Cargando…
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...
Autores principales: | , |
---|---|
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 |
_version_ | 1784867505106321408 |
---|---|
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. |
format | Online Article Text |
id | pubmed-9829650 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT chaudetdumasbastien crosspointsinthedirichletneumannmethodiwellposednessandconvergenceissues AT gandermartinj crosspointsinthedirichletneumannmethodiwellposednessandconvergenceissues |