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Mathematics > Numerical Analysis

arXiv:2310.09381 (math)
[Submitted on 13 Oct 2023]

Title:A Local Fourier Analysis for Additive Schwarz Smoothers

Authors:Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. Gaspar, James H. Adler, Xiaozhe Hu, Ludmil Zikatanov
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Abstract: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 overlapping, 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 type of relaxations are widely used.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2310.09381 [math.NA]
  (or arXiv:2310.09381v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2310.09381

Submission history

From: Carmen Rodrigo [view email]
[v1] Fri, 13 Oct 2023 20:00:18 UTC (21 KB)
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