scholarly journals New Preconditioning Techniques for Saddle Point Problems Arising from the Time-Harmonic Maxwell Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Qingbing Liu
Keyword(s):  
Saddle Point ◽  
Numerical Experiments ◽  
Maxwell Equations ◽  
Saddle Point Problems ◽  
Finite Element Discretization ◽  
Preconditioning Techniques ◽  
Element Discretization ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
Saddle Point Matrices

We study two parameterized preconditioners for iteratively solving the saddle point linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations in electromagnetic problems. We establish some spectral properties of the preconditioned saddle point matrices, involving the choice of the parameter. Meanwhile, we provide some results of numerical experiments to show the effectiveness of the proposed parameterized preconditioners.

A Modified Relaxed Positive-Semidefinite and Skew-Hermitian Splitting Preconditioner for Generalized Saddle Point Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 192-210 ◽  
Author(s):  
Yang Cao ◽  
An Wang ◽  
Yu-Juan Chen
Keyword(s):  
Saddle Point ◽  
Minimal Polynomial ◽  
Mixed Finite Element ◽  
Positive Semidefinite ◽  
Saddle Point Problems ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Oseen Equation ◽  
Preconditioned Matrix ◽  
Generalized Saddle Point Problems

AbstractBased on the relaxed factorization techniques studied recently and the idea of the simple-like preconditioner, a modified relaxed positive-semidefinite and skew-Hermitian splitting (MRPSS) preconditioner is proposed for generalized saddle point problems. Some properties, including the eigenvalue distribution, the eigenvector distribution and the minimal polynomial of the preconditioned matrix are studied. Numerical examples arising from the mixed finite element discretization of the Oseen equation are illustrated to show the efficiency of the new preconditioner.

scholarly journals New Preconditioners with Two Variable Relaxation Parameters for the Discretized Time-Harmonic Maxwell Equations in Mixed Form

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yuping Zeng ◽  
Chenliang Li
Keyword(s):  
Finite Element ◽  
Theoretical Analysis ◽  
Maxwell Equations ◽  
Schur Complement ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Mixed Form ◽  
Numerical Tests ◽  
Relaxation Parameters ◽  
Time Harmonic

We provide new preconditioners with two variable relaxation parameters for the saddle point linear systems arising from finite element discretization of time-harmonic Maxwell equations in mixed form. The new preconditioners are of block-triangular forms and Schur complement-free. They are extensions of the results in Cheng et al., 2009, Grief and Schötzau, 2007, and Huang et al., 2009. Theoretical analysis shows that all eigenvalues of the preconditioned matrices are tightly clustered, and numerical tests confirm our analysis.

Saddle point least squares iterative solvers for the time harmonic Maxwell equations

2017 ◽  
Vol 74 (11) ◽  
pp. 2915-2928 ◽  
Author(s):  
Constantin Bacuta ◽  
Jacob Jacavage ◽  
Klajdi Qirko ◽  
Francisco-Javier Sayas
Keyword(s):  
Saddle Point ◽  
Least Squares ◽  
Maxwell Equations ◽  
Iterative Solvers ◽  
Time Harmonic

A Fast Shift-Splitting Iteration Method for Nonsymmetric Saddle Point Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 172-191 ◽  
Author(s):  
Quan-Yu Dou ◽  
Jun-Feng Yin ◽  
Ze-Yu Liao
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Saddle Point Problems ◽  
Splitting Technique ◽  
Splitting Iteration Method

AbstractBased on the shift-splitting technique and the idea of Hermitian and skew-Hermitian splitting, a fast shift-splitting iteration method is proposed for solving nonsingular and singular nonsymmetric saddle point problems in this paper. Convergence and semi-convergence of the proposed iteration method for nonsingular and singular cases are carefully studied, respectively. Numerical experiments are implemented to demonstrate the feasibility and effectiveness of the proposed method.

scholarly journals ANALYSIS OF THE INEXACT UZAWA ALGORITHMS FOR NONLINEAR SADDLE-POINT PROBLEMS

2010 ◽  
Vol 51 (3) ◽  
pp. 369-382 ◽  
Author(s):  
JIAN-LEI LI ◽  
TING-ZHU HUANG ◽  
LIANG LI
Keyword(s):  
Saddle Point ◽  
Numerical Experiments ◽  
Sufficient Condition ◽  
Saddle Point Problems ◽  
Simple Sufficient Condition ◽  
Inexact Uzawa Algorithms

AbstractInexact Uzawa algorithms for solving nonlinear saddle-point problems are proposed. A simple sufficient condition for the convergence of the inexact Uzawa algorithms is obtained. Numerical experiments show that the inexact Uzawa algorithms are convergent.

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