower speed of convergence) when traditional relaxation methods are used to treat high dimensional problems.By using the method and the technique,the boundary value problems of the 3-D Poisson equation are solved.Numerical experiments results shown that the new high order compact difference schemes fit our expectation and the multigrid algorithm is very efficient.