Parameterized preconditioning for generalized saddle point problems arising from the Stokes equation
type: Item
instance of: scholarly article
title: Parameterized preconditioning for generalized saddle point problems arising from the Stokes equation
zbMATH Open document ID: 1236.65031
author: Zheng Li
author: Tie Zhang
author: Chang-Jun Li
published in: Journal of Computational and Applied Mathematics
publication date: 2011-12-21T00:00:00Z
review text: A parameterized preconditioning framework to improve the conditions of the generalized saddle point problems is proposed. This is done by multiplying the submatrices by some parameters to precondition the system of saddle point problems. The authors give the explicit expression of the quasi-optimal preconditioning parameter by minimizing the upper bounds of the spectral condition numbers of the matrices based on the eigenvalue estimates. They apply the proposed techniques to the generalized saddle point problems derived from the mixed finite element discretization of the stationary Stokes equation. More specifically, the proposed parametrized preconditioners are combined with well-known iterative methods, and the numerical results demonstrate that they are efficient.
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5991214
zbMATH Keywords: parameterized preconditioning
zbMATH Keywords: generalized saddle point problem
zbMATH Keywords: spectral condition number
zbMATH Keywords: eigenvalue estimate
zbMATH Keywords: mixed finite element
zbMATH Keywords: stationary Stokes equation
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.cam.2011.09.015
OpenAlex ID: W2021423841
cites work: Numerical solution of saddle point problems
cites work: Eigenvalue estimates for preconditioned saddle point matrices
cites work: Parallel iterative methods for sparse linear systems
cites work: Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
cites work: An iterative method with variable relaxation parameters for saddle-point problems
cites work: Fast Uzawa algorithm for generalized saddle point problems
cites work: SOR-like methods for augmented systems
cites work: Q4946578
cites work: Optimum parameter for the SOR-like method for augmented systems
cites work: Two-parameter GSOR method for the augmented system
cites work: On generalized successive overrelaxation methods for augmented linear systems
cites work: Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
cites work: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems
cites work: Optimal parameters in the HSS-like methods for saddle-point problems
cites work: A note on an SOR-like method for augmented systems
cites work: Fast Nonsymmetric Iterations and Preconditioning for Navier–Stokes Equations
cites work: Q4938110
cites work: Minimum residual methods for augmented systems
cites work: A Preconditioned Iterative Method for Saddlepoint Problems
cites work: Spectral Properties of the Hermitian and Skew-Hermitian Splitting Preconditioner for Saddle Point Problems
cites work: On the eigenvalues of a class of saddle point matrices
cites work: The spectral properties of the Hermitian and skew-Hermitian splitting preconditioner for generalized saddle point problems
cites work: Constraint Preconditioners for Symmetric Indefinite Matrices
cites work: Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks
cites work: Stabilized finite element method for the stationary Navier-Stokes equations
cites work: Q4015008
DOI: 10.1016/J.CAM.2011.09.015
description: scientific article; zbMATH DE number 5991214