On the Validity of the Local Fourier Analysis (Journal of Computational Mathematics, 2019)
Local Fourier analysis (LFA) is a useful tool in predicting the convergence factorsof geometric multigrid methods (GMG). As is well known, on rectangular domains withperiodic boundary conditions this analysis gives the exact convergence factors of suchmethods. When other boundary conditions are considered, however, this analysis wasjudged as been heuristic, with limited capabilities in predicting multigrid convergencerates. In this work, using the Fourier method, we extend these results by proving thatsuch analysis yields the exact convergence factors for a wider class of problems, some ofwhich cannot be handled by the traditional rigorous Fourier analysis.