On the validity of the local Fourier analysis*

Carmen Rodrigo, Francisco J. Gaspar, Ludmil T. Zikatanov

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)340-348
Number of pages9
JournalJournal of Computational Mathematics
Volume37
Issue number3
DOIs
StatePublished - Jan 1 2019

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Fourier analysis
Fourier Analysis
Boundary conditions
Fourier Method
Multigrid Method
Periodic Boundary Conditions
Convergence Rate
Heuristics

All Science Journal Classification (ASJC) codes

  • Computational Mathematics

Cite this

Rodrigo, Carmen ; Gaspar, Francisco J. ; Zikatanov, Ludmil T. / On the validity of the local Fourier analysis* In: Journal of Computational Mathematics. 2019 ; Vol. 37, No. 3. pp. 340-348.
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On the validity of the local Fourier analysis* . / Rodrigo, Carmen; Gaspar, Francisco J.; Zikatanov, Ludmil T.

In: Journal of Computational Mathematics, Vol. 37, No. 3, 01.01.2019, p. 340-348.

Research output: Contribution to journalArticle

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