Geodesic
BEM-based finite element tearing and interconnecting methods
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 230-249
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 BEM-based 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 Steklov-Poincaré 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.
Classification : 65F10, 65N22, 65N30, 65N38
Keywords: finite elements, boundary elements, BEM-based FEM, domain decomposition, FETI, BETI, Trefftz methods, polyhedral meshes 
@article{ETNA_2015__44__a19,
     author = {Hofreither,  Clemens and Langer,  Ulrich and Pechstein,  Clemens},
     title = {BEM-based finite element tearing and interconnecting methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {230--249},
     year = {2015},
     volume = {44},
     zbl = {1327.65060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a19/}
}
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%A Pechstein,  Clemens
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%J Electronic transactions on numerical analysis
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%G en
%F ETNA_2015__44__a19
Hofreither,  Clemens; Langer,  Ulrich; Pechstein,  Clemens. BEM-based finite element tearing and interconnecting methods. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 230-249. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a19/