On the convergence rate of the dirichlet-neumann iteration for coupled poisson problems on unstructured grids
(2020) 9th International Symposium on Finite Volumes for Complex Applications, FVCA 2020 In Springer Proceedings in Mathematics and Statistics 323. p.355-363- Abstract
We consider thermal fluid structure interaction with a partitioned approach, where typically, a finite volume and a finite element code would be coupled. As a model problem, we consider two coupled Poisson problems with heat conductivities $$\lambda _1$$, $$\lambda _2$$ in one dimension on intervals of length $$l:1$$ and $$l:2$$. Hereby, we consider linear discretizations on arbitrary meshes, such as finite volumes, finite differences, finite elements. For these, we prove that the convergence rate of the Dirichlet-Neumann iteration is given by $$\lambda _1l_2/\lambda _2l_1$$ and is thus independent of discretization and mesh.
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https://lup.lub.lu.se/record/e9e94360-0995-4f53-8de1-db5db507fe11
- author
- Görtz, Morgan and Birken, Philipp LU
- organization
- publishing date
- 2020
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Convergence Rate, Dirichlet-Neumann iteration, Partitioned Approach, Thermal Fluid-Structure-Interaction
- host publication
- Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020
- series title
- Springer Proceedings in Mathematics and Statistics
- editor
- Klöfkorn, Robert ; Keilegavlen, Eirik ; Radu, Florin A. and Fuhrmann, Jürgen
- volume
- 323
- pages
- 9 pages
- publisher
- Springer Gabler
- conference name
- 9th International Symposium on Finite Volumes for Complex Applications, FVCA 2020
- conference location
- Bergen, Norway
- conference dates
- 2020-06-15 - 2020-06-19
- external identifiers
-
- scopus:85087013252
- ISSN
- 2194-1017
- 2194-1009
- ISBN
- 9783030436506
- DOI
- 10.1007/978-3-030-43651-3_32
- language
- English
- LU publication?
- yes
- id
- e9e94360-0995-4f53-8de1-db5db507fe11
- date added to LUP
- 2020-07-13 11:13:47
- date last changed
- 2024-05-15 16:08:58
@inproceedings{e9e94360-0995-4f53-8de1-db5db507fe11, abstract = {{<p>We consider thermal fluid structure interaction with a partitioned approach, where typically, a finite volume and a finite element code would be coupled. As a model problem, we consider two coupled Poisson problems with heat conductivities $$\lambda _1$$, $$\lambda _2$$ in one dimension on intervals of length $$l:1$$ and $$l:2$$. Hereby, we consider linear discretizations on arbitrary meshes, such as finite volumes, finite differences, finite elements. For these, we prove that the convergence rate of the Dirichlet-Neumann iteration is given by $$\lambda _1l_2/\lambda _2l_1$$ and is thus independent of discretization and mesh.</p>}}, author = {{Görtz, Morgan and Birken, Philipp}}, booktitle = {{Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020}}, editor = {{Klöfkorn, Robert and Keilegavlen, Eirik and Radu, Florin A. and Fuhrmann, Jürgen}}, isbn = {{9783030436506}}, issn = {{2194-1017}}, keywords = {{Convergence Rate; Dirichlet-Neumann iteration; Partitioned Approach; Thermal Fluid-Structure-Interaction}}, language = {{eng}}, pages = {{355--363}}, publisher = {{Springer Gabler}}, series = {{Springer Proceedings in Mathematics and Statistics}}, title = {{On the convergence rate of the dirichlet-neumann iteration for coupled poisson problems on unstructured grids}}, url = {{http://dx.doi.org/10.1007/978-3-030-43651-3_32}}, doi = {{10.1007/978-3-030-43651-3_32}}, volume = {{323}}, year = {{2020}}, }