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- Görtz, Morgan, et al.
(author)
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On the convergence rate of the dirichlet-neumann iteration for coupled poisson problems on unstructured grids
- 2020
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In: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020. - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783030436506 ; 323, s. 355-363
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Conference paper (peer-reviewed)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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