The Dual, Overlapping Primal FETI (FETI-DOP) Domain Decomposition

A global domain decomposition (DD) preconditioner based on the dual-primal idea is presented. The key attribute of the proposed preconditioner is an auxiliary primal coarse problem that is fully overlapping to the original problem at domain interface regions only, and uses entire-domain basis functions to reduce the primal problem size. A two-level reduction solution process that iterates on the Lagrange multipliers is adopted, resulting in an efficient FETI solver. When compared to other dual-primal DD methods, the proposed method is computationally more efficient and, more importantly, is applicable to both conforming and non-conforming mesh decompositions. Numerical results on scattering and propagation problems are used to demonstrate its performance. The proposed method is found to outperform existing state-of-the-art FETI variants in all problems studied.