Comparison of Second- and Fourth-Order Discretizations for Multigrid Poisson Solvers

Abstract

We combine a compact high-order difference approximation with multigrid V-cycle algorithm to solve the two-dimensional Poisson equation with Dirichlet boundary conditions. This scheme, along with several different orderings of grid space and projection operators, is compared with the five-point formula to show the dramatic improvement in computed accuracy, on serial and vector machines.