BDDC and FETI-DP algorithms with a change of basis formulation on adaptive primal constraints

BDDC (Balancing Domain Decomposition by Constraints) and FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithms with adaptively enriched primal constraints are considered. The coarse component of the two algorithms is built on the set of primal unknowns consisting of those at subdomain vertices and those from the adaptive primal constraints after a change of basis. For the FETI-DP algorithm, a more general form of a preconditioner is proposed to extend the algorithm to the set of primal unknowns including those from the adaptive primal constraints. In addition, it can be shown that the two algorithms share the same spectra except those equal to one or zero when the same set of adaptive primal constraints are employed. Numerical results are included for both two and three dimensional model problems.