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arXiv · 1311.5782

Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements

Michael Feischl·Thomas Führer·Dirk Praetorius·Ernst P. Stephan
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Abstract

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.

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Michael Feischl, Thomas Führer, Dirk Praetorius, Ernst P. Stephan. 2013-11-22. Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements. https://doi.org/10.1002/num.22025

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