Recent Progress in Parallel Schur Complement Preconditioning for Computational Fluid

We consider preconditioning methods for nonself-adjoint advective-diffusive systems based on a nonoverlapping Schur complement procedure for arbitrary triangulated domains. The triangulation is first partitioned using the METIS multi-level $k$-way partitioning code. This partitioning of the triangulation induces a natural 2x2 partitioning of the demoralization matrix. By considering various inverse approximations of the 2x2 system we have developed a family of robust preconditioning techniques. The performance of these approximations will be discussed and numerous examples shown to illustrate the efficiency of the technique.