On the Convergence Rate of the Dirichlet-Neumann Iteration for Coupled Poisson Problems on Unstructured Grids

M. Görtz, P. Birken. FVCA 9, Bergen, Norway, 10 June 2020.


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 in one dimension on intervals of arbitrary length. 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 the models heat conductivity and domain lengths and is thus independent of discretization and mesh.

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