Distributed Schur Complement Techniques for General Sparse Linear Systems

This paper presents a few preconditioning techniques for solving general sparse linear systems on distributed memory environments. These techniques utilize the Schur complement system for deriving the preconditioning matrix in a number of ways. Two of these pre-conditioners consist of an approximate solution process for the global system, which exploit approximate LU factorizations for diagonal blocks of the Schur complement. Another precon-ditioner uses a sparse approximate-inverse technique to obtain certain local approximations of the Schur complement. Comparisons are reported for systems of varying diiculty.