New Analysis of Overlapping Schwarz Methods for Vector Field Problems in Three Dimensions with Generally Shaped Domains
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914759787413504 |
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| author | Oh, Duk-Soon Zhang, Shangyou |
| author_facet | Oh, Duk-Soon Zhang, Shangyou |
| contents | This paper introduces a novel approach to analyzing overlapping Schwarz methods for Nédélec and Raviart--Thomas vector field problems. The theory is based on new regular stable decompositions for vector fields that are robust to the topology of the domain. Enhanced estimates for the condition numbers of the preconditioned linear systems are derived, dependent linearly on the relative overlap between the overlapping subdomains. Furthermore, we present the numerical experiments which support our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Analysis of Overlapping Schwarz Methods for Vector Field Problems in Three Dimensions with Generally Shaped Domains Oh, Duk-Soon Zhang, Shangyou Numerical Analysis 65N55, 65N30, 65F08, 65F10 This paper introduces a novel approach to analyzing overlapping Schwarz methods for Nédélec and Raviart--Thomas vector field problems. The theory is based on new regular stable decompositions for vector fields that are robust to the topology of the domain. Enhanced estimates for the condition numbers of the preconditioned linear systems are derived, dependent linearly on the relative overlap between the overlapping subdomains. Furthermore, we present the numerical experiments which support our theoretical results. |
| title | New Analysis of Overlapping Schwarz Methods for Vector Field Problems in Three Dimensions with Generally Shaped Domains |
| topic | Numerical Analysis 65N55, 65N30, 65F08, 65F10 |
| url | https://arxiv.org/abs/2404.11986 |