History
BDDC was introduced by Dohrmann as a simpler primal alternative to the FETI-DP domain decomposition method by Farhat et al. The name of the method was coined by Mandel and Dohrmann, because it can be understood as further development of the BDD (balancing domain decomposition) method. The same method was also proposed independently by Fragakis and Papadrakakis under the name P-FETI-DP, and by Cros, which, however, was not recognized for some time. See for a proof that these are all actually the same method as BDDC. Mandel, Dohrmann, and Tezaur proved that the eigenvalues of BDDC and FETI-DP are identical, except for the eigenvalue equal to one, which may be present in BDDC but not for FETI-DP, and thus their number of iterations is practically the same. Much simpler proofs of this fact were obtained later by Li and Widlund and by Brenner and Sung.
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