Multigrid Method and Fourth Order Compact Diierence Scheme for 2d Poisson Equation with Unequal Meshsize Discretization

A fourth order compact diierence scheme with unequal meshsizes in diierent coordinate directions is employed to discretize two dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss-Seidel relaxation are designed to solve the resulting sparse linear systems. Numerical experiments are conducted to test accuracy of the fourth order compact diierence scheme and to compare it with the standard second order diierence scheme. Convergence behavior of the partial semicoarsening and line Gauss-Seidel relaxation multigrid methods is examined experimentally.

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