TY - JOUR
T1 - On the validity of the local Fourier analysis*
AU - Rodrigo, Carmen
AU - Gaspar, Francisco J.
AU - Zikatanov, Ludmil T.
N1 - Publisher Copyright:
© 2019 Global Science Press. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
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U2 - 10.4208/jcm.1803-m2017-0294
DO - 10.4208/jcm.1803-m2017-0294
M3 - Article
AN - SCOPUS:85062702088
SN - 0254-9409
VL - 37
SP - 340
EP - 348
JO - Journal of Computational Mathematics
JF - Journal of Computational Mathematics
IS - 3
ER -