异质耦合的抽象框架:稳定性、近似性和应用

Silvia Bertoluzza, Erik Burman
{"title":"异质耦合的抽象框架:稳定性、近似性和应用","authors":"Silvia Bertoluzza, Erik Burman","doi":"arxiv-2312.11733","DOIUrl":null,"url":null,"abstract":"Introducing a coupling framework reminiscent of FETI methods, but here on\nabstract form, we establish conditions for stability and minimal requirements\nfor well-posedness on the continuous level, as well as conditions on local\nsolvers for the approximation of subproblems. We then discuss stability of the\nresulting Lagrange multiplier methods and show stability under a mesh\nconditions between the local discretizations and the mortar space. If this\ncondition is not satisfied we show how a stabilization, acting only on the\nmultiplier can be used to achieve stability. The design of preconditioners of\nthe Schur complement system is discussed in the unstabilized case. Finally we\ndiscuss some applications that enter the framework.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"111 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An abstract framework for heterogeneous coupling: stability, approximation and applications\",\"authors\":\"Silvia Bertoluzza, Erik Burman\",\"doi\":\"arxiv-2312.11733\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Introducing a coupling framework reminiscent of FETI methods, but here on\\nabstract form, we establish conditions for stability and minimal requirements\\nfor well-posedness on the continuous level, as well as conditions on local\\nsolvers for the approximation of subproblems. We then discuss stability of the\\nresulting Lagrange multiplier methods and show stability under a mesh\\nconditions between the local discretizations and the mortar space. If this\\ncondition is not satisfied we show how a stabilization, acting only on the\\nmultiplier can be used to achieve stability. The design of preconditioners of\\nthe Schur complement system is discussed in the unstabilized case. Finally we\\ndiscuss some applications that enter the framework.\",\"PeriodicalId\":501061,\"journal\":{\"name\":\"arXiv - CS - Numerical Analysis\",\"volume\":\"111 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2312.11733\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2312.11733","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

我们引入了一个类似于 FETI 方法的耦合框架(但这里是抽象的形式),建立了稳定性条件和对连续层面问题解决的最低要求,以及对近似子问题的局部求解器的条件。然后,我们讨论了拉格朗日乘数方法的稳定性,并展示了在局部离散和灰泥空间之间的网格条件下的稳定性。如果该条件不满足,我们将展示如何使用仅作用于乘法器的稳定方法来实现稳定性。在未稳定的情况下,我们还讨论了舒尔补码系统的预处理器的设计。最后,我们讨论了进入该框架的一些应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An abstract framework for heterogeneous coupling: stability, approximation and applications
Introducing a coupling framework reminiscent of FETI methods, but here on abstract form, we establish conditions for stability and minimal requirements for well-posedness on the continuous level, as well as conditions on local solvers for the approximation of subproblems. We then discuss stability of the resulting Lagrange multiplier methods and show stability under a mesh conditions between the local discretizations and the mortar space. If this condition is not satisfied we show how a stabilization, acting only on the multiplier can be used to achieve stability. The design of preconditioners of the Schur complement system is discussed in the unstabilized case. Finally we discuss some applications that enter the framework.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信