M. Feischl, T. Führer, D. Praetorius, E. Stephan:

"Optimal preconditioning for the coupling of adaptive finite and boundary elements";

in: "ASC Report 12/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 12.

We consider the adaptive coupling of finite element method (FEM) and

boundary element (BEM) in 2D. It is well-known that the condition number of the Galerkin matrix depends on the minimal diameter of the elements in the triangulation and therefore can grow severely if the triangulation is locally refined. Usually, this affects the solver, i.e., the number of iterations used by an iterative solver can be arbitrarily large. Thus, the construction of an optimal reconditioner is a necessary task to ensure performance as well as reliable results. Here, optimality is understood in the sense that the condition number of the preconditioned system remains bounded independently of the (minimal and maximal) diameter as well as the number of elements. In our talk, we present some block-diagonal preconditioner for the non-symmetric Johnson-NŽedŽelec FEM-BEM coupling on locally refined triangulations. The diagonal blocks correspond to local additive Schwarz preconditioners for either the FEM part or the BEM part. We report on the optimality result for this preconditioning from [5] and underline this mathematical result by numerical experiments.

FEM-BEM coupling, preconditioner, additive Schwarz, adaptivity

http://www.asc.tuwien.ac.at/preprint/2014/asc12x2014.pdf

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