Xueping Guo

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a r t i c l e i n f o a b s t r a c t Keywords: Saddle point problems Matrix splittings Iterative methods Preconditioning Stokes problem Oseen problem Stretched grids In this paper we introduce a new preconditioner for linear systems of saddle point type arising from the numerical solution of the Navier–Stokes equations. Our approach is based on a(More)
Newton-HSS methods, that are variants of inexact Newton methods different from Newton-Krylov methods, have been shown to be competitive methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices [Bai and Guo, 2010]. In that paper, only local convergence was proved. In this paper, we prove a Kantorovich-type(More)
The Hermitian and skew-Hermitian splitting (HSS) method is an unconditionally convergent iterative method for solving large sparse non-Hermitian positive definite system of linear equations. In this paper, we establish a class of multi-step modified Newton-HSS (MMN-HSS) methods for solving large sparse system of nonlinear equations with positive definite(More)
Preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) method is an unconditionally convergent iterative method for solving large sparse complex symmetric systems of linear equations. By making use of the PMHSS iteration as the inner solver to approximately solve the Newton equations, we establish a modified Newton-PMHSS method for solving(More)
In this paper we introduce a new preconditioner for linear systems of saddle point type arising from the numerical solution of the Navier–Stokes equations. Our approach is based on a dimensional splitting of the problem along the components of the velocity field, resulting in a convergent fixed-point iteration. The basic iteration is accelerated by a Krylov(More)
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