@Article{JCM-37-3,
author = {Rodrigo, Carmen and J., Gaspar, Francisco and Zikatanov, T., Ludmil},
title = {On the Validity of the Local Fourier Analysis},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {3},
pages = {340--348},
abstract = {<p style="text-align: justify;">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. When other boundary conditions are considered, however, this analysis was
judged as been heuristic, with limited capabilities in predicting multigrid convergence
rates. 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, some of
which cannot be handled by the traditional rigorous Fourier analysis.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1803-m2017-0294},
url = {https://global-sci.com/article/84412/on-the-validity-of-the-local-fourier-analysis}
}