BDD requires only solution of subdomain problems rather than access to the matrices of those problems, so it is applicable to situations where only the solution operators are available, such as in oil reservoir simulation by mixed finite elements.
The BDDC method uses the same corner basis functions as,[3] but in an additive rather than multiplicative fashion.
[4] 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 [5] has the same eigenvalues and thus essentially the same performance as BDD.
In the simplest case, the coarse space of BDD consists of functions constant on each subdomain and averaged on the interfaces.