Neumann-Neumann type domain decomposition of elliptic problems on metric graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929387693146112 |
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| author | Kovács, Mihály Vághy, Mihály András |
| author_facet | Kovács, Mihály Vághy, Mihály András |
| contents | In this paper we develop a Neumann-Neumann type domain decomposition method for elliptic problems on metric graphs. We describe the iteration in the continuous and discrete setting and rewrite the latter as a preconditioner for the Schur complement system. Then we formulate the discrete iteration as an abstract additive Schwarz iteration and prove that it convergences to the finite element solution with a rate that is independent of the finite element mesh size. We show that the condition number of the Schur complement is also independent of the finite element mesh size. We provide an implementation and test it on various examples of interest and compare it to other preconditioners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neumann-Neumann type domain decomposition of elliptic problems on metric graphs Kovács, Mihály Vághy, Mihály András Numerical Analysis 65N55 (Primary) 35R02, 65F08, 65N22 (Secondary) In this paper we develop a Neumann-Neumann type domain decomposition method for elliptic problems on metric graphs. We describe the iteration in the continuous and discrete setting and rewrite the latter as a preconditioner for the Schur complement system. Then we formulate the discrete iteration as an abstract additive Schwarz iteration and prove that it convergences to the finite element solution with a rate that is independent of the finite element mesh size. We show that the condition number of the Schur complement is also independent of the finite element mesh size. We provide an implementation and test it on various examples of interest and compare it to other preconditioners. |
| title | Neumann-Neumann type domain decomposition of elliptic problems on metric graphs |
| topic | Numerical Analysis 65N55 (Primary) 35R02, 65F08, 65N22 (Secondary) |
| url | https://arxiv.org/abs/2402.05707 |