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M. Feischl, T. Führer, D. Praetorius, E. Stephan:
"Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements";
in: "ASC Report 36/2013", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, S. 1 - 36.

We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the condition number of the preconditioned system stays uniformly bounded, independently
of the refinement level and the local mesh-size of the underlying adaptively refined triangulations. Although the focus is on the non-symmetric Johnson-N´ed´elec one equation coupling, the principle ideas also apply to other formulations like the symmetric
FEM-BEM coupling. Numerical experiments underline our theoretical findings.

FEM-BEM coupling, preconditioner, multilevel additive Schwarz, adaptivity.

http://www.asc.tuwien.ac.at/preprint/2013/asc36x2013.pdf