Multigrid Method with Adaptive Gauss-Seidel Smoother for Solving Poisson Equations

In this paper, an adaptive full multigrid method is presented for the iterative solution of the large scale sparse linear systems resulting from the finite difference discretization of two dimensional Poisson equation. This method is based on a hybrid Gauss-Seidel iterative algorithm, which is build by a modified stencil elimination procedure. Numerical experiments are conducted to show the feasibility and efficiency of the new method.