We study two implementation strategies to utilize Schur complement technique in multilevel recursive incomplete LU preconditioning techniques (RILUM) for solving general sparse matrices. The first strategy constructs a RILUM to precondition the original matrix. The second strategy solves the first Schur complement matrix using the lower level parts of the RILUM as the preconditioner. We discuss computational and memory costs of both strategies and the potential effect on grid independent convergence rate of RILUM with different implementation strategies.
This research was supported in part by the U.S. National Science Foundation under grant CCR-9902022 and in part by the University of Kentucky Center for Computational Sciences.
Zhang, Jun, "On Preconditioning Schur Complement and Schur Complement Preconditioning" (2000). Computer Science Faculty Publications. 9.