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FETI solvers for non-standard finite element equations based on boundary integral operators. (English) Zbl 1382.65402

Erhel, Jocelyne (ed.) et al., Domain decomposition methods in science and engineering XXI. Proceedings of the 21st international conference, Inria Rennes Center, France, June 25–29, 2012. Cham: Springer (ISBN 978-3-319-05788-0/hbk; 978-3-319-35548-1/pbk; 978-3-319-05789-7/ebook). Lecture Notes in Computational Science and Engineering 98, 729-737 (2014).
Summary: We present efficient domain decomposition solvers for a class of non-standard finite element methods (FEMs). These methods utilize partial differential equations-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 boundary element method (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.
For the entire collection see [Zbl 1381.65002].

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65Y05 Parallel numerical computation
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References:

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