Balancing ___domain decomposition method: Difference between revisions

Revision as of 21:58, 15 March 2008

Revision as of 06:59, 8 April 2008

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</ref>. The dual counterpart to BDD is [[FETI]], which enforces the equality of the solution between the subdomain by Lagrange multipliers. The base versions of BDD and FETI are not mathematically equivalent, though a special version of FETI designed to be robust for hard problems <ref name="Bhardwaj-2000-AFM"> M. Bhardwaj, D. Day, C. Farhat, M. Lesoinne, K. Pierson, and D. Rixen, ''Application of the FETI method to ASCI problems -- scalability results on 1000 processors and discussion of highly heterogeneous problems'', International Journal for Numerical Methods in Engineering, 47 (2000), pp. 513&ndash;535.

</ref> has the same [[eigenvalue]]s and thus essentially the same performance as BDD .<ref name="Fragakis-2007-FDD"> Y. Fragakis, ''Force and displacement duality in Domain Decomposition Methods for Solid and Structural Mechanics''. To appear in Comput. Methods Appl. Mech. Engrg., 2007.

</ref><ref name="Sousedik-2008-EPD"> B. Sousedík and J. Mandel, ''On the equivalence of primal and dual substructuring preconditioners''. arXiv:math/0802.4328, 2008.</ref>.

The operator of the system solved by BDD is the same as obtained by eliminating the unknowns in the interiors of the subdomain, thus reducing the problem to the [[Schur complement]] on the subdomain interface. Since the BDD preconditioner involves the solution of [[Neumann problem]]s on all subdomain, it belongs to class of [[Neumann-Neumann methods]], named so because they solve a Neumann problem on both sides of the interface between subdomains.