FETI-DP, BDDC, and block Cholesky methods

The FETI-DP and BDDC algorithms are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal continuity constraints in these algorithms, a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom. With the new formulation of these algorithms, a simplified proof is provided that the spectra of a pair of FETI-DP and BDDC algorithms, with the same set of primal constraints, are essentially the same. Numerical experiments for a two-dimensional Laplace's equation also confirm this result.