The Effect of the Schedule on the CPU Time for 2D Poisson Equation

Abstract

The aim of this paper is to minimize the CPU time necessary for solving the 2D Poisson equation with Dirichlet boundary conditions. We study the influence of: several schedules for the inner iterations (v) in the red-black Gauss-Seidel solver; number of levels of grids (L); and unknowns number (N) for grids of 33x33 to 8193x8193 nodes. It was verified that: (1) the small CPU time was obtained with the Hortmann schedule; (2) the order of p in the best schedule (type I Hortmann) is 0.99996.