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README.md

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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).