Abstract
The finite element method and the boundary element method often have complementary properties in different situations. The domain decomposition technique allows to use the discretization method which is most appropriate for the subdomain under consideration. The coupling is based on the transmission conditions. The Dirichlet to Neumann (D2N) and Neumann to Dirichlet (N2D) maps are playing a crucial role in representing the transmission conditions. In this paper we study the D2N and N2D maps and their finite and boundary element approximations. Different formulations of the transmission conditions lead to different domain decomposition schemes with different properties. In any case we have to solve large scale systems of coupled finite and boundary element equations. The efficiency of iterative methods heavily depends on the availability of efficient preconditioners. We consider various solution strategies and provide appropriate preconditioners resulting in asymptotically almost optimal solvers.
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Langer, U., Steinbach, O. (2007). Coupled Finite and Boundary Element Domain Decomposition Methods. In: Schanz, M., Steinbach, O. (eds) Boundary Element Analysis. Lecture Notes in Applied and Computational Mechanics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47533-0_3
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DOI: https://doi.org/10.1007/978-3-540-47533-0_3
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