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Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues

Cross-points in domain decomposition, i.e., points where more than two subdomains meet, have received substantial attention over the past years, since domain decomposition methods often need special attention in their definition at cross-points, in particular if the transmission conditions of the do...

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Autores principales: Chaudet-Dumas, Bastien, Gander, Martin J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9829650/
https://www.ncbi.nlm.nih.gov/pubmed/36643714
http://dx.doi.org/10.1007/s11075-022-01445-1
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author Chaudet-Dumas, Bastien
Gander, Martin J.
author_facet Chaudet-Dumas, Bastien
Gander, Martin J.
author_sort Chaudet-Dumas, Bastien
collection PubMed
description Cross-points in domain decomposition, i.e., points where more than two subdomains meet, have received substantial attention over the past years, since domain decomposition methods often need special attention in their definition at cross-points, in particular if the transmission conditions of the domain decomposition method contain derivatives, like in the Dirichlet-Neumann method. We study here for the first time the convergence of the Dirichlet-Neumann method at the continuous level in the presence of cross-points. We show that its iterates can be uniquely decomposed into two parts, an even symmetric part that converges geometrically, like when there are no cross-points present, and an odd symmetric part, which generates a singularity at the cross-point and is not convergent. We illustrate our analysis with numerical experiments.
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spelling pubmed-98296502023-01-11 Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues Chaudet-Dumas, Bastien Gander, Martin J. Numer Algorithms Original Paper Cross-points in domain decomposition, i.e., points where more than two subdomains meet, have received substantial attention over the past years, since domain decomposition methods often need special attention in their definition at cross-points, in particular if the transmission conditions of the domain decomposition method contain derivatives, like in the Dirichlet-Neumann method. We study here for the first time the convergence of the Dirichlet-Neumann method at the continuous level in the presence of cross-points. We show that its iterates can be uniquely decomposed into two parts, an even symmetric part that converges geometrically, like when there are no cross-points present, and an odd symmetric part, which generates a singularity at the cross-point and is not convergent. We illustrate our analysis with numerical experiments. Springer US 2022-11-08 2023 /pmc/articles/PMC9829650/ /pubmed/36643714 http://dx.doi.org/10.1007/s11075-022-01445-1 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Chaudet-Dumas, Bastien
Gander, Martin J.
Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues
title Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues
title_full Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues
title_fullStr Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues
title_full_unstemmed Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues
title_short Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues
title_sort cross-points in the dirichlet-neumann method i: well-posedness and convergence issues
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9829650/
https://www.ncbi.nlm.nih.gov/pubmed/36643714
http://dx.doi.org/10.1007/s11075-022-01445-1
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