On Preconditioning Schur Complement and Schur Complement Preconditioning

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA


Abstract

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 independentconvergence rate of RILUM with different implementation strategies.

Keywords: Sparse matrices, Schur complement, RILUM, preconditioning techniques

AMS subject classifications: 65F10, 65N06