Local Fourier analysis (LFA) is a useful tool in predicting the convergence factors of geometric multigrid methods (GMG). As is well known, on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such methods. In this work, using the Fourier method, we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems.
@article{arxiv.1710.00408,
title = {On the validity of the local Fourier analysis},
author = {Carmen Rodrigo and Francisco J. Gaspar and Ludmil T. Zikatanov},
journal= {arXiv preprint arXiv:1710.00408},
year = {2017}
}