Balancing ___domain decomposition method: Difference between revisions

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</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 belongsis toa classmember of the [[Neumann&ndash;-Neumann methods|Neumann-Neumann class of methods]], named so named because they solve a Neumann problem on both sides of the interface between subdomains.

In the simplest case, the [[coarse problem|coarse space]] of BDD consists of functions constant on each subdomain and averaged on the interfaces. More generally, on each subdomain, the coarse space needs to only contain the [[nullspace]] of the problem as a subspace.