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On the convergence rate of the dirichlet-neumann iteration for coupled poisson problems on unstructured grids

Görtz, Morgan and Birken, Philipp LU (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.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
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
2025-10-14 11:40:40
@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}},
}