Evaluating block preconditioners in the solution of saddle point systems

this paper presents a new approach to precondition linear systems of the saddle point kind. specifically we consider block diagonal, block triangular and block indefinite preconditioning techniques on nonsymmetric systems. these preconditioners require the computation of some inverses and we propose to use sparse approximate inverses (spai) to construct these approximations. the computation of these inverses involves solving a set of uncoupled least squares problems, which can be easily parallelized on a memory distributed machine. comparison with other techniques suggests that block diagonal and block triangular preconditioning can be more effective if they are combined with spai techniques in the computation of approximate inverses. results are promising and show the effectiveness of these preconditioners when improving the convergence of krylov methods such as gmres, which suggests the application of this approach in the large-scale setting.