A new alternating positive semidefinite splitting preconditioner for saddle point problems from time-harmonic eddy current models

2018 ◽  
Vol 13 (2) ◽  
pp. 313-340 ◽  
Author(s):  
Yifen Ke ◽  
Changfeng Ma ◽  
Zhiru Ren
Keyword(s):  
Saddle Point ◽  
Eddy Current ◽  
Positive Semidefinite ◽  
Saddle Point Problems ◽  
Time Harmonic

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 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.

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