Volume 44, pp. 230-249, 2015.

BEM-based Finite Element Tearing and Interconnecting Methods

Clemens Hofreither, Ulrich Langer, and Clemens Pechstein

Abstract

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.

Full Text (PDF) [387 KB]

Key words

finite elements, boundary elements, BEM-based FEM, domain decomposition, FETI, BETI, Trefftz methods, polyhedral meshes

AMS subject classifications

65F10, 65N22, 65N30, 65N38

Links to the cited ETNA articles

[10]Vol. 37 (2010), pp. 413-436 Clemens Hofreither, Ulrich Langer, and Clemens Pechstein: Analysis of a non-standard finite element method based on boundary integral operators

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