are domain decomposition preconditioners
named so because they solve a Neumann problem
on each subdomain on both sides of the interface between the subdomains. Just like all domain decomposition methods, so that the number of iterations does not grow with the number of subdomains, Neumann-Neumann methods require the solution of a coarse problem to provide global communication. The balancing domain decomposition
is a Neumann-Neumann method with a special kind of coarse problem.