BDDC and FETI-DP preconditioners for spectral element discretizations

Two of the most recent and important nonoverlapping domain decomposition methods, the BDDC method (Balancing Domain Decomposition by Constraints) and the FETI-DP method (Dual-Primal Finite Element Tearing and Interconnecting) are here extended to spectral element discretizations of second-order elliptic problems. In spite of the more severe ill-conditioning of the spectral element discrete systems, compared with low-order finite elements and finite differences, these methods retain their good properties of scalability, quasi-optimality and independence on the discontinuities of the elliptic operator coefficients across subdomain interfaces.