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