Distributed Schur complement techniques for general sparse linear systems

This paper presents a few preconditioning techniques for solving general sp arse linear systems on distributed memory environments. These techniques ut ilize the Schur complement system for deriving the preconditioning matrix i n a number of ways. Two of these preconditioners consist of an approximate solution process for the global system, which exploits approximate LU facto rizations for diagonal blocks of the Schur complement. Another precondition er uses a sparse approximate-inverse technique to obtain certain local appr oximations of the Schur complement. Comparisons are reported for systems of varying difficulty.