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Volume 37, Issue 3
On the Validity of the Local Fourier Analysis

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

DOI: 10.4208/jcm.1803-m2017-0294

J. Comp. Math., 37 (2019), pp. 340-348.

Published online: 2018-09

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Local Fourier analysis, multigrid, Fourier method.

  • AMS Subject Headings

65N55, 65T50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

carmenr@unizar.es (Carmen Rodrigo)

F.J.Gaspar@cwi.nl (Francisco J. Gaspar)

ludmil@psu.edu (Ludmil T. Zikatanov)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-340, author = {Rodrigo , CarmenGaspar , Francisco J. and Zikatanov , Ludmil T.}, title = {On the Validity of the Local Fourier Analysis}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {3}, pages = {340--348}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1803-m2017-0294}, url = {http://global-sci.org/intro/article_detail/jcm/12725.html} }
TY - JOUR T1 - On the Validity of the Local Fourier Analysis AU - Rodrigo , Carmen AU - Gaspar , Francisco J. AU - Zikatanov , Ludmil T. JO - Journal of Computational Mathematics VL - 3 SP - 340 EP - 348 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1803-m2017-0294 UR - https://global-sci.org/intro/article_detail/jcm/12725.html KW - Local Fourier analysis, multigrid, Fourier method. 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.

Carmen Rodrigo, Francisco J. Gaspar & Ludmil T. Zikatanov. (2019). On the Validity of the Local Fourier Analysis. Journal of Computational Mathematics. 37 (3). 340-348. doi:10.4208/jcm.1803-m2017-0294
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