Introduction

This repository demonstrates some Finite Difference methods for solving the Poisson problem

∇u := u_xx + u_yy = f

with periodic boundary conditions in SaC. (Uniform, structured mesh.)

Files

Each file contains a comment at the top giving some explanation. We use red-black order, which is illustrated in red_black_reorder_2d.sac. We are working towards a Full Multigrid method, which is a combination of other techniques. In order:

• discretize_rb.sac: shows how to implement a linear approximation for the Laplacian operator.
• sor_red_black.sac: successive overrelaxation using red-black order. Complexity O(n^3 log(n))
• v_cycle_rb.sac: V-cycle, complexity O(n^2 log(n))
• fmg_rb.sac: Full multigrid, complexity O(n^2).