Block LU preconditioners for symmetric and nonsymmetric saddle point problems

In this paper, a general-purpose block LU preconditioner for saddle point problems is presented. The main difference between the approach presented here and that of other studies is that an explicit, accurate approximation of the Schur complement matrix is efficiently computed. This is used to compute a preconditioner to the Schur complement matrix, which in turn defines a preconditioner for the global system. A number of different variants are developed and results are reported for a few linear systems arising from CFD applications.