Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solve

A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of precon-ditioned iterative solvers. However, when solving large-scale highly-indefinite linear systems, this hybrid solver often suffers from either slow convergence or large memory requirements to solve the Schur complement systems. To overcome this challenge, we in this paper discuss techniques to preprocess the Schur complement systems in paral-lel. Numerical results of solving large-scale highly-indefinite linear systems from various applications demonstrate that these techniques improve the reliability and performance of the hybrid solver and enable efficient solutions of these linear systems on hundreds of processors, which was previously infeasible using existing state-of-the-art solvers.