FETI Solvers for Non-standard Finite Element Equations Based on Boundary Integral Operators
We present efficient Domain Decomposition solvers for a class of non-standard Finite Element Methods. These methods utilize PDE-harmonic trial functions in every element of a polyhedral mesh, and use boundary element techniques locally in order to generate the finite element stiffness matrices. For these reasons, the terms BEM-based FEM or Trefftz-FEM are sometimes used. In the present paper, we show that Finite Element Tearing and Interconnecting (FETI) methods can be used to solve the resulting linear systems in a quasi-optimal, robust and parallel manner. An important theoretical tool are spectral equivalences between FEM- and BEM-approximated Steklov–Poincaré operators.
The authors gratefully acknowledge the financial support by the Austrian Science Fund (FWF) under the grant DK W1214, project DK4.
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