JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics BEM-based Finite Element Tearing and Interconnecting Methods
نویسندگان
چکیده
We present efficient domain decomposition solvers for a class of non-standard finite element methods (FEM). These methods utilize PDE-harmonic trial functions in every element of a polyhedral mesh, and use boundary element techniques locally in order to assemble the finite element stiffness matrices. For these reasons, the terms BEMbased FEM or Trefftz-FEM are sometimes used in connection with this method. 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. Spectral equivalences between certain approximations of element-local SteklovPoincaré operators play a central role in transferring the known convergence results for FETI to this new method. The theoretical results are supplemented by numerical tests confirming the theoretical predictions.
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1 Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, USA, [email protected] 2 Institute of Computational Mathematics, Johannes Kepler University, Linz, Austria, [email protected]; [email protected] 3 Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria, ulrich.lan...
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1 FWF-Start Project Y-192 “3D hp-Finite Elements”, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria [email protected] 2 Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstraße 69, 4040 Linz, Austria [email protected] 3 Institute of Computational Mathematics, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria ulanger...
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