Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
---|---|---|
Page(s) | 2371 - 2396 | |
DOI | https://doi.org/10.1051/m2an/2023051 | |
Published online | 18 July 2023 |
Discrete-time analysis of optimized Schwarz waveform relaxation with Robin parameters depending on the targeted iteration count
1
Université Sorbonne Paris Nord, LAGA, CNRS UMR 7539, Institut Galilée, 99 Av. J.-B. Clément, 93430 Villetaneuse, France
2
Université Paris-Saclay, CEA, Service de Génie Logiciel pour la Simulation, 91191 Gif-sur-Yvette, France
* Corresponding author: pascal.omnes@cea.fr
Received:
26
August
2022
Accepted:
2
June
2023
We propose a new approach that provides new results in the convergence analysis of optimized Schwarz waveform relaxation (OSWR) iterations for parabolic problems, and allows to define efficient optimized Robin parameters that depend on the targeted iteration count, a property that is shared by the actual observed optimal parameters, while traditional Fourier analysis in the time direction leads to iteration independent parameters. This new approach is based on the exact resolution of the time semi-discrete error equations. It allows to recommend a couple (number of iterations, Robin parameter) to reach a given accuracy. While the general ideas may apply to an arbitrary space dimension, the analysis is first presented in the one dimensional case. Numerical experiments illustrate the performance obtained with such iteration-dependent optimized Robin parameters.
Mathematics Subject Classification: 65M55 / 35K20 / 65M12 / 65M22 / 65B99
Key words: Optimized Schwarz waveform relaxation discrete-time convergence analysis / iteration-dependent Robin parameters
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.