Volume 45, pp. 219-240, 2016.

Cross-points in domain decomposition methods with a finite element discretization

Martin J. Gander and Kévin Santugini

Abstract

Non-overlapping domain decomposition methods necessarily have to exchange Dirichlet and Neumann traces at interfaces in order to allow for convergence to the underlying mono-domain solution. Well-known such non-overlapping methods are the Dirichlet-Neumann method, the FETI and Neumann-Neumann methods, and optimized Schwarz methods. For all these methods, cross-points in the domain decomposition configuration where more than two subdomains meet do not pose any problem at the continuous level, but care must be taken when the methods are discretized. We show in this paper two possible approaches for the consistent discretization of Neumann conditions at cross-points in a finite element setting: the auxiliary variable method and complete communication.

Full Text (PDF) [538 KB]

Key words

domain decomposition, cross-points, finite element discretization, auxiliary variables, complete communication

AMS subject classifications

65N55, 65N30, 65F10

Links to the cited ETNA articles

[11]Vol. 31 (2008), pp. 228-255 Martin J. Gander: Schwarz methods over the course of time

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