In this paper we analyze a two-level preconditioner for finite element systems arising in approximations of second order elliptic boundary value problems by Crouzeix-Raviart non-conforming triangular linear elements. This study is focused on the efficient implementation of the modified incomplete LU factorization MIC(0) as a preconditioner in the PCG iterative method for the linear algebraic sy...

A exible version of the QMR algorithm is presented which allows for the use of a diierent preconditioner at each step of the algorithm. In particular, inexact solutions of the preconditioned equations are allowed, as well as the use of some (inner) iterative method as a preconditioner. Several theorems are presented relating the norm of the residual of the new method with the norm of the residu...

We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylovsubspace-based iterative solvers such as the GMRES algorit...

We consider the BDDC preconditioner for Reissner-Mindlin plate problems, discretized with the MITC element, introduced and analyzed in [11]. In that contribution the authors prove that the condition number of the ensuing linear system is independent of the plate thickness and scalable with respect to the mesh. We here prove, in addition, that the BDDC preconditioner of [11] is also quasi-optima...

In an earlier paper we constructed and analyzed a multigrid preconditioner for the system of linear algebraic equations arising from the finite element discretization of boundary value problems associated to the differential operator I − graddiv. In this paper we analyze the procedure without assuming that the underlying domain is convex and show that, also in this case, the preconditioner is s...