Mathematical modeling of real-life phenomena and engineering problems often involves solving very large and frequently ill-conditioned sparse linear systems of equations—preconditioning techniques are often employed to address this issue. On sequential architectures, this can be a very time-consuming process. Therefore, the need to develop efficient parallel methods for parallel architectures is essential.

This paper describes such a method: a package of parallel routines for sparse matrix computations. Specifically, the authors have implemented various versions of additive Schwarz preconditioners combined with a coarse-level correction to produce a two-level preconditioning method. The algorithms are used on top of the parallel sparse basic linear algebra subroutines (PSBLAS) library [1] for the parallel handling of sparse linear systems. The subroutines are written in Fortran 95.

A number of examples, both academic and real applications, show that these preconditioners may be used in combination with the PSBLAS solvers to produce very effective methods of solving large-scale sparse linear systems, even those with high condition numbers.