A local Fourier analysis for additive Schwarz smoothers

In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is cru...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2024-03, Vol.158, p.13-20
Main Authors: Pé de la Riva, Álvaro, Rodrigo, Carmen, Gaspar, Francisco J., Adler, James H., Hu, Xiaozhe, Zikatanov, Ludmil
Format: Article
Language:English
Subjects:
Additive Schwarz smoothers
High-order finite element methods
Local Fourier analysis
Multigrid methods
Saddle point problems
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Summary:In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is crucial in practice since it allows one to know a priori the answer to questions such as what is the size of the patch to use within these relaxations, the size of the overlap, or even the optimal values for the weights involved in the smoother. Results are shown for a class of additive and restricted additive Schwarz relaxations used within a multigrid framework applied to high-order finite-element discretizations and saddle point problems, which are two of the contexts in which these types of relaxations are widely used.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2023.12.039