Balancing domain decomposition (BDD) and finite element tearing and interconnecting (FETI) are two families of approaches for the numerical solution of very large linear systems of equations, typically arising in connection with finite element methods for partial differential equations on parallel architectures. Currently, the most advanced members of these families are the BDD by constraints (BDDC) and the dual-primal FETI (FETI-DP).

This paper presents these methods from a new abstract mathematical perspective, using a purely algebraic approach. This way, Mandel and Sousedík are able to reveal many structural similarities between BDDC and FETI-DP under very weak conditions. In particular, they show that the primal version of FETI-DP, known as P-FETI-DP, actually coincides with BDDC. The results give a deep insight into the character of BDDC and FETI-DP from a novel point of view. This insight should enhance understanding of the behavior of the methods, and provide a basis for further development leading to improved performance.