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Published in:
2020 | OriginalPaper | Chapter
On the Convergence Rate of the Dirichlet-Neumann Iteration for Coupled Poisson Problems on Unstructured Grids
Authors : Morgan Görtz, Philipp Birken
Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
Publisher: Springer International Publishing
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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.