An alternating positive semidefinite splitting preconditioner for the three-by-three block saddle point problems

Using the idea of dimensional splitting method we present an iteration method for solving three-by-three block saddle point problems which can appear in linear programming and finite element discretization of the Maxwell equation. We prove that the method is convergent unconditionally. Then the induced preconditioner is used to accelerate the convergence of the GMRES method for solving the system. Numerical results are presented to compare the performance of the method with some existing ones

An alternating positive semidefinite splitting preconditioner for the three-by-three block saddle point problems

Using the idea of dimensional splitting method we present an iteration method for solving three-by-three block saddle point problems which can appear in linear programming and finite element discretization of the Maxwell equation. We prove that the method is convergent unconditionally. Then the induced preconditioner is used to accelerate the convergence of the GMRES method for solving the system. Numerical results are presented to compare the performance of the method with some existing ones

On block diagonal and block triangular iterative schemes and preconditioners for stabilized saddle point problems

We review the use of block diagonal and block lower/upper triangular splittings for constructing iterative methods and preconditioners for solving stabilized saddle point problems. We introduce new variants of these splittings and obtain new results on the convergence of the associated stationary iterations and new bounds on the eigenvalues of the corresponding preconditioned matrices. We further consider inexact versions as preconditioners for flexible Krylov subspace methods, and show experimentally that our techniques can be highly effective for solving linear systems of saddle point type arising from stabilized finite element discretizations of two model problems, one from incompressible fluid mechanics and the other from magnetostatics

Preconditioners for Krylov subspace methods: An overview

When simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large-scale systems of equations. One major class of solution methods is that of preconditioned iterative methods, involving preconditioners which are computationally cheap to apply while also capturing information contained in the linear system. In this article, we give a short survey of the field of preconditioning. We introduce a range of preconditioners for partial differential equations, followed by optimization problems, before discussing preconditioners constructed with less standard objectives in mind